# 1 "float16.cpp"
# 1 "<built-in>" 1
# 1 "<built-in>" 3
# 785 "<built-in>" 3
# 1 "<command line>" 1
# 1 "<built-in>" 2
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 1 3
# 33 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 3
extern "C" {
  __attribute__((__visibility__("default")))
  __attribute__((weak))
  __attribute__((noreturn))
  __attribute__((device)) void __cxa_pure_virtual(void) {
    __builtin_trap();
  }
  __attribute__((__visibility__("default")))
  __attribute__((weak))
  __attribute__((noreturn))
  __attribute__((device)) void __cxa_deleted_virtual(void) {
    __builtin_trap();
  }
}



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 1 3
# 296 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 3
namespace std
{
  typedef long unsigned int size_t;
  typedef long int ptrdiff_t;


  typedef decltype(nullptr) nullptr_t;


#pragma GCC visibility push(default)


  extern "C++" __attribute__ ((__noreturn__, __always_inline__))
  inline void __terminate() noexcept
  {
    void terminate() noexcept __attribute__ ((__noreturn__));
    terminate();
  }
#pragma GCC visibility pop
}
# 329 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 3
namespace std
{
  inline namespace __cxx11 __attribute__((__abi_tag__ ("cxx11"))) { }
}
namespace __gnu_cxx
{
  inline namespace __cxx11 __attribute__((__abi_tag__ ("cxx11"))) { }
}
# 508 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 3
namespace std
{
#pragma GCC visibility push(default)




  constexpr inline bool
  __is_constant_evaluated() noexcept
  {





    return __builtin_is_constant_evaluated();



  }
#pragma GCC visibility pop
}
# 655 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/os_defines.h" 1 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/os_defines.h" 3
# 1 "/usr/include/features.h" 1 3 4
# 392 "/usr/include/features.h" 3 4
# 1 "/usr/include/features-time64.h" 1 3 4
# 20 "/usr/include/features-time64.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 21 "/usr/include/features-time64.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 1 3 4
# 19 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 2 3 4
# 22 "/usr/include/features-time64.h" 2 3 4
# 393 "/usr/include/features.h" 2 3 4
# 467 "/usr/include/features.h" 3 4
# 1 "/usr/include/stdc-predef.h" 1 3 4
# 468 "/usr/include/features.h" 2 3 4
# 489 "/usr/include/features.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 1 3 4
# 561 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 562 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/long-double.h" 1 3 4
# 563 "/usr/include/x86_64-linux-gnu/sys/cdefs.h" 2 3 4
# 490 "/usr/include/features.h" 2 3 4
# 513 "/usr/include/features.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 1 3 4
# 10 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/gnu/stubs-64.h" 1 3 4
# 11 "/usr/include/x86_64-linux-gnu/gnu/stubs.h" 2 3 4
# 514 "/usr/include/features.h" 2 3 4
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/os_defines.h" 2 3
# 656 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 2 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/cpu_defines.h" 1 3
# 659 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++config.h" 2 3
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 1 3
# 36 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
# 67 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
extern "C++" {

namespace std __attribute__ ((__visibility__ ("default")))
{


  struct __true_type { };
  struct __false_type { };

  template<bool>
    struct __truth_type
    { typedef __false_type __type; };

  template<>
    struct __truth_type<true>
    { typedef __true_type __type; };



  template<class _Sp, class _Tp>
    struct __traitor
    {
      enum { __value = bool(_Sp::__value) || bool(_Tp::__value) };
      typedef typename __truth_type<__value>::__type __type;
    };


  template<typename, typename>
    struct __are_same
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<typename _Tp>
    struct __are_same<_Tp, _Tp>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<typename _Tp>
    struct __is_void
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_void<void>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_integer
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };





  template<>
    struct __is_integer<bool>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<signed char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<>
    struct __is_integer<wchar_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };
# 184 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
  template<>
    struct __is_integer<char16_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<char32_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<>
    struct __is_integer<short>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned short>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<int>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned int>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<long long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned long long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };
# 289 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
  template<typename _Tp>
    struct __is_floating
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };


  template<>
    struct __is_floating<float>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_floating<double>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_floating<long double>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_pointer
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<typename _Tp>
    struct __is_pointer<_Tp*>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_arithmetic
    : public __traitor<__is_integer<_Tp>, __is_floating<_Tp> >
    { };




  template<typename _Tp>
    struct __is_scalar
    : public __traitor<__is_arithmetic<_Tp>, __is_pointer<_Tp> >
    { };




  template<typename _Tp>
    struct __is_char
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_char<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<>
    struct __is_char<wchar_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<typename _Tp>
    struct __is_byte
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_byte<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_byte<signed char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_byte<unsigned char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };
# 425 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
  template<typename> struct iterator_traits;


  template<typename _Tp>
    struct __is_nonvolatile_trivially_copyable
    {
      enum { __value = __is_trivially_copyable(_Tp) };
    };




  template<typename _Tp>
    struct __is_nonvolatile_trivially_copyable<volatile _Tp>
    {
      enum { __value = 0 };
    };


  template<typename _OutputIter, typename _InputIter>
    struct __memcpyable
    {
      enum { __value = 0 };
    };

  template<typename _Tp>
    struct __memcpyable<_Tp*, _Tp*>
    : __is_nonvolatile_trivially_copyable<_Tp>
    { };

  template<typename _Tp>
    struct __memcpyable<_Tp*, const _Tp*>
    : __is_nonvolatile_trivially_copyable<_Tp>
    { };






  template<typename _Iter1, typename _Iter2>
    struct __memcmpable
    {
      enum { __value = 0 };
    };


  template<typename _Tp>
    struct __memcmpable<_Tp*, _Tp*>
    : __is_nonvolatile_trivially_copyable<_Tp>
    { };

  template<typename _Tp>
    struct __memcmpable<const _Tp*, _Tp*>
    : __is_nonvolatile_trivially_copyable<_Tp>
    { };

  template<typename _Tp>
    struct __memcmpable<_Tp*, const _Tp*>
    : __is_nonvolatile_trivially_copyable<_Tp>
    { };







  template<typename _Tp, bool _TreatAsBytes =



 __is_byte<_Tp>::__value

    >
    struct __is_memcmp_ordered
    {
      static const bool __value = _Tp(-1) > _Tp(1);
    };

  template<typename _Tp>
    struct __is_memcmp_ordered<_Tp, false>
    {
      static const bool __value = false;
    };


  template<typename _Tp, typename _Up, bool = sizeof(_Tp) == sizeof(_Up)>
    struct __is_memcmp_ordered_with
    {
      static const bool __value = __is_memcmp_ordered<_Tp>::__value
 && __is_memcmp_ordered<_Up>::__value;
    };

  template<typename _Tp, typename _Up>
    struct __is_memcmp_ordered_with<_Tp, _Up, false>
    {
      static const bool __value = false;
    };
# 550 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cpp_type_traits.h" 3
  template<typename _Tp>
    struct __is_move_iterator
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };



  template<typename _Iterator>

    inline _Iterator
    __miter_base(_Iterator __it)
    { return __it; }


}
}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/type_traits.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/type_traits.h" 3




extern "C++" {

namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{



  template<bool, typename>
    struct __enable_if
    { };

  template<typename _Tp>
    struct __enable_if<true, _Tp>
    { typedef _Tp __type; };



  template<bool _Cond, typename _Iftrue, typename _Iffalse>
    struct __conditional_type
    { typedef _Iftrue __type; };

  template<typename _Iftrue, typename _Iffalse>
    struct __conditional_type<false, _Iftrue, _Iffalse>
    { typedef _Iffalse __type; };



  template<typename _Tp>
    struct __add_unsigned
    {
    private:
      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;

    public:
      typedef typename __if_type::__type __type;
    };

  template<>
    struct __add_unsigned<char>
    { typedef unsigned char __type; };

  template<>
    struct __add_unsigned<signed char>
    { typedef unsigned char __type; };

  template<>
    struct __add_unsigned<short>
    { typedef unsigned short __type; };

  template<>
    struct __add_unsigned<int>
    { typedef unsigned int __type; };

  template<>
    struct __add_unsigned<long>
    { typedef unsigned long __type; };

  template<>
    struct __add_unsigned<long long>
    { typedef unsigned long long __type; };


  template<>
    struct __add_unsigned<bool>;

  template<>
    struct __add_unsigned<wchar_t>;



  template<typename _Tp>
    struct __remove_unsigned
    {
    private:
      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;

    public:
      typedef typename __if_type::__type __type;
    };

  template<>
    struct __remove_unsigned<char>
    { typedef signed char __type; };

  template<>
    struct __remove_unsigned<unsigned char>
    { typedef signed char __type; };

  template<>
    struct __remove_unsigned<unsigned short>
    { typedef short __type; };

  template<>
    struct __remove_unsigned<unsigned int>
    { typedef int __type; };

  template<>
    struct __remove_unsigned<unsigned long>
    { typedef long __type; };

  template<>
    struct __remove_unsigned<unsigned long long>
    { typedef long long __type; };


  template<>
    struct __remove_unsigned<bool>;

  template<>
    struct __remove_unsigned<wchar_t>;



  template<typename _Type>
    constexpr
    inline bool
    __is_null_pointer(_Type* __ptr)
    { return __ptr == 0; }

  template<typename _Type>
    constexpr
    inline bool
    __is_null_pointer(_Type)
    { return false; }


  constexpr bool
  __is_null_pointer(std::nullptr_t)
  { return true; }




  template<typename _Tp, bool = std::__is_integer<_Tp>::__value>
    struct __promote
    { typedef double __type; };




  template<typename _Tp>
    struct __promote<_Tp, false>
    { };

  template<>
    struct __promote<long double>
    { typedef long double __type; };

  template<>
    struct __promote<double>
    { typedef double __type; };

  template<>
    struct __promote<float>
    { typedef float __type; };
# 211 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/type_traits.h" 3
  template<typename _Tp, typename _Up,
           typename _Tp2 = typename __promote<_Tp>::__type,
           typename _Up2 = typename __promote<_Up>::__type>
    struct __promote_2
    {
      typedef __typeof__(_Tp2() + _Up2()) __type;
    };

  template<typename _Tp, typename _Up, typename _Vp,
           typename _Tp2 = typename __promote<_Tp>::__type,
           typename _Up2 = typename __promote<_Up>::__type,
           typename _Vp2 = typename __promote<_Vp>::__type>
    struct __promote_3
    {
      typedef __typeof__(_Tp2() + _Up2() + _Vp2()) __type;
    };

  template<typename _Tp, typename _Up, typename _Vp, typename _Wp,
           typename _Tp2 = typename __promote<_Tp>::__type,
           typename _Up2 = typename __promote<_Up>::__type,
           typename _Vp2 = typename __promote<_Vp>::__type,
           typename _Wp2 = typename __promote<_Wp>::__type>
    struct __promote_4
    {
      typedef __typeof__(_Tp2() + _Up2() + _Vp2() + _Wp2()) __type;
    };



}
}
# 44 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 2 3

# 1 "/usr/include/math.h" 1 3 4
# 27 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 28 "/usr/include/math.h" 2 3 4






extern "C" {


# 1 "/usr/include/x86_64-linux-gnu/bits/types.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 28 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 1 3 4
# 19 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/timesize.h" 2 3 4
# 29 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4


typedef unsigned char __u_char;
typedef unsigned short int __u_short;
typedef unsigned int __u_int;
typedef unsigned long int __u_long;


typedef signed char __int8_t;
typedef unsigned char __uint8_t;
typedef signed short int __int16_t;
typedef unsigned short int __uint16_t;
typedef signed int __int32_t;
typedef unsigned int __uint32_t;

typedef signed long int __int64_t;
typedef unsigned long int __uint64_t;






typedef __int8_t __int_least8_t;
typedef __uint8_t __uint_least8_t;
typedef __int16_t __int_least16_t;
typedef __uint16_t __uint_least16_t;
typedef __int32_t __int_least32_t;
typedef __uint32_t __uint_least32_t;
typedef __int64_t __int_least64_t;
typedef __uint64_t __uint_least64_t;



typedef long int __quad_t;
typedef unsigned long int __u_quad_t;







typedef long int __intmax_t;
typedef unsigned long int __uintmax_t;
# 141 "/usr/include/x86_64-linux-gnu/bits/types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/typesizes.h" 1 3 4
# 142 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/time64.h" 1 3 4
# 143 "/usr/include/x86_64-linux-gnu/bits/types.h" 2 3 4


typedef unsigned long int __dev_t;
typedef unsigned int __uid_t;
typedef unsigned int __gid_t;
typedef unsigned long int __ino_t;
typedef unsigned long int __ino64_t;
typedef unsigned int __mode_t;
typedef unsigned long int __nlink_t;
typedef long int __off_t;
typedef long int __off64_t;
typedef int __pid_t;
typedef struct { int __val[2]; } __fsid_t;
typedef long int __clock_t;
typedef unsigned long int __rlim_t;
typedef unsigned long int __rlim64_t;
typedef unsigned int __id_t;
typedef long int __time_t;
typedef unsigned int __useconds_t;
typedef long int __suseconds_t;
typedef long int __suseconds64_t;

typedef int __daddr_t;
typedef int __key_t;


typedef int __clockid_t;


typedef void * __timer_t;


typedef long int __blksize_t;




typedef long int __blkcnt_t;
typedef long int __blkcnt64_t;


typedef unsigned long int __fsblkcnt_t;
typedef unsigned long int __fsblkcnt64_t;


typedef unsigned long int __fsfilcnt_t;
typedef unsigned long int __fsfilcnt64_t;


typedef long int __fsword_t;

typedef long int __ssize_t;


typedef long int __syscall_slong_t;

typedef unsigned long int __syscall_ulong_t;



typedef __off64_t __loff_t;
typedef char *__caddr_t;


typedef long int __intptr_t;


typedef unsigned int __socklen_t;




typedef int __sig_atomic_t;
# 38 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 1 3 4
# 25 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libm-simd-decl-stubs.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/math-vector.h" 2 3 4
# 41 "/usr/include/math.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/floatn.h" 1 3 4
# 120 "/usr/include/x86_64-linux-gnu/bits/floatn.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/long-double.h" 1 3 4
# 25 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 2 3 4
# 214 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 3 4
typedef float _Float32;
# 251 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 3 4
typedef double _Float64;
# 268 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 3 4
typedef double _Float32x;
# 285 "/usr/include/x86_64-linux-gnu/bits/floatn-common.h" 3 4
typedef long double _Float64x;
# 121 "/usr/include/x86_64-linux-gnu/bits/floatn.h" 2 3 4
# 44 "/usr/include/math.h" 2 3 4
# 152 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/flt-eval-method.h" 1 3 4
# 153 "/usr/include/math.h" 2 3 4
# 163 "/usr/include/math.h" 3 4
typedef float float_t;
typedef double double_t;
# 204 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/fp-logb.h" 1 3 4
# 205 "/usr/include/math.h" 2 3 4
# 247 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/fp-fast.h" 1 3 4
# 248 "/usr/include/math.h" 2 3 4



enum
  {
    FP_INT_UPWARD =

      0,
    FP_INT_DOWNWARD =

      1,
    FP_INT_TOWARDZERO =

      2,
    FP_INT_TONEARESTFROMZERO =

      3,
    FP_INT_TONEAREST =

      4,
  };
# 312 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassify (double __value) noexcept (true)
     __attribute__ ((__const__));


extern int __signbit (double __value) noexcept (true)
     __attribute__ ((__const__));



extern int __isinf (double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __finite (double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __isnan (double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __iseqsig (double __x, double __y) noexcept (true);


extern int __issignaling (double __value) noexcept (true)
     __attribute__ ((__const__));
# 313 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern double acos (double __x) noexcept (true); extern double __acos (double __x) noexcept (true);

 extern double asin (double __x) noexcept (true); extern double __asin (double __x) noexcept (true);

 extern double atan (double __x) noexcept (true); extern double __atan (double __x) noexcept (true);

 extern double atan2 (double __y, double __x) noexcept (true); extern double __atan2 (double __y, double __x) noexcept (true);


 extern double cos (double __x) noexcept (true); extern double __cos (double __x) noexcept (true);

 extern double sin (double __x) noexcept (true); extern double __sin (double __x) noexcept (true);

 extern double tan (double __x) noexcept (true); extern double __tan (double __x) noexcept (true);




 extern double cosh (double __x) noexcept (true); extern double __cosh (double __x) noexcept (true);

 extern double sinh (double __x) noexcept (true); extern double __sinh (double __x) noexcept (true);

 extern double tanh (double __x) noexcept (true); extern double __tanh (double __x) noexcept (true);



 extern void sincos (double __x, double *__sinx, double *__cosx) noexcept (true); extern void __sincos (double __x, double *__sinx, double *__cosx) noexcept (true);





 extern double acosh (double __x) noexcept (true); extern double __acosh (double __x) noexcept (true);

 extern double asinh (double __x) noexcept (true); extern double __asinh (double __x) noexcept (true);

 extern double atanh (double __x) noexcept (true); extern double __atanh (double __x) noexcept (true);





 extern double exp (double __x) noexcept (true); extern double __exp (double __x) noexcept (true);


extern double frexp (double __x, int *__exponent) noexcept (true); extern double __frexp (double __x, int *__exponent) noexcept (true);


extern double ldexp (double __x, int __exponent) noexcept (true); extern double __ldexp (double __x, int __exponent) noexcept (true);


 extern double log (double __x) noexcept (true); extern double __log (double __x) noexcept (true);


 extern double log10 (double __x) noexcept (true); extern double __log10 (double __x) noexcept (true);


extern double modf (double __x, double *__iptr) noexcept (true); extern double __modf (double __x, double *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern double exp10 (double __x) noexcept (true); extern double __exp10 (double __x) noexcept (true);




 extern double expm1 (double __x) noexcept (true); extern double __expm1 (double __x) noexcept (true);


 extern double log1p (double __x) noexcept (true); extern double __log1p (double __x) noexcept (true);


extern double logb (double __x) noexcept (true); extern double __logb (double __x) noexcept (true);




 extern double exp2 (double __x) noexcept (true); extern double __exp2 (double __x) noexcept (true);


 extern double log2 (double __x) noexcept (true); extern double __log2 (double __x) noexcept (true);






 extern double pow (double __x, double __y) noexcept (true); extern double __pow (double __x, double __y) noexcept (true);


extern double sqrt (double __x) noexcept (true); extern double __sqrt (double __x) noexcept (true);



 extern double hypot (double __x, double __y) noexcept (true); extern double __hypot (double __x, double __y) noexcept (true);




 extern double cbrt (double __x) noexcept (true); extern double __cbrt (double __x) noexcept (true);






extern double ceil (double __x) noexcept (true) __attribute__ ((__const__)); extern double __ceil (double __x) noexcept (true) __attribute__ ((__const__));


extern double fabs (double __x) noexcept (true) __attribute__ ((__const__)); extern double __fabs (double __x) noexcept (true) __attribute__ ((__const__));


extern double floor (double __x) noexcept (true) __attribute__ ((__const__)); extern double __floor (double __x) noexcept (true) __attribute__ ((__const__));


extern double fmod (double __x, double __y) noexcept (true); extern double __fmod (double __x, double __y) noexcept (true);
# 183 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern int finite (double __value) noexcept (true)
  __attribute__ ((__const__));


extern double drem (double __x, double __y) noexcept (true); extern double __drem (double __x, double __y) noexcept (true);



extern double significand (double __x) noexcept (true); extern double __significand (double __x) noexcept (true);






extern double copysign (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __copysign (double __x, double __y) noexcept (true) __attribute__ ((__const__));




extern double nan (const char *__tagb) noexcept (true); extern double __nan (const char *__tagb) noexcept (true);
# 220 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern double j0 (double) noexcept (true); extern double __j0 (double) noexcept (true);
extern double j1 (double) noexcept (true); extern double __j1 (double) noexcept (true);
extern double jn (int, double) noexcept (true); extern double __jn (int, double) noexcept (true);
extern double y0 (double) noexcept (true); extern double __y0 (double) noexcept (true);
extern double y1 (double) noexcept (true); extern double __y1 (double) noexcept (true);
extern double yn (int, double) noexcept (true); extern double __yn (int, double) noexcept (true);





 extern double erf (double) noexcept (true); extern double __erf (double) noexcept (true);
 extern double erfc (double) noexcept (true); extern double __erfc (double) noexcept (true);
extern double lgamma (double) noexcept (true); extern double __lgamma (double) noexcept (true);




extern double tgamma (double) noexcept (true); extern double __tgamma (double) noexcept (true);





extern double gamma (double) noexcept (true); extern double __gamma (double) noexcept (true);







extern double lgamma_r (double, int *__signgamp) noexcept (true); extern double __lgamma_r (double, int *__signgamp) noexcept (true);






extern double rint (double __x) noexcept (true); extern double __rint (double __x) noexcept (true);


extern double nextafter (double __x, double __y) noexcept (true); extern double __nextafter (double __x, double __y) noexcept (true);

extern double nexttoward (double __x, long double __y) noexcept (true); extern double __nexttoward (double __x, long double __y) noexcept (true);




extern double nextdown (double __x) noexcept (true); extern double __nextdown (double __x) noexcept (true);

extern double nextup (double __x) noexcept (true); extern double __nextup (double __x) noexcept (true);



extern double remainder (double __x, double __y) noexcept (true); extern double __remainder (double __x, double __y) noexcept (true);



extern double scalbn (double __x, int __n) noexcept (true); extern double __scalbn (double __x, int __n) noexcept (true);



extern int ilogb (double __x) noexcept (true); extern int __ilogb (double __x) noexcept (true);




extern long int llogb (double __x) noexcept (true); extern long int __llogb (double __x) noexcept (true);




extern double scalbln (double __x, long int __n) noexcept (true); extern double __scalbln (double __x, long int __n) noexcept (true);



extern double nearbyint (double __x) noexcept (true); extern double __nearbyint (double __x) noexcept (true);



extern double round (double __x) noexcept (true) __attribute__ ((__const__)); extern double __round (double __x) noexcept (true) __attribute__ ((__const__));



extern double trunc (double __x) noexcept (true) __attribute__ ((__const__)); extern double __trunc (double __x) noexcept (true) __attribute__ ((__const__));




extern double remquo (double __x, double __y, int *__quo) noexcept (true); extern double __remquo (double __x, double __y, int *__quo) noexcept (true);






extern long int lrint (double __x) noexcept (true); extern long int __lrint (double __x) noexcept (true);
__extension__
extern long long int llrint (double __x) noexcept (true); extern long long int __llrint (double __x) noexcept (true);



extern long int lround (double __x) noexcept (true); extern long int __lround (double __x) noexcept (true);
__extension__
extern long long int llround (double __x) noexcept (true); extern long long int __llround (double __x) noexcept (true);



extern double fdim (double __x, double __y) noexcept (true); extern double __fdim (double __x, double __y) noexcept (true);



extern double fmax (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fmin (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) noexcept (true) __attribute__ ((__const__));



extern double fma (double __x, double __y, double __z) noexcept (true); extern double __fma (double __x, double __y, double __z) noexcept (true);




extern double roundeven (double __x) noexcept (true) __attribute__ ((__const__)); extern double __roundeven (double __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfp (double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfp (double __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfp (double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfp (double __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpx (double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpx (double __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpx (double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpx (double __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalize (double *__cx, const double *__x) noexcept (true);






extern double fmaxmag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaxmag (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fminmag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminmag (double __x, double __y) noexcept (true) __attribute__ ((__const__));




extern double fmaximum (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fminimum (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fmaximum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fminimum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fmaximum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fminimum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_mag (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fmaximum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fmaximum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));


extern double fminimum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__)); extern double __fminimum_mag_num (double __x, double __y) noexcept (true) __attribute__ ((__const__));




extern int totalorder (const double *__x, const double *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermag (const double *__x, const double *__y) noexcept (true)

     __attribute__ ((__pure__));


extern double getpayload (const double *__x) noexcept (true); extern double __getpayload (const double *__x) noexcept (true);


extern int setpayload (double *__x, double __payload) noexcept (true);


extern int setpayloadsig (double *__x, double __payload) noexcept (true);







extern double scalb (double __x, double __n) noexcept (true); extern double __scalb (double __x, double __n) noexcept (true);
# 314 "/usr/include/math.h" 2 3 4
# 329 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassifyf (float __value) noexcept (true)
     __attribute__ ((__const__));


extern int __signbitf (float __value) noexcept (true)
     __attribute__ ((__const__));



extern int __isinff (float __value) noexcept (true)
  __attribute__ ((__const__));


extern int __finitef (float __value) noexcept (true)
  __attribute__ ((__const__));


extern int __isnanf (float __value) noexcept (true)
  __attribute__ ((__const__));


extern int __iseqsigf (float __x, float __y) noexcept (true);


extern int __issignalingf (float __value) noexcept (true)
     __attribute__ ((__const__));
# 330 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern float acosf (float __x) noexcept (true); extern float __acosf (float __x) noexcept (true);

 extern float asinf (float __x) noexcept (true); extern float __asinf (float __x) noexcept (true);

 extern float atanf (float __x) noexcept (true); extern float __atanf (float __x) noexcept (true);

 extern float atan2f (float __y, float __x) noexcept (true); extern float __atan2f (float __y, float __x) noexcept (true);


 extern float cosf (float __x) noexcept (true); extern float __cosf (float __x) noexcept (true);

 extern float sinf (float __x) noexcept (true); extern float __sinf (float __x) noexcept (true);

 extern float tanf (float __x) noexcept (true); extern float __tanf (float __x) noexcept (true);




 extern float coshf (float __x) noexcept (true); extern float __coshf (float __x) noexcept (true);

 extern float sinhf (float __x) noexcept (true); extern float __sinhf (float __x) noexcept (true);

 extern float tanhf (float __x) noexcept (true); extern float __tanhf (float __x) noexcept (true);



 extern void sincosf (float __x, float *__sinx, float *__cosx) noexcept (true); extern void __sincosf (float __x, float *__sinx, float *__cosx) noexcept (true);





 extern float acoshf (float __x) noexcept (true); extern float __acoshf (float __x) noexcept (true);

 extern float asinhf (float __x) noexcept (true); extern float __asinhf (float __x) noexcept (true);

 extern float atanhf (float __x) noexcept (true); extern float __atanhf (float __x) noexcept (true);





 extern float expf (float __x) noexcept (true); extern float __expf (float __x) noexcept (true);


extern float frexpf (float __x, int *__exponent) noexcept (true); extern float __frexpf (float __x, int *__exponent) noexcept (true);


extern float ldexpf (float __x, int __exponent) noexcept (true); extern float __ldexpf (float __x, int __exponent) noexcept (true);


 extern float logf (float __x) noexcept (true); extern float __logf (float __x) noexcept (true);


 extern float log10f (float __x) noexcept (true); extern float __log10f (float __x) noexcept (true);


extern float modff (float __x, float *__iptr) noexcept (true); extern float __modff (float __x, float *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern float exp10f (float __x) noexcept (true); extern float __exp10f (float __x) noexcept (true);




 extern float expm1f (float __x) noexcept (true); extern float __expm1f (float __x) noexcept (true);


 extern float log1pf (float __x) noexcept (true); extern float __log1pf (float __x) noexcept (true);


extern float logbf (float __x) noexcept (true); extern float __logbf (float __x) noexcept (true);




 extern float exp2f (float __x) noexcept (true); extern float __exp2f (float __x) noexcept (true);


 extern float log2f (float __x) noexcept (true); extern float __log2f (float __x) noexcept (true);






 extern float powf (float __x, float __y) noexcept (true); extern float __powf (float __x, float __y) noexcept (true);


extern float sqrtf (float __x) noexcept (true); extern float __sqrtf (float __x) noexcept (true);



 extern float hypotf (float __x, float __y) noexcept (true); extern float __hypotf (float __x, float __y) noexcept (true);




 extern float cbrtf (float __x) noexcept (true); extern float __cbrtf (float __x) noexcept (true);






extern float ceilf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __ceilf (float __x) noexcept (true) __attribute__ ((__const__));


extern float fabsf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __fabsf (float __x) noexcept (true) __attribute__ ((__const__));


extern float floorf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __floorf (float __x) noexcept (true) __attribute__ ((__const__));


extern float fmodf (float __x, float __y) noexcept (true); extern float __fmodf (float __x, float __y) noexcept (true);
# 177 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern int isinff (float __value) noexcept (true)
  __attribute__ ((__const__));




extern int finitef (float __value) noexcept (true)
  __attribute__ ((__const__));


extern float dremf (float __x, float __y) noexcept (true); extern float __dremf (float __x, float __y) noexcept (true);



extern float significandf (float __x) noexcept (true); extern float __significandf (float __x) noexcept (true);






extern float copysignf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __copysignf (float __x, float __y) noexcept (true) __attribute__ ((__const__));




extern float nanf (const char *__tagb) noexcept (true); extern float __nanf (const char *__tagb) noexcept (true);
# 213 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern int isnanf (float __value) noexcept (true)
  __attribute__ ((__const__));





extern float j0f (float) noexcept (true); extern float __j0f (float) noexcept (true);
extern float j1f (float) noexcept (true); extern float __j1f (float) noexcept (true);
extern float jnf (int, float) noexcept (true); extern float __jnf (int, float) noexcept (true);
extern float y0f (float) noexcept (true); extern float __y0f (float) noexcept (true);
extern float y1f (float) noexcept (true); extern float __y1f (float) noexcept (true);
extern float ynf (int, float) noexcept (true); extern float __ynf (int, float) noexcept (true);





 extern float erff (float) noexcept (true); extern float __erff (float) noexcept (true);
 extern float erfcf (float) noexcept (true); extern float __erfcf (float) noexcept (true);
extern float lgammaf (float) noexcept (true); extern float __lgammaf (float) noexcept (true);




extern float tgammaf (float) noexcept (true); extern float __tgammaf (float) noexcept (true);





extern float gammaf (float) noexcept (true); extern float __gammaf (float) noexcept (true);







extern float lgammaf_r (float, int *__signgamp) noexcept (true); extern float __lgammaf_r (float, int *__signgamp) noexcept (true);






extern float rintf (float __x) noexcept (true); extern float __rintf (float __x) noexcept (true);


extern float nextafterf (float __x, float __y) noexcept (true); extern float __nextafterf (float __x, float __y) noexcept (true);

extern float nexttowardf (float __x, long double __y) noexcept (true); extern float __nexttowardf (float __x, long double __y) noexcept (true);




extern float nextdownf (float __x) noexcept (true); extern float __nextdownf (float __x) noexcept (true);

extern float nextupf (float __x) noexcept (true); extern float __nextupf (float __x) noexcept (true);



extern float remainderf (float __x, float __y) noexcept (true); extern float __remainderf (float __x, float __y) noexcept (true);



extern float scalbnf (float __x, int __n) noexcept (true); extern float __scalbnf (float __x, int __n) noexcept (true);



extern int ilogbf (float __x) noexcept (true); extern int __ilogbf (float __x) noexcept (true);




extern long int llogbf (float __x) noexcept (true); extern long int __llogbf (float __x) noexcept (true);




extern float scalblnf (float __x, long int __n) noexcept (true); extern float __scalblnf (float __x, long int __n) noexcept (true);



extern float nearbyintf (float __x) noexcept (true); extern float __nearbyintf (float __x) noexcept (true);



extern float roundf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __roundf (float __x) noexcept (true) __attribute__ ((__const__));



extern float truncf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __truncf (float __x) noexcept (true) __attribute__ ((__const__));




extern float remquof (float __x, float __y, int *__quo) noexcept (true); extern float __remquof (float __x, float __y, int *__quo) noexcept (true);






extern long int lrintf (float __x) noexcept (true); extern long int __lrintf (float __x) noexcept (true);
__extension__
extern long long int llrintf (float __x) noexcept (true); extern long long int __llrintf (float __x) noexcept (true);



extern long int lroundf (float __x) noexcept (true); extern long int __lroundf (float __x) noexcept (true);
__extension__
extern long long int llroundf (float __x) noexcept (true); extern long long int __llroundf (float __x) noexcept (true);



extern float fdimf (float __x, float __y) noexcept (true); extern float __fdimf (float __x, float __y) noexcept (true);



extern float fmaxf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaxf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminf (float __x, float __y) noexcept (true) __attribute__ ((__const__));



extern float fmaf (float __x, float __y, float __z) noexcept (true); extern float __fmaf (float __x, float __y, float __z) noexcept (true);




extern float roundevenf (float __x) noexcept (true) __attribute__ ((__const__)); extern float __roundevenf (float __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpf (float __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf (float __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpf (float __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf (float __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxf (float __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf (float __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxf (float __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf (float __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizef (float *__cx, const float *__x) noexcept (true);






extern float fmaxmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaxmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminmagf (float __x, float __y) noexcept (true) __attribute__ ((__const__));




extern float fmaximumf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximumf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminimumf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimumf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fmaximum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminimum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fmaximum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminimum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_magf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fmaximum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fmaximum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));


extern float fminimum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__)); extern float __fminimum_mag_numf (float __x, float __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderf (const float *__x, const float *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagf (const float *__x, const float *__y) noexcept (true)

     __attribute__ ((__pure__));


extern float getpayloadf (const float *__x) noexcept (true); extern float __getpayloadf (const float *__x) noexcept (true);


extern int setpayloadf (float *__x, float __payload) noexcept (true);


extern int setpayloadsigf (float *__x, float __payload) noexcept (true);







extern float scalbf (float __x, float __n) noexcept (true); extern float __scalbf (float __x, float __n) noexcept (true);
# 331 "/usr/include/math.h" 2 3 4
# 398 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/mathcalls-helper-functions.h" 3 4
extern int __fpclassifyl (long double __value) noexcept (true)
     __attribute__ ((__const__));


extern int __signbitl (long double __value) noexcept (true)
     __attribute__ ((__const__));



extern int __isinfl (long double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __finitel (long double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __isnanl (long double __value) noexcept (true)
  __attribute__ ((__const__));


extern int __iseqsigl (long double __x, long double __y) noexcept (true);


extern int __issignalingl (long double __value) noexcept (true)
     __attribute__ ((__const__));
# 399 "/usr/include/math.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern long double acosl (long double __x) noexcept (true); extern long double __acosl (long double __x) noexcept (true);

 extern long double asinl (long double __x) noexcept (true); extern long double __asinl (long double __x) noexcept (true);

 extern long double atanl (long double __x) noexcept (true); extern long double __atanl (long double __x) noexcept (true);

 extern long double atan2l (long double __y, long double __x) noexcept (true); extern long double __atan2l (long double __y, long double __x) noexcept (true);


 extern long double cosl (long double __x) noexcept (true); extern long double __cosl (long double __x) noexcept (true);

 extern long double sinl (long double __x) noexcept (true); extern long double __sinl (long double __x) noexcept (true);

 extern long double tanl (long double __x) noexcept (true); extern long double __tanl (long double __x) noexcept (true);




 extern long double coshl (long double __x) noexcept (true); extern long double __coshl (long double __x) noexcept (true);

 extern long double sinhl (long double __x) noexcept (true); extern long double __sinhl (long double __x) noexcept (true);

 extern long double tanhl (long double __x) noexcept (true); extern long double __tanhl (long double __x) noexcept (true);



 extern void sincosl (long double __x, long double *__sinx, long double *__cosx) noexcept (true); extern void __sincosl (long double __x, long double *__sinx, long double *__cosx) noexcept (true);





 extern long double acoshl (long double __x) noexcept (true); extern long double __acoshl (long double __x) noexcept (true);

 extern long double asinhl (long double __x) noexcept (true); extern long double __asinhl (long double __x) noexcept (true);

 extern long double atanhl (long double __x) noexcept (true); extern long double __atanhl (long double __x) noexcept (true);





 extern long double expl (long double __x) noexcept (true); extern long double __expl (long double __x) noexcept (true);


extern long double frexpl (long double __x, int *__exponent) noexcept (true); extern long double __frexpl (long double __x, int *__exponent) noexcept (true);


extern long double ldexpl (long double __x, int __exponent) noexcept (true); extern long double __ldexpl (long double __x, int __exponent) noexcept (true);


 extern long double logl (long double __x) noexcept (true); extern long double __logl (long double __x) noexcept (true);


 extern long double log10l (long double __x) noexcept (true); extern long double __log10l (long double __x) noexcept (true);


extern long double modfl (long double __x, long double *__iptr) noexcept (true); extern long double __modfl (long double __x, long double *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern long double exp10l (long double __x) noexcept (true); extern long double __exp10l (long double __x) noexcept (true);




 extern long double expm1l (long double __x) noexcept (true); extern long double __expm1l (long double __x) noexcept (true);


 extern long double log1pl (long double __x) noexcept (true); extern long double __log1pl (long double __x) noexcept (true);


extern long double logbl (long double __x) noexcept (true); extern long double __logbl (long double __x) noexcept (true);




 extern long double exp2l (long double __x) noexcept (true); extern long double __exp2l (long double __x) noexcept (true);


 extern long double log2l (long double __x) noexcept (true); extern long double __log2l (long double __x) noexcept (true);






 extern long double powl (long double __x, long double __y) noexcept (true); extern long double __powl (long double __x, long double __y) noexcept (true);


extern long double sqrtl (long double __x) noexcept (true); extern long double __sqrtl (long double __x) noexcept (true);



 extern long double hypotl (long double __x, long double __y) noexcept (true); extern long double __hypotl (long double __x, long double __y) noexcept (true);




 extern long double cbrtl (long double __x) noexcept (true); extern long double __cbrtl (long double __x) noexcept (true);






extern long double ceill (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __ceill (long double __x) noexcept (true) __attribute__ ((__const__));


extern long double fabsl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __fabsl (long double __x) noexcept (true) __attribute__ ((__const__));


extern long double floorl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __floorl (long double __x) noexcept (true) __attribute__ ((__const__));


extern long double fmodl (long double __x, long double __y) noexcept (true); extern long double __fmodl (long double __x, long double __y) noexcept (true);
# 177 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern int isinfl (long double __value) noexcept (true)
  __attribute__ ((__const__));




extern int finitel (long double __value) noexcept (true)
  __attribute__ ((__const__));


extern long double dreml (long double __x, long double __y) noexcept (true); extern long double __dreml (long double __x, long double __y) noexcept (true);



extern long double significandl (long double __x) noexcept (true); extern long double __significandl (long double __x) noexcept (true);






extern long double copysignl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __copysignl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));




extern long double nanl (const char *__tagb) noexcept (true); extern long double __nanl (const char *__tagb) noexcept (true);
# 213 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern int isnanl (long double __value) noexcept (true)
  __attribute__ ((__const__));





extern long double j0l (long double) noexcept (true); extern long double __j0l (long double) noexcept (true);
extern long double j1l (long double) noexcept (true); extern long double __j1l (long double) noexcept (true);
extern long double jnl (int, long double) noexcept (true); extern long double __jnl (int, long double) noexcept (true);
extern long double y0l (long double) noexcept (true); extern long double __y0l (long double) noexcept (true);
extern long double y1l (long double) noexcept (true); extern long double __y1l (long double) noexcept (true);
extern long double ynl (int, long double) noexcept (true); extern long double __ynl (int, long double) noexcept (true);





 extern long double erfl (long double) noexcept (true); extern long double __erfl (long double) noexcept (true);
 extern long double erfcl (long double) noexcept (true); extern long double __erfcl (long double) noexcept (true);
extern long double lgammal (long double) noexcept (true); extern long double __lgammal (long double) noexcept (true);




extern long double tgammal (long double) noexcept (true); extern long double __tgammal (long double) noexcept (true);





extern long double gammal (long double) noexcept (true); extern long double __gammal (long double) noexcept (true);







extern long double lgammal_r (long double, int *__signgamp) noexcept (true); extern long double __lgammal_r (long double, int *__signgamp) noexcept (true);






extern long double rintl (long double __x) noexcept (true); extern long double __rintl (long double __x) noexcept (true);


extern long double nextafterl (long double __x, long double __y) noexcept (true); extern long double __nextafterl (long double __x, long double __y) noexcept (true);

extern long double nexttowardl (long double __x, long double __y) noexcept (true); extern long double __nexttowardl (long double __x, long double __y) noexcept (true);




extern long double nextdownl (long double __x) noexcept (true); extern long double __nextdownl (long double __x) noexcept (true);

extern long double nextupl (long double __x) noexcept (true); extern long double __nextupl (long double __x) noexcept (true);



extern long double remainderl (long double __x, long double __y) noexcept (true); extern long double __remainderl (long double __x, long double __y) noexcept (true);



extern long double scalbnl (long double __x, int __n) noexcept (true); extern long double __scalbnl (long double __x, int __n) noexcept (true);



extern int ilogbl (long double __x) noexcept (true); extern int __ilogbl (long double __x) noexcept (true);




extern long int llogbl (long double __x) noexcept (true); extern long int __llogbl (long double __x) noexcept (true);




extern long double scalblnl (long double __x, long int __n) noexcept (true); extern long double __scalblnl (long double __x, long int __n) noexcept (true);



extern long double nearbyintl (long double __x) noexcept (true); extern long double __nearbyintl (long double __x) noexcept (true);



extern long double roundl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __roundl (long double __x) noexcept (true) __attribute__ ((__const__));



extern long double truncl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __truncl (long double __x) noexcept (true) __attribute__ ((__const__));




extern long double remquol (long double __x, long double __y, int *__quo) noexcept (true); extern long double __remquol (long double __x, long double __y, int *__quo) noexcept (true);






extern long int lrintl (long double __x) noexcept (true); extern long int __lrintl (long double __x) noexcept (true);
__extension__
extern long long int llrintl (long double __x) noexcept (true); extern long long int __llrintl (long double __x) noexcept (true);



extern long int lroundl (long double __x) noexcept (true); extern long int __lroundl (long double __x) noexcept (true);
__extension__
extern long long int llroundl (long double __x) noexcept (true); extern long long int __llroundl (long double __x) noexcept (true);



extern long double fdiml (long double __x, long double __y) noexcept (true); extern long double __fdiml (long double __x, long double __y) noexcept (true);



extern long double fmaxl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaxl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));



extern long double fmal (long double __x, long double __y, long double __z) noexcept (true); extern long double __fmal (long double __x, long double __y, long double __z) noexcept (true);




extern long double roundevenl (long double __x) noexcept (true) __attribute__ ((__const__)); extern long double __roundevenl (long double __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpl (long double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpl (long double __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpl (long double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpl (long double __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxl (long double __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxl (long double __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxl (long double __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxl (long double __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizel (long double *__cx, const long double *__x) noexcept (true);






extern long double fmaxmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaxmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminmagl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));




extern long double fmaximuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminimuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimuml (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fmaximum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminimum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fmaximum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminimum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_magl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fmaximum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fmaximum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));


extern long double fminimum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__)); extern long double __fminimum_mag_numl (long double __x, long double __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderl (const long double *__x, const long double *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagl (const long double *__x, const long double *__y) noexcept (true)

     __attribute__ ((__pure__));


extern long double getpayloadl (const long double *__x) noexcept (true); extern long double __getpayloadl (const long double *__x) noexcept (true);


extern int setpayloadl (long double *__x, long double __payload) noexcept (true);


extern int setpayloadsigl (long double *__x, long double __payload) noexcept (true);







extern long double scalbl (long double __x, long double __n) noexcept (true); extern long double __scalbl (long double __x, long double __n) noexcept (true);
# 400 "/usr/include/math.h" 2 3 4
# 450 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern _Float32 acosf32 (_Float32 __x) noexcept (true); extern _Float32 __acosf32 (_Float32 __x) noexcept (true);

 extern _Float32 asinf32 (_Float32 __x) noexcept (true); extern _Float32 __asinf32 (_Float32 __x) noexcept (true);

 extern _Float32 atanf32 (_Float32 __x) noexcept (true); extern _Float32 __atanf32 (_Float32 __x) noexcept (true);

 extern _Float32 atan2f32 (_Float32 __y, _Float32 __x) noexcept (true); extern _Float32 __atan2f32 (_Float32 __y, _Float32 __x) noexcept (true);


 extern _Float32 cosf32 (_Float32 __x) noexcept (true); extern _Float32 __cosf32 (_Float32 __x) noexcept (true);

 extern _Float32 sinf32 (_Float32 __x) noexcept (true); extern _Float32 __sinf32 (_Float32 __x) noexcept (true);

 extern _Float32 tanf32 (_Float32 __x) noexcept (true); extern _Float32 __tanf32 (_Float32 __x) noexcept (true);




 extern _Float32 coshf32 (_Float32 __x) noexcept (true); extern _Float32 __coshf32 (_Float32 __x) noexcept (true);

 extern _Float32 sinhf32 (_Float32 __x) noexcept (true); extern _Float32 __sinhf32 (_Float32 __x) noexcept (true);

 extern _Float32 tanhf32 (_Float32 __x) noexcept (true); extern _Float32 __tanhf32 (_Float32 __x) noexcept (true);



 extern void sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) noexcept (true); extern void __sincosf32 (_Float32 __x, _Float32 *__sinx, _Float32 *__cosx) noexcept (true);





 extern _Float32 acoshf32 (_Float32 __x) noexcept (true); extern _Float32 __acoshf32 (_Float32 __x) noexcept (true);

 extern _Float32 asinhf32 (_Float32 __x) noexcept (true); extern _Float32 __asinhf32 (_Float32 __x) noexcept (true);

 extern _Float32 atanhf32 (_Float32 __x) noexcept (true); extern _Float32 __atanhf32 (_Float32 __x) noexcept (true);





 extern _Float32 expf32 (_Float32 __x) noexcept (true); extern _Float32 __expf32 (_Float32 __x) noexcept (true);


extern _Float32 frexpf32 (_Float32 __x, int *__exponent) noexcept (true); extern _Float32 __frexpf32 (_Float32 __x, int *__exponent) noexcept (true);


extern _Float32 ldexpf32 (_Float32 __x, int __exponent) noexcept (true); extern _Float32 __ldexpf32 (_Float32 __x, int __exponent) noexcept (true);


 extern _Float32 logf32 (_Float32 __x) noexcept (true); extern _Float32 __logf32 (_Float32 __x) noexcept (true);


 extern _Float32 log10f32 (_Float32 __x) noexcept (true); extern _Float32 __log10f32 (_Float32 __x) noexcept (true);


extern _Float32 modff32 (_Float32 __x, _Float32 *__iptr) noexcept (true); extern _Float32 __modff32 (_Float32 __x, _Float32 *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern _Float32 exp10f32 (_Float32 __x) noexcept (true); extern _Float32 __exp10f32 (_Float32 __x) noexcept (true);




 extern _Float32 expm1f32 (_Float32 __x) noexcept (true); extern _Float32 __expm1f32 (_Float32 __x) noexcept (true);


 extern _Float32 log1pf32 (_Float32 __x) noexcept (true); extern _Float32 __log1pf32 (_Float32 __x) noexcept (true);


extern _Float32 logbf32 (_Float32 __x) noexcept (true); extern _Float32 __logbf32 (_Float32 __x) noexcept (true);




 extern _Float32 exp2f32 (_Float32 __x) noexcept (true); extern _Float32 __exp2f32 (_Float32 __x) noexcept (true);


 extern _Float32 log2f32 (_Float32 __x) noexcept (true); extern _Float32 __log2f32 (_Float32 __x) noexcept (true);






 extern _Float32 powf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __powf32 (_Float32 __x, _Float32 __y) noexcept (true);


extern _Float32 sqrtf32 (_Float32 __x) noexcept (true); extern _Float32 __sqrtf32 (_Float32 __x) noexcept (true);



 extern _Float32 hypotf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __hypotf32 (_Float32 __x, _Float32 __y) noexcept (true);




 extern _Float32 cbrtf32 (_Float32 __x) noexcept (true); extern _Float32 __cbrtf32 (_Float32 __x) noexcept (true);






extern _Float32 ceilf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __ceilf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));


extern _Float32 fabsf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fabsf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));


extern _Float32 floorf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __floorf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));


extern _Float32 fmodf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __fmodf32 (_Float32 __x, _Float32 __y) noexcept (true);
# 198 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 copysignf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __copysignf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));




extern _Float32 nanf32 (const char *__tagb) noexcept (true); extern _Float32 __nanf32 (const char *__tagb) noexcept (true);
# 220 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 j0f32 (_Float32) noexcept (true); extern _Float32 __j0f32 (_Float32) noexcept (true);
extern _Float32 j1f32 (_Float32) noexcept (true); extern _Float32 __j1f32 (_Float32) noexcept (true);
extern _Float32 jnf32 (int, _Float32) noexcept (true); extern _Float32 __jnf32 (int, _Float32) noexcept (true);
extern _Float32 y0f32 (_Float32) noexcept (true); extern _Float32 __y0f32 (_Float32) noexcept (true);
extern _Float32 y1f32 (_Float32) noexcept (true); extern _Float32 __y1f32 (_Float32) noexcept (true);
extern _Float32 ynf32 (int, _Float32) noexcept (true); extern _Float32 __ynf32 (int, _Float32) noexcept (true);





 extern _Float32 erff32 (_Float32) noexcept (true); extern _Float32 __erff32 (_Float32) noexcept (true);
 extern _Float32 erfcf32 (_Float32) noexcept (true); extern _Float32 __erfcf32 (_Float32) noexcept (true);
extern _Float32 lgammaf32 (_Float32) noexcept (true); extern _Float32 __lgammaf32 (_Float32) noexcept (true);




extern _Float32 tgammaf32 (_Float32) noexcept (true); extern _Float32 __tgammaf32 (_Float32) noexcept (true);
# 252 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32 lgammaf32_r (_Float32, int *__signgamp) noexcept (true); extern _Float32 __lgammaf32_r (_Float32, int *__signgamp) noexcept (true);






extern _Float32 rintf32 (_Float32 __x) noexcept (true); extern _Float32 __rintf32 (_Float32 __x) noexcept (true);


extern _Float32 nextafterf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __nextafterf32 (_Float32 __x, _Float32 __y) noexcept (true);






extern _Float32 nextdownf32 (_Float32 __x) noexcept (true); extern _Float32 __nextdownf32 (_Float32 __x) noexcept (true);

extern _Float32 nextupf32 (_Float32 __x) noexcept (true); extern _Float32 __nextupf32 (_Float32 __x) noexcept (true);



extern _Float32 remainderf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __remainderf32 (_Float32 __x, _Float32 __y) noexcept (true);



extern _Float32 scalbnf32 (_Float32 __x, int __n) noexcept (true); extern _Float32 __scalbnf32 (_Float32 __x, int __n) noexcept (true);



extern int ilogbf32 (_Float32 __x) noexcept (true); extern int __ilogbf32 (_Float32 __x) noexcept (true);




extern long int llogbf32 (_Float32 __x) noexcept (true); extern long int __llogbf32 (_Float32 __x) noexcept (true);




extern _Float32 scalblnf32 (_Float32 __x, long int __n) noexcept (true); extern _Float32 __scalblnf32 (_Float32 __x, long int __n) noexcept (true);



extern _Float32 nearbyintf32 (_Float32 __x) noexcept (true); extern _Float32 __nearbyintf32 (_Float32 __x) noexcept (true);



extern _Float32 roundf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __roundf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));



extern _Float32 truncf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __truncf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));




extern _Float32 remquof32 (_Float32 __x, _Float32 __y, int *__quo) noexcept (true); extern _Float32 __remquof32 (_Float32 __x, _Float32 __y, int *__quo) noexcept (true);






extern long int lrintf32 (_Float32 __x) noexcept (true); extern long int __lrintf32 (_Float32 __x) noexcept (true);
__extension__
extern long long int llrintf32 (_Float32 __x) noexcept (true); extern long long int __llrintf32 (_Float32 __x) noexcept (true);



extern long int lroundf32 (_Float32 __x) noexcept (true); extern long int __lroundf32 (_Float32 __x) noexcept (true);
__extension__
extern long long int llroundf32 (_Float32 __x) noexcept (true); extern long long int __llroundf32 (_Float32 __x) noexcept (true);



extern _Float32 fdimf32 (_Float32 __x, _Float32 __y) noexcept (true); extern _Float32 __fdimf32 (_Float32 __x, _Float32 __y) noexcept (true);



extern _Float32 fmaxf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaxf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));



extern _Float32 fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) noexcept (true); extern _Float32 __fmaf32 (_Float32 __x, _Float32 __y, _Float32 __z) noexcept (true);




extern _Float32 roundevenf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__)); extern _Float32 __roundevenf32 (_Float32 __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf32 (_Float32 __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizef32 (_Float32 *__cx, const _Float32 *__x) noexcept (true);






extern _Float32 fmaxmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaxmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminmagf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));




extern _Float32 fmaximumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminimumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimumf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fmaximum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminimum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fmaximum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminimum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_magf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fmaximum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fmaximum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));


extern _Float32 fminimum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__)); extern _Float32 __fminimum_mag_numf32 (_Float32 __x, _Float32 __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderf32 (const _Float32 *__x, const _Float32 *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagf32 (const _Float32 *__x, const _Float32 *__y) noexcept (true)

     __attribute__ ((__pure__));


extern _Float32 getpayloadf32 (const _Float32 *__x) noexcept (true); extern _Float32 __getpayloadf32 (const _Float32 *__x) noexcept (true);


extern int setpayloadf32 (_Float32 *__x, _Float32 __payload) noexcept (true);


extern int setpayloadsigf32 (_Float32 *__x, _Float32 __payload) noexcept (true);
# 451 "/usr/include/math.h" 2 3 4
# 467 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern _Float64 acosf64 (_Float64 __x) noexcept (true); extern _Float64 __acosf64 (_Float64 __x) noexcept (true);

 extern _Float64 asinf64 (_Float64 __x) noexcept (true); extern _Float64 __asinf64 (_Float64 __x) noexcept (true);

 extern _Float64 atanf64 (_Float64 __x) noexcept (true); extern _Float64 __atanf64 (_Float64 __x) noexcept (true);

 extern _Float64 atan2f64 (_Float64 __y, _Float64 __x) noexcept (true); extern _Float64 __atan2f64 (_Float64 __y, _Float64 __x) noexcept (true);


 extern _Float64 cosf64 (_Float64 __x) noexcept (true); extern _Float64 __cosf64 (_Float64 __x) noexcept (true);

 extern _Float64 sinf64 (_Float64 __x) noexcept (true); extern _Float64 __sinf64 (_Float64 __x) noexcept (true);

 extern _Float64 tanf64 (_Float64 __x) noexcept (true); extern _Float64 __tanf64 (_Float64 __x) noexcept (true);




 extern _Float64 coshf64 (_Float64 __x) noexcept (true); extern _Float64 __coshf64 (_Float64 __x) noexcept (true);

 extern _Float64 sinhf64 (_Float64 __x) noexcept (true); extern _Float64 __sinhf64 (_Float64 __x) noexcept (true);

 extern _Float64 tanhf64 (_Float64 __x) noexcept (true); extern _Float64 __tanhf64 (_Float64 __x) noexcept (true);



 extern void sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) noexcept (true); extern void __sincosf64 (_Float64 __x, _Float64 *__sinx, _Float64 *__cosx) noexcept (true);





 extern _Float64 acoshf64 (_Float64 __x) noexcept (true); extern _Float64 __acoshf64 (_Float64 __x) noexcept (true);

 extern _Float64 asinhf64 (_Float64 __x) noexcept (true); extern _Float64 __asinhf64 (_Float64 __x) noexcept (true);

 extern _Float64 atanhf64 (_Float64 __x) noexcept (true); extern _Float64 __atanhf64 (_Float64 __x) noexcept (true);





 extern _Float64 expf64 (_Float64 __x) noexcept (true); extern _Float64 __expf64 (_Float64 __x) noexcept (true);


extern _Float64 frexpf64 (_Float64 __x, int *__exponent) noexcept (true); extern _Float64 __frexpf64 (_Float64 __x, int *__exponent) noexcept (true);


extern _Float64 ldexpf64 (_Float64 __x, int __exponent) noexcept (true); extern _Float64 __ldexpf64 (_Float64 __x, int __exponent) noexcept (true);


 extern _Float64 logf64 (_Float64 __x) noexcept (true); extern _Float64 __logf64 (_Float64 __x) noexcept (true);


 extern _Float64 log10f64 (_Float64 __x) noexcept (true); extern _Float64 __log10f64 (_Float64 __x) noexcept (true);


extern _Float64 modff64 (_Float64 __x, _Float64 *__iptr) noexcept (true); extern _Float64 __modff64 (_Float64 __x, _Float64 *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern _Float64 exp10f64 (_Float64 __x) noexcept (true); extern _Float64 __exp10f64 (_Float64 __x) noexcept (true);




 extern _Float64 expm1f64 (_Float64 __x) noexcept (true); extern _Float64 __expm1f64 (_Float64 __x) noexcept (true);


 extern _Float64 log1pf64 (_Float64 __x) noexcept (true); extern _Float64 __log1pf64 (_Float64 __x) noexcept (true);


extern _Float64 logbf64 (_Float64 __x) noexcept (true); extern _Float64 __logbf64 (_Float64 __x) noexcept (true);




 extern _Float64 exp2f64 (_Float64 __x) noexcept (true); extern _Float64 __exp2f64 (_Float64 __x) noexcept (true);


 extern _Float64 log2f64 (_Float64 __x) noexcept (true); extern _Float64 __log2f64 (_Float64 __x) noexcept (true);






 extern _Float64 powf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __powf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float64 sqrtf64 (_Float64 __x) noexcept (true); extern _Float64 __sqrtf64 (_Float64 __x) noexcept (true);



 extern _Float64 hypotf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __hypotf64 (_Float64 __x, _Float64 __y) noexcept (true);




 extern _Float64 cbrtf64 (_Float64 __x) noexcept (true); extern _Float64 __cbrtf64 (_Float64 __x) noexcept (true);






extern _Float64 ceilf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __ceilf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));


extern _Float64 fabsf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fabsf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));


extern _Float64 floorf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __floorf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));


extern _Float64 fmodf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __fmodf64 (_Float64 __x, _Float64 __y) noexcept (true);
# 198 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 copysignf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __copysignf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));




extern _Float64 nanf64 (const char *__tagb) noexcept (true); extern _Float64 __nanf64 (const char *__tagb) noexcept (true);
# 220 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 j0f64 (_Float64) noexcept (true); extern _Float64 __j0f64 (_Float64) noexcept (true);
extern _Float64 j1f64 (_Float64) noexcept (true); extern _Float64 __j1f64 (_Float64) noexcept (true);
extern _Float64 jnf64 (int, _Float64) noexcept (true); extern _Float64 __jnf64 (int, _Float64) noexcept (true);
extern _Float64 y0f64 (_Float64) noexcept (true); extern _Float64 __y0f64 (_Float64) noexcept (true);
extern _Float64 y1f64 (_Float64) noexcept (true); extern _Float64 __y1f64 (_Float64) noexcept (true);
extern _Float64 ynf64 (int, _Float64) noexcept (true); extern _Float64 __ynf64 (int, _Float64) noexcept (true);





 extern _Float64 erff64 (_Float64) noexcept (true); extern _Float64 __erff64 (_Float64) noexcept (true);
 extern _Float64 erfcf64 (_Float64) noexcept (true); extern _Float64 __erfcf64 (_Float64) noexcept (true);
extern _Float64 lgammaf64 (_Float64) noexcept (true); extern _Float64 __lgammaf64 (_Float64) noexcept (true);




extern _Float64 tgammaf64 (_Float64) noexcept (true); extern _Float64 __tgammaf64 (_Float64) noexcept (true);
# 252 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64 lgammaf64_r (_Float64, int *__signgamp) noexcept (true); extern _Float64 __lgammaf64_r (_Float64, int *__signgamp) noexcept (true);






extern _Float64 rintf64 (_Float64 __x) noexcept (true); extern _Float64 __rintf64 (_Float64 __x) noexcept (true);


extern _Float64 nextafterf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __nextafterf64 (_Float64 __x, _Float64 __y) noexcept (true);






extern _Float64 nextdownf64 (_Float64 __x) noexcept (true); extern _Float64 __nextdownf64 (_Float64 __x) noexcept (true);

extern _Float64 nextupf64 (_Float64 __x) noexcept (true); extern _Float64 __nextupf64 (_Float64 __x) noexcept (true);



extern _Float64 remainderf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __remainderf64 (_Float64 __x, _Float64 __y) noexcept (true);



extern _Float64 scalbnf64 (_Float64 __x, int __n) noexcept (true); extern _Float64 __scalbnf64 (_Float64 __x, int __n) noexcept (true);



extern int ilogbf64 (_Float64 __x) noexcept (true); extern int __ilogbf64 (_Float64 __x) noexcept (true);




extern long int llogbf64 (_Float64 __x) noexcept (true); extern long int __llogbf64 (_Float64 __x) noexcept (true);




extern _Float64 scalblnf64 (_Float64 __x, long int __n) noexcept (true); extern _Float64 __scalblnf64 (_Float64 __x, long int __n) noexcept (true);



extern _Float64 nearbyintf64 (_Float64 __x) noexcept (true); extern _Float64 __nearbyintf64 (_Float64 __x) noexcept (true);



extern _Float64 roundf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __roundf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));



extern _Float64 truncf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __truncf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));




extern _Float64 remquof64 (_Float64 __x, _Float64 __y, int *__quo) noexcept (true); extern _Float64 __remquof64 (_Float64 __x, _Float64 __y, int *__quo) noexcept (true);






extern long int lrintf64 (_Float64 __x) noexcept (true); extern long int __lrintf64 (_Float64 __x) noexcept (true);
__extension__
extern long long int llrintf64 (_Float64 __x) noexcept (true); extern long long int __llrintf64 (_Float64 __x) noexcept (true);



extern long int lroundf64 (_Float64 __x) noexcept (true); extern long int __lroundf64 (_Float64 __x) noexcept (true);
__extension__
extern long long int llroundf64 (_Float64 __x) noexcept (true); extern long long int __llroundf64 (_Float64 __x) noexcept (true);



extern _Float64 fdimf64 (_Float64 __x, _Float64 __y) noexcept (true); extern _Float64 __fdimf64 (_Float64 __x, _Float64 __y) noexcept (true);



extern _Float64 fmaxf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaxf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));



extern _Float64 fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true); extern _Float64 __fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);




extern _Float64 roundevenf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__)); extern _Float64 __roundevenf64 (_Float64 __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf64 (_Float64 __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizef64 (_Float64 *__cx, const _Float64 *__x) noexcept (true);






extern _Float64 fmaxmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaxmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminmagf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));




extern _Float64 fmaximumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminimumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimumf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fmaximum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminimum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fmaximum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminimum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_magf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fmaximum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fmaximum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));


extern _Float64 fminimum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__)); extern _Float64 __fminimum_mag_numf64 (_Float64 __x, _Float64 __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderf64 (const _Float64 *__x, const _Float64 *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagf64 (const _Float64 *__x, const _Float64 *__y) noexcept (true)

     __attribute__ ((__pure__));


extern _Float64 getpayloadf64 (const _Float64 *__x) noexcept (true); extern _Float64 __getpayloadf64 (const _Float64 *__x) noexcept (true);


extern int setpayloadf64 (_Float64 *__x, _Float64 __payload) noexcept (true);


extern int setpayloadsigf64 (_Float64 *__x, _Float64 __payload) noexcept (true);
# 468 "/usr/include/math.h" 2 3 4
# 501 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern _Float32x acosf32x (_Float32x __x) noexcept (true); extern _Float32x __acosf32x (_Float32x __x) noexcept (true);

 extern _Float32x asinf32x (_Float32x __x) noexcept (true); extern _Float32x __asinf32x (_Float32x __x) noexcept (true);

 extern _Float32x atanf32x (_Float32x __x) noexcept (true); extern _Float32x __atanf32x (_Float32x __x) noexcept (true);

 extern _Float32x atan2f32x (_Float32x __y, _Float32x __x) noexcept (true); extern _Float32x __atan2f32x (_Float32x __y, _Float32x __x) noexcept (true);


 extern _Float32x cosf32x (_Float32x __x) noexcept (true); extern _Float32x __cosf32x (_Float32x __x) noexcept (true);

 extern _Float32x sinf32x (_Float32x __x) noexcept (true); extern _Float32x __sinf32x (_Float32x __x) noexcept (true);

 extern _Float32x tanf32x (_Float32x __x) noexcept (true); extern _Float32x __tanf32x (_Float32x __x) noexcept (true);




 extern _Float32x coshf32x (_Float32x __x) noexcept (true); extern _Float32x __coshf32x (_Float32x __x) noexcept (true);

 extern _Float32x sinhf32x (_Float32x __x) noexcept (true); extern _Float32x __sinhf32x (_Float32x __x) noexcept (true);

 extern _Float32x tanhf32x (_Float32x __x) noexcept (true); extern _Float32x __tanhf32x (_Float32x __x) noexcept (true);



 extern void sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) noexcept (true); extern void __sincosf32x (_Float32x __x, _Float32x *__sinx, _Float32x *__cosx) noexcept (true);





 extern _Float32x acoshf32x (_Float32x __x) noexcept (true); extern _Float32x __acoshf32x (_Float32x __x) noexcept (true);

 extern _Float32x asinhf32x (_Float32x __x) noexcept (true); extern _Float32x __asinhf32x (_Float32x __x) noexcept (true);

 extern _Float32x atanhf32x (_Float32x __x) noexcept (true); extern _Float32x __atanhf32x (_Float32x __x) noexcept (true);





 extern _Float32x expf32x (_Float32x __x) noexcept (true); extern _Float32x __expf32x (_Float32x __x) noexcept (true);


extern _Float32x frexpf32x (_Float32x __x, int *__exponent) noexcept (true); extern _Float32x __frexpf32x (_Float32x __x, int *__exponent) noexcept (true);


extern _Float32x ldexpf32x (_Float32x __x, int __exponent) noexcept (true); extern _Float32x __ldexpf32x (_Float32x __x, int __exponent) noexcept (true);


 extern _Float32x logf32x (_Float32x __x) noexcept (true); extern _Float32x __logf32x (_Float32x __x) noexcept (true);


 extern _Float32x log10f32x (_Float32x __x) noexcept (true); extern _Float32x __log10f32x (_Float32x __x) noexcept (true);


extern _Float32x modff32x (_Float32x __x, _Float32x *__iptr) noexcept (true); extern _Float32x __modff32x (_Float32x __x, _Float32x *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern _Float32x exp10f32x (_Float32x __x) noexcept (true); extern _Float32x __exp10f32x (_Float32x __x) noexcept (true);




 extern _Float32x expm1f32x (_Float32x __x) noexcept (true); extern _Float32x __expm1f32x (_Float32x __x) noexcept (true);


 extern _Float32x log1pf32x (_Float32x __x) noexcept (true); extern _Float32x __log1pf32x (_Float32x __x) noexcept (true);


extern _Float32x logbf32x (_Float32x __x) noexcept (true); extern _Float32x __logbf32x (_Float32x __x) noexcept (true);




 extern _Float32x exp2f32x (_Float32x __x) noexcept (true); extern _Float32x __exp2f32x (_Float32x __x) noexcept (true);


 extern _Float32x log2f32x (_Float32x __x) noexcept (true); extern _Float32x __log2f32x (_Float32x __x) noexcept (true);






 extern _Float32x powf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __powf32x (_Float32x __x, _Float32x __y) noexcept (true);


extern _Float32x sqrtf32x (_Float32x __x) noexcept (true); extern _Float32x __sqrtf32x (_Float32x __x) noexcept (true);



 extern _Float32x hypotf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __hypotf32x (_Float32x __x, _Float32x __y) noexcept (true);




 extern _Float32x cbrtf32x (_Float32x __x) noexcept (true); extern _Float32x __cbrtf32x (_Float32x __x) noexcept (true);






extern _Float32x ceilf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __ceilf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));


extern _Float32x fabsf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fabsf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));


extern _Float32x floorf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __floorf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));


extern _Float32x fmodf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __fmodf32x (_Float32x __x, _Float32x __y) noexcept (true);
# 198 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x copysignf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __copysignf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));




extern _Float32x nanf32x (const char *__tagb) noexcept (true); extern _Float32x __nanf32x (const char *__tagb) noexcept (true);
# 220 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x j0f32x (_Float32x) noexcept (true); extern _Float32x __j0f32x (_Float32x) noexcept (true);
extern _Float32x j1f32x (_Float32x) noexcept (true); extern _Float32x __j1f32x (_Float32x) noexcept (true);
extern _Float32x jnf32x (int, _Float32x) noexcept (true); extern _Float32x __jnf32x (int, _Float32x) noexcept (true);
extern _Float32x y0f32x (_Float32x) noexcept (true); extern _Float32x __y0f32x (_Float32x) noexcept (true);
extern _Float32x y1f32x (_Float32x) noexcept (true); extern _Float32x __y1f32x (_Float32x) noexcept (true);
extern _Float32x ynf32x (int, _Float32x) noexcept (true); extern _Float32x __ynf32x (int, _Float32x) noexcept (true);





 extern _Float32x erff32x (_Float32x) noexcept (true); extern _Float32x __erff32x (_Float32x) noexcept (true);
 extern _Float32x erfcf32x (_Float32x) noexcept (true); extern _Float32x __erfcf32x (_Float32x) noexcept (true);
extern _Float32x lgammaf32x (_Float32x) noexcept (true); extern _Float32x __lgammaf32x (_Float32x) noexcept (true);




extern _Float32x tgammaf32x (_Float32x) noexcept (true); extern _Float32x __tgammaf32x (_Float32x) noexcept (true);
# 252 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float32x lgammaf32x_r (_Float32x, int *__signgamp) noexcept (true); extern _Float32x __lgammaf32x_r (_Float32x, int *__signgamp) noexcept (true);






extern _Float32x rintf32x (_Float32x __x) noexcept (true); extern _Float32x __rintf32x (_Float32x __x) noexcept (true);


extern _Float32x nextafterf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __nextafterf32x (_Float32x __x, _Float32x __y) noexcept (true);






extern _Float32x nextdownf32x (_Float32x __x) noexcept (true); extern _Float32x __nextdownf32x (_Float32x __x) noexcept (true);

extern _Float32x nextupf32x (_Float32x __x) noexcept (true); extern _Float32x __nextupf32x (_Float32x __x) noexcept (true);



extern _Float32x remainderf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __remainderf32x (_Float32x __x, _Float32x __y) noexcept (true);



extern _Float32x scalbnf32x (_Float32x __x, int __n) noexcept (true); extern _Float32x __scalbnf32x (_Float32x __x, int __n) noexcept (true);



extern int ilogbf32x (_Float32x __x) noexcept (true); extern int __ilogbf32x (_Float32x __x) noexcept (true);




extern long int llogbf32x (_Float32x __x) noexcept (true); extern long int __llogbf32x (_Float32x __x) noexcept (true);




extern _Float32x scalblnf32x (_Float32x __x, long int __n) noexcept (true); extern _Float32x __scalblnf32x (_Float32x __x, long int __n) noexcept (true);



extern _Float32x nearbyintf32x (_Float32x __x) noexcept (true); extern _Float32x __nearbyintf32x (_Float32x __x) noexcept (true);



extern _Float32x roundf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __roundf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));



extern _Float32x truncf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __truncf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));




extern _Float32x remquof32x (_Float32x __x, _Float32x __y, int *__quo) noexcept (true); extern _Float32x __remquof32x (_Float32x __x, _Float32x __y, int *__quo) noexcept (true);






extern long int lrintf32x (_Float32x __x) noexcept (true); extern long int __lrintf32x (_Float32x __x) noexcept (true);
__extension__
extern long long int llrintf32x (_Float32x __x) noexcept (true); extern long long int __llrintf32x (_Float32x __x) noexcept (true);



extern long int lroundf32x (_Float32x __x) noexcept (true); extern long int __lroundf32x (_Float32x __x) noexcept (true);
__extension__
extern long long int llroundf32x (_Float32x __x) noexcept (true); extern long long int __llroundf32x (_Float32x __x) noexcept (true);



extern _Float32x fdimf32x (_Float32x __x, _Float32x __y) noexcept (true); extern _Float32x __fdimf32x (_Float32x __x, _Float32x __y) noexcept (true);



extern _Float32x fmaxf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaxf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));



extern _Float32x fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true); extern _Float32x __fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true);




extern _Float32x roundevenf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__)); extern _Float32x __roundevenf32x (_Float32x __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf32x (_Float32x __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizef32x (_Float32x *__cx, const _Float32x *__x) noexcept (true);






extern _Float32x fmaxmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaxmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminmagf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));




extern _Float32x fmaximumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminimumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimumf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fmaximum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminimum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fmaximum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminimum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_magf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fmaximum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fmaximum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));


extern _Float32x fminimum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__)); extern _Float32x __fminimum_mag_numf32x (_Float32x __x, _Float32x __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderf32x (const _Float32x *__x, const _Float32x *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagf32x (const _Float32x *__x, const _Float32x *__y) noexcept (true)

     __attribute__ ((__pure__));


extern _Float32x getpayloadf32x (const _Float32x *__x) noexcept (true); extern _Float32x __getpayloadf32x (const _Float32x *__x) noexcept (true);


extern int setpayloadf32x (_Float32x *__x, _Float32x __payload) noexcept (true);


extern int setpayloadsigf32x (_Float32x *__x, _Float32x __payload) noexcept (true);
# 502 "/usr/include/math.h" 2 3 4
# 518 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 1 3 4
# 53 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
 extern _Float64x acosf64x (_Float64x __x) noexcept (true); extern _Float64x __acosf64x (_Float64x __x) noexcept (true);

 extern _Float64x asinf64x (_Float64x __x) noexcept (true); extern _Float64x __asinf64x (_Float64x __x) noexcept (true);

 extern _Float64x atanf64x (_Float64x __x) noexcept (true); extern _Float64x __atanf64x (_Float64x __x) noexcept (true);

 extern _Float64x atan2f64x (_Float64x __y, _Float64x __x) noexcept (true); extern _Float64x __atan2f64x (_Float64x __y, _Float64x __x) noexcept (true);


 extern _Float64x cosf64x (_Float64x __x) noexcept (true); extern _Float64x __cosf64x (_Float64x __x) noexcept (true);

 extern _Float64x sinf64x (_Float64x __x) noexcept (true); extern _Float64x __sinf64x (_Float64x __x) noexcept (true);

 extern _Float64x tanf64x (_Float64x __x) noexcept (true); extern _Float64x __tanf64x (_Float64x __x) noexcept (true);




 extern _Float64x coshf64x (_Float64x __x) noexcept (true); extern _Float64x __coshf64x (_Float64x __x) noexcept (true);

 extern _Float64x sinhf64x (_Float64x __x) noexcept (true); extern _Float64x __sinhf64x (_Float64x __x) noexcept (true);

 extern _Float64x tanhf64x (_Float64x __x) noexcept (true); extern _Float64x __tanhf64x (_Float64x __x) noexcept (true);



 extern void sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) noexcept (true); extern void __sincosf64x (_Float64x __x, _Float64x *__sinx, _Float64x *__cosx) noexcept (true);





 extern _Float64x acoshf64x (_Float64x __x) noexcept (true); extern _Float64x __acoshf64x (_Float64x __x) noexcept (true);

 extern _Float64x asinhf64x (_Float64x __x) noexcept (true); extern _Float64x __asinhf64x (_Float64x __x) noexcept (true);

 extern _Float64x atanhf64x (_Float64x __x) noexcept (true); extern _Float64x __atanhf64x (_Float64x __x) noexcept (true);





 extern _Float64x expf64x (_Float64x __x) noexcept (true); extern _Float64x __expf64x (_Float64x __x) noexcept (true);


extern _Float64x frexpf64x (_Float64x __x, int *__exponent) noexcept (true); extern _Float64x __frexpf64x (_Float64x __x, int *__exponent) noexcept (true);


extern _Float64x ldexpf64x (_Float64x __x, int __exponent) noexcept (true); extern _Float64x __ldexpf64x (_Float64x __x, int __exponent) noexcept (true);


 extern _Float64x logf64x (_Float64x __x) noexcept (true); extern _Float64x __logf64x (_Float64x __x) noexcept (true);


 extern _Float64x log10f64x (_Float64x __x) noexcept (true); extern _Float64x __log10f64x (_Float64x __x) noexcept (true);


extern _Float64x modff64x (_Float64x __x, _Float64x *__iptr) noexcept (true); extern _Float64x __modff64x (_Float64x __x, _Float64x *__iptr) noexcept (true) __attribute__ ((__nonnull__ (2)));



 extern _Float64x exp10f64x (_Float64x __x) noexcept (true); extern _Float64x __exp10f64x (_Float64x __x) noexcept (true);




 extern _Float64x expm1f64x (_Float64x __x) noexcept (true); extern _Float64x __expm1f64x (_Float64x __x) noexcept (true);


 extern _Float64x log1pf64x (_Float64x __x) noexcept (true); extern _Float64x __log1pf64x (_Float64x __x) noexcept (true);


extern _Float64x logbf64x (_Float64x __x) noexcept (true); extern _Float64x __logbf64x (_Float64x __x) noexcept (true);




 extern _Float64x exp2f64x (_Float64x __x) noexcept (true); extern _Float64x __exp2f64x (_Float64x __x) noexcept (true);


 extern _Float64x log2f64x (_Float64x __x) noexcept (true); extern _Float64x __log2f64x (_Float64x __x) noexcept (true);






 extern _Float64x powf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __powf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float64x sqrtf64x (_Float64x __x) noexcept (true); extern _Float64x __sqrtf64x (_Float64x __x) noexcept (true);



 extern _Float64x hypotf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __hypotf64x (_Float64x __x, _Float64x __y) noexcept (true);




 extern _Float64x cbrtf64x (_Float64x __x) noexcept (true); extern _Float64x __cbrtf64x (_Float64x __x) noexcept (true);






extern _Float64x ceilf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __ceilf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));


extern _Float64x fabsf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fabsf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));


extern _Float64x floorf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __floorf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));


extern _Float64x fmodf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __fmodf64x (_Float64x __x, _Float64x __y) noexcept (true);
# 198 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x copysignf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __copysignf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));




extern _Float64x nanf64x (const char *__tagb) noexcept (true); extern _Float64x __nanf64x (const char *__tagb) noexcept (true);
# 220 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x j0f64x (_Float64x) noexcept (true); extern _Float64x __j0f64x (_Float64x) noexcept (true);
extern _Float64x j1f64x (_Float64x) noexcept (true); extern _Float64x __j1f64x (_Float64x) noexcept (true);
extern _Float64x jnf64x (int, _Float64x) noexcept (true); extern _Float64x __jnf64x (int, _Float64x) noexcept (true);
extern _Float64x y0f64x (_Float64x) noexcept (true); extern _Float64x __y0f64x (_Float64x) noexcept (true);
extern _Float64x y1f64x (_Float64x) noexcept (true); extern _Float64x __y1f64x (_Float64x) noexcept (true);
extern _Float64x ynf64x (int, _Float64x) noexcept (true); extern _Float64x __ynf64x (int, _Float64x) noexcept (true);





 extern _Float64x erff64x (_Float64x) noexcept (true); extern _Float64x __erff64x (_Float64x) noexcept (true);
 extern _Float64x erfcf64x (_Float64x) noexcept (true); extern _Float64x __erfcf64x (_Float64x) noexcept (true);
extern _Float64x lgammaf64x (_Float64x) noexcept (true); extern _Float64x __lgammaf64x (_Float64x) noexcept (true);




extern _Float64x tgammaf64x (_Float64x) noexcept (true); extern _Float64x __tgammaf64x (_Float64x) noexcept (true);
# 252 "/usr/include/x86_64-linux-gnu/bits/mathcalls.h" 3 4
extern _Float64x lgammaf64x_r (_Float64x, int *__signgamp) noexcept (true); extern _Float64x __lgammaf64x_r (_Float64x, int *__signgamp) noexcept (true);






extern _Float64x rintf64x (_Float64x __x) noexcept (true); extern _Float64x __rintf64x (_Float64x __x) noexcept (true);


extern _Float64x nextafterf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __nextafterf64x (_Float64x __x, _Float64x __y) noexcept (true);






extern _Float64x nextdownf64x (_Float64x __x) noexcept (true); extern _Float64x __nextdownf64x (_Float64x __x) noexcept (true);

extern _Float64x nextupf64x (_Float64x __x) noexcept (true); extern _Float64x __nextupf64x (_Float64x __x) noexcept (true);



extern _Float64x remainderf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __remainderf64x (_Float64x __x, _Float64x __y) noexcept (true);



extern _Float64x scalbnf64x (_Float64x __x, int __n) noexcept (true); extern _Float64x __scalbnf64x (_Float64x __x, int __n) noexcept (true);



extern int ilogbf64x (_Float64x __x) noexcept (true); extern int __ilogbf64x (_Float64x __x) noexcept (true);




extern long int llogbf64x (_Float64x __x) noexcept (true); extern long int __llogbf64x (_Float64x __x) noexcept (true);




extern _Float64x scalblnf64x (_Float64x __x, long int __n) noexcept (true); extern _Float64x __scalblnf64x (_Float64x __x, long int __n) noexcept (true);



extern _Float64x nearbyintf64x (_Float64x __x) noexcept (true); extern _Float64x __nearbyintf64x (_Float64x __x) noexcept (true);



extern _Float64x roundf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __roundf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));



extern _Float64x truncf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __truncf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));




extern _Float64x remquof64x (_Float64x __x, _Float64x __y, int *__quo) noexcept (true); extern _Float64x __remquof64x (_Float64x __x, _Float64x __y, int *__quo) noexcept (true);






extern long int lrintf64x (_Float64x __x) noexcept (true); extern long int __lrintf64x (_Float64x __x) noexcept (true);
__extension__
extern long long int llrintf64x (_Float64x __x) noexcept (true); extern long long int __llrintf64x (_Float64x __x) noexcept (true);



extern long int lroundf64x (_Float64x __x) noexcept (true); extern long int __lroundf64x (_Float64x __x) noexcept (true);
__extension__
extern long long int llroundf64x (_Float64x __x) noexcept (true); extern long long int __llroundf64x (_Float64x __x) noexcept (true);



extern _Float64x fdimf64x (_Float64x __x, _Float64x __y) noexcept (true); extern _Float64x __fdimf64x (_Float64x __x, _Float64x __y) noexcept (true);



extern _Float64x fmaxf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaxf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));



extern _Float64x fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true); extern _Float64x __fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);




extern _Float64x roundevenf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__)); extern _Float64x __roundevenf64x (_Float64x __x) noexcept (true) __attribute__ ((__const__));



extern __intmax_t fromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true);




extern __uintmax_t ufromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true);





extern __intmax_t fromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __intmax_t __fromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true);





extern __uintmax_t ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true); extern __uintmax_t __ufromfpxf64x (_Float64x __x, int __round, unsigned int __width) noexcept (true);



extern int canonicalizef64x (_Float64x *__cx, const _Float64x *__x) noexcept (true);






extern _Float64x fmaxmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaxmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminmagf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));




extern _Float64x fmaximumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminimumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimumf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fmaximum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminimum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fmaximum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminimum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_magf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fmaximum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fmaximum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));


extern _Float64x fminimum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__)); extern _Float64x __fminimum_mag_numf64x (_Float64x __x, _Float64x __y) noexcept (true) __attribute__ ((__const__));




extern int totalorderf64x (const _Float64x *__x, const _Float64x *__y) noexcept (true)

     __attribute__ ((__pure__));


extern int totalordermagf64x (const _Float64x *__x, const _Float64x *__y) noexcept (true)

     __attribute__ ((__pure__));


extern _Float64x getpayloadf64x (const _Float64x *__x) noexcept (true); extern _Float64x __getpayloadf64x (const _Float64x *__x) noexcept (true);


extern int setpayloadf64x (_Float64x *__x, _Float64x __payload) noexcept (true);


extern int setpayloadsigf64x (_Float64x *__x, _Float64x __payload) noexcept (true);
# 519 "/usr/include/math.h" 2 3 4
# 566 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern float fadd (double __x, double __y) noexcept (true);


extern float fdiv (double __x, double __y) noexcept (true);


extern float ffma (double __x, double __y, double __z) noexcept (true);


extern float fmul (double __x, double __y) noexcept (true);


extern float fsqrt (double __x) noexcept (true);


extern float fsub (double __x, double __y) noexcept (true);
# 567 "/usr/include/math.h" 2 3 4
# 587 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern float faddl (long double __x, long double __y) noexcept (true);


extern float fdivl (long double __x, long double __y) noexcept (true);


extern float ffmal (long double __x, long double __y, long double __z) noexcept (true);


extern float fmull (long double __x, long double __y) noexcept (true);


extern float fsqrtl (long double __x) noexcept (true);


extern float fsubl (long double __x, long double __y) noexcept (true);
# 588 "/usr/include/math.h" 2 3 4
# 616 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern double daddl (long double __x, long double __y) noexcept (true);


extern double ddivl (long double __x, long double __y) noexcept (true);


extern double dfmal (long double __x, long double __y, long double __z) noexcept (true);


extern double dmull (long double __x, long double __y) noexcept (true);


extern double dsqrtl (long double __x) noexcept (true);


extern double dsubl (long double __x, long double __y) noexcept (true);
# 617 "/usr/include/math.h" 2 3 4
# 697 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf32x (_Float32x __x, _Float32x __y) noexcept (true);


extern _Float32 f32divf32x (_Float32x __x, _Float32x __y) noexcept (true);


extern _Float32 f32fmaf32x (_Float32x __x, _Float32x __y, _Float32x __z) noexcept (true);


extern _Float32 f32mulf32x (_Float32x __x, _Float32x __y) noexcept (true);


extern _Float32 f32sqrtf32x (_Float32x __x) noexcept (true);


extern _Float32 f32subf32x (_Float32x __x, _Float32x __y) noexcept (true);
# 698 "/usr/include/math.h" 2 3 4
# 707 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32 f32divf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32 f32fmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);


extern _Float32 f32mulf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32 f32sqrtf64 (_Float64 __x) noexcept (true);


extern _Float32 f32subf64 (_Float64 __x, _Float64 __y) noexcept (true);
# 708 "/usr/include/math.h" 2 3 4
# 717 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32 f32addf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32 f32divf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32 f32fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);


extern _Float32 f32mulf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32 f32sqrtf64x (_Float64x __x) noexcept (true);


extern _Float32 f32subf64x (_Float64x __x, _Float64x __y) noexcept (true);
# 718 "/usr/include/math.h" 2 3 4
# 747 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32x f32xaddf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32x f32xdivf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32x f32xfmaf64 (_Float64 __x, _Float64 __y, _Float64 __z) noexcept (true);


extern _Float32x f32xmulf64 (_Float64 __x, _Float64 __y) noexcept (true);


extern _Float32x f32xsqrtf64 (_Float64 __x) noexcept (true);


extern _Float32x f32xsubf64 (_Float64 __x, _Float64 __y) noexcept (true);
# 748 "/usr/include/math.h" 2 3 4
# 757 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float32x f32xaddf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32x f32xdivf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32x f32xfmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);


extern _Float32x f32xmulf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float32x f32xsqrtf64x (_Float64x __x) noexcept (true);


extern _Float32x f32xsubf64x (_Float64x __x, _Float64x __y) noexcept (true);
# 758 "/usr/include/math.h" 2 3 4
# 787 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/mathcalls-narrow.h" 3 4
extern _Float64 f64addf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float64 f64divf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float64 f64fmaf64x (_Float64x __x, _Float64x __y, _Float64x __z) noexcept (true);


extern _Float64 f64mulf64x (_Float64x __x, _Float64x __y) noexcept (true);


extern _Float64 f64sqrtf64x (_Float64x __x) noexcept (true);


extern _Float64 f64subf64x (_Float64x __x, _Float64x __y) noexcept (true);
# 788 "/usr/include/math.h" 2 3 4
# 854 "/usr/include/math.h" 3 4
extern int signgam;
# 934 "/usr/include/math.h" 3 4
enum
  {
    FP_NAN =

      0,
    FP_INFINITE =

      1,
    FP_ZERO =

      2,
    FP_SUBNORMAL =

      3,
    FP_NORMAL =

      4
  };
# 1054 "/usr/include/math.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/iscanonical.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/iscanonical.h" 3 4
extern int __iscanonicall (long double __x)
     noexcept (true) __attribute__ ((__const__));
# 46 "/usr/include/x86_64-linux-gnu/bits/iscanonical.h" 3 4
extern "C++" {
inline int iscanonical (float __val) { return ((void) (__typeof (__val)) (__val), 1); }
inline int iscanonical (double __val) { return ((void) (__typeof (__val)) (__val), 1); }
inline int iscanonical (long double __val) { return __iscanonicall (__val); }



}
# 1055 "/usr/include/math.h" 2 3 4
# 1066 "/usr/include/math.h" 3 4
extern "C++" {
inline int issignaling (float __val) { return __issignalingf (__val); }
inline int issignaling (double __val) { return __issignaling (__val); }
inline int
issignaling (long double __val)
{



  return __issignalingl (__val);

}





}
# 1097 "/usr/include/math.h" 3 4
extern "C++" {
# 1128 "/usr/include/math.h" 3 4
template <class __T> inline bool
iszero (__T __val)
{
  return __val == 0;
}

}
# 1363 "/usr/include/math.h" 3 4
extern "C++" {
template<typename> struct __iseqsig_type;

template<> struct __iseqsig_type<float>
{
  static int __call (float __x, float __y) throw ()
  {
    return __iseqsigf (__x, __y);
  }
};

template<> struct __iseqsig_type<double>
{
  static int __call (double __x, double __y) throw ()
  {
    return __iseqsig (__x, __y);
  }
};

template<> struct __iseqsig_type<long double>
{
  static int __call (long double __x, long double __y) throw ()
  {

    return __iseqsigl (__x, __y);



  }
};
# 1454 "/usr/include/math.h" 3 4
template<typename _T1, typename _T2>
inline int
iseqsig (_T1 __x, _T2 __y) throw ()
{

  typedef decltype (((__x) + (__y) + 0.0f)) _T3;



  return __iseqsig_type<_T3>::__call (__x, __y);
}

}




}
# 46 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/std_abs.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/std_abs.h" 3




# 1 "/usr/include/stdlib.h" 1 3 4
# 26 "/usr/include/stdlib.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/stdlib.h" 2 3 4





# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 46 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 3 4
typedef long unsigned int size_t;
# 33 "/usr/include/stdlib.h" 2 3 4

extern "C" {





# 1 "/usr/include/x86_64-linux-gnu/bits/waitflags.h" 1 3 4
# 41 "/usr/include/stdlib.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/waitstatus.h" 1 3 4
# 42 "/usr/include/stdlib.h" 2 3 4
# 59 "/usr/include/stdlib.h" 3 4
typedef struct
  {
    int quot;
    int rem;
  } div_t;



typedef struct
  {
    long int quot;
    long int rem;
  } ldiv_t;





__extension__ typedef struct
  {
    long long int quot;
    long long int rem;
  } lldiv_t;
# 98 "/usr/include/stdlib.h" 3 4
extern size_t __ctype_get_mb_cur_max (void) noexcept (true) ;



extern double atof (const char *__nptr)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern int atoi (const char *__nptr)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern long int atol (const char *__nptr)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;



__extension__ extern long long int atoll (const char *__nptr)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;



extern double strtod (const char *__restrict __nptr,
        char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern float strtof (const char *__restrict __nptr,
       char **__restrict __endptr) noexcept (true) __attribute__ ((__nonnull__ (1)));

extern long double strtold (const char *__restrict __nptr,
       char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 141 "/usr/include/stdlib.h" 3 4
extern _Float32 strtof32 (const char *__restrict __nptr,
     char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern _Float64 strtof64 (const char *__restrict __nptr,
     char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 159 "/usr/include/stdlib.h" 3 4
extern _Float32x strtof32x (const char *__restrict __nptr,
       char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern _Float64x strtof64x (const char *__restrict __nptr,
       char **__restrict __endptr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 177 "/usr/include/stdlib.h" 3 4
extern long int strtol (const char *__restrict __nptr,
   char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));

extern unsigned long int strtoul (const char *__restrict __nptr,
      char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



__extension__
extern long long int strtoq (const char *__restrict __nptr,
        char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));

__extension__
extern unsigned long long int strtouq (const char *__restrict __nptr,
           char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));




__extension__
extern long long int strtoll (const char *__restrict __nptr,
         char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));

__extension__
extern unsigned long long int strtoull (const char *__restrict __nptr,
     char **__restrict __endptr, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));




extern int strfromd (char *__dest, size_t __size, const char *__format,
       double __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));

extern int strfromf (char *__dest, size_t __size, const char *__format,
       float __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));

extern int strfroml (char *__dest, size_t __size, const char *__format,
       long double __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));
# 233 "/usr/include/stdlib.h" 3 4
extern int strfromf32 (char *__dest, size_t __size, const char * __format,
         _Float32 __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));



extern int strfromf64 (char *__dest, size_t __size, const char * __format,
         _Float64 __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));
# 251 "/usr/include/stdlib.h" 3 4
extern int strfromf32x (char *__dest, size_t __size, const char * __format,
   _Float32x __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));



extern int strfromf64x (char *__dest, size_t __size, const char * __format,
   _Float64x __f)
     noexcept (true) __attribute__ ((__nonnull__ (3)));
# 273 "/usr/include/stdlib.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/locale_t.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/types/locale_t.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/__locale_t.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/types/__locale_t.h" 3 4
struct __locale_struct
{

  struct __locale_data *__locales[13];


  const unsigned short int *__ctype_b;
  const int *__ctype_tolower;
  const int *__ctype_toupper;


  const char *__names[13];
};

typedef struct __locale_struct *__locale_t;
# 23 "/usr/include/x86_64-linux-gnu/bits/types/locale_t.h" 2 3 4

typedef __locale_t locale_t;
# 274 "/usr/include/stdlib.h" 2 3 4

extern long int strtol_l (const char *__restrict __nptr,
     char **__restrict __endptr, int __base,
     locale_t __loc) noexcept (true) __attribute__ ((__nonnull__ (1, 4)));

extern unsigned long int strtoul_l (const char *__restrict __nptr,
        char **__restrict __endptr,
        int __base, locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));

__extension__
extern long long int strtoll_l (const char *__restrict __nptr,
    char **__restrict __endptr, int __base,
    locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));

__extension__
extern unsigned long long int strtoull_l (const char *__restrict __nptr,
       char **__restrict __endptr,
       int __base, locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 4)));

extern double strtod_l (const char *__restrict __nptr,
   char **__restrict __endptr, locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));

extern float strtof_l (const char *__restrict __nptr,
         char **__restrict __endptr, locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));

extern long double strtold_l (const char *__restrict __nptr,
         char **__restrict __endptr,
         locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 317 "/usr/include/stdlib.h" 3 4
extern _Float32 strtof32_l (const char *__restrict __nptr,
       char **__restrict __endptr,
       locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));



extern _Float64 strtof64_l (const char *__restrict __nptr,
       char **__restrict __endptr,
       locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 338 "/usr/include/stdlib.h" 3 4
extern _Float32x strtof32x_l (const char *__restrict __nptr,
         char **__restrict __endptr,
         locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));



extern _Float64x strtof64x_l (const char *__restrict __nptr,
         char **__restrict __endptr,
         locale_t __loc)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 386 "/usr/include/stdlib.h" 3 4
extern char *l64a (long int __n) noexcept (true) ;


extern long int a64l (const char *__s)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;




# 1 "/usr/include/x86_64-linux-gnu/sys/types.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
extern "C" {





typedef __u_char u_char;
typedef __u_short u_short;
typedef __u_int u_int;
typedef __u_long u_long;
typedef __quad_t quad_t;
typedef __u_quad_t u_quad_t;
typedef __fsid_t fsid_t;


typedef __loff_t loff_t;




typedef __ino_t ino_t;






typedef __ino64_t ino64_t;




typedef __dev_t dev_t;




typedef __gid_t gid_t;




typedef __mode_t mode_t;




typedef __nlink_t nlink_t;




typedef __uid_t uid_t;





typedef __off_t off_t;






typedef __off64_t off64_t;




typedef __pid_t pid_t;





typedef __id_t id_t;




typedef __ssize_t ssize_t;





typedef __daddr_t daddr_t;
typedef __caddr_t caddr_t;





typedef __key_t key_t;




# 1 "/usr/include/x86_64-linux-gnu/bits/types/clock_t.h" 1 3 4






typedef __clock_t clock_t;
# 127 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/types/clockid_t.h" 1 3 4






typedef __clockid_t clockid_t;
# 129 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/time_t.h" 1 3 4
# 10 "/usr/include/x86_64-linux-gnu/bits/types/time_t.h" 3 4
typedef __time_t time_t;
# 130 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/timer_t.h" 1 3 4






typedef __timer_t timer_t;
# 131 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4



typedef __useconds_t useconds_t;



typedef __suseconds_t suseconds_t;





# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 145 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4



typedef unsigned long int ulong;
typedef unsigned short int ushort;
typedef unsigned int uint;




# 1 "/usr/include/x86_64-linux-gnu/bits/stdint-intn.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/stdint-intn.h" 3 4
typedef __int8_t int8_t;
typedef __int16_t int16_t;
typedef __int32_t int32_t;
typedef __int64_t int64_t;
# 156 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4


typedef __uint8_t u_int8_t;
typedef __uint16_t u_int16_t;
typedef __uint32_t u_int32_t;
typedef __uint64_t u_int64_t;


typedef int register_t __attribute__ ((__mode__ (__word__)));
# 176 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
# 1 "/usr/include/endian.h" 1 3 4
# 24 "/usr/include/endian.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/endian.h" 1 3 4
# 35 "/usr/include/x86_64-linux-gnu/bits/endian.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/endianness.h" 1 3 4
# 36 "/usr/include/x86_64-linux-gnu/bits/endian.h" 2 3 4
# 25 "/usr/include/endian.h" 2 3 4
# 35 "/usr/include/endian.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 1 3 4
# 33 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 3 4
static __inline __uint16_t
__bswap_16 (__uint16_t __bsx)
{



  return ((__uint16_t) ((((__bsx) >> 8) & 0xff) | (((__bsx) & 0xff) << 8)));

}






static __inline __uint32_t
__bswap_32 (__uint32_t __bsx)
{



  return ((((__bsx) & 0xff000000u) >> 24) | (((__bsx) & 0x00ff0000u) >> 8) | (((__bsx) & 0x0000ff00u) << 8) | (((__bsx) & 0x000000ffu) << 24));

}
# 69 "/usr/include/x86_64-linux-gnu/bits/byteswap.h" 3 4
__extension__ static __inline __uint64_t
__bswap_64 (__uint64_t __bsx)
{



  return ((((__bsx) & 0xff00000000000000ull) >> 56) | (((__bsx) & 0x00ff000000000000ull) >> 40) | (((__bsx) & 0x0000ff0000000000ull) >> 24) | (((__bsx) & 0x000000ff00000000ull) >> 8) | (((__bsx) & 0x00000000ff000000ull) << 8) | (((__bsx) & 0x0000000000ff0000ull) << 24) | (((__bsx) & 0x000000000000ff00ull) << 40) | (((__bsx) & 0x00000000000000ffull) << 56));

}
# 36 "/usr/include/endian.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/uintn-identity.h" 1 3 4
# 32 "/usr/include/x86_64-linux-gnu/bits/uintn-identity.h" 3 4
static __inline __uint16_t
__uint16_identity (__uint16_t __x)
{
  return __x;
}

static __inline __uint32_t
__uint32_identity (__uint32_t __x)
{
  return __x;
}

static __inline __uint64_t
__uint64_identity (__uint64_t __x)
{
  return __x;
}
# 37 "/usr/include/endian.h" 2 3 4
# 177 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/sys/select.h" 1 3 4
# 30 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/select.h" 1 3 4
# 31 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/sigset_t.h" 1 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/types/__sigset_t.h" 1 3 4




typedef struct
{
  unsigned long int __val[(1024 / (8 * sizeof (unsigned long int)))];
} __sigset_t;
# 5 "/usr/include/x86_64-linux-gnu/bits/types/sigset_t.h" 2 3 4


typedef __sigset_t sigset_t;
# 34 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_timeval.h" 1 3 4







struct timeval
{




  __time_t tv_sec;
  __suseconds_t tv_usec;

};
# 38 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_timespec.h" 1 3 4
# 11 "/usr/include/x86_64-linux-gnu/bits/types/struct_timespec.h" 3 4
struct timespec
{



  __time_t tv_sec;




  __syscall_slong_t tv_nsec;
# 31 "/usr/include/x86_64-linux-gnu/bits/types/struct_timespec.h" 3 4
};
# 40 "/usr/include/x86_64-linux-gnu/sys/select.h" 2 3 4
# 49 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
typedef long int __fd_mask;
# 59 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
typedef struct
  {



    __fd_mask fds_bits[1024 / (8 * (int) sizeof (__fd_mask))];





  } fd_set;






typedef __fd_mask fd_mask;
# 91 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
extern "C" {
# 102 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
extern int select (int __nfds, fd_set *__restrict __readfds,
     fd_set *__restrict __writefds,
     fd_set *__restrict __exceptfds,
     struct timeval *__restrict __timeout);
# 127 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
extern int pselect (int __nfds, fd_set *__restrict __readfds,
      fd_set *__restrict __writefds,
      fd_set *__restrict __exceptfds,
      const struct timespec *__restrict __timeout,
      const __sigset_t *__restrict __sigmask);
# 153 "/usr/include/x86_64-linux-gnu/sys/select.h" 3 4
}
# 180 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4





typedef __blksize_t blksize_t;






typedef __blkcnt_t blkcnt_t;



typedef __fsblkcnt_t fsblkcnt_t;



typedef __fsfilcnt_t fsfilcnt_t;
# 219 "/usr/include/x86_64-linux-gnu/sys/types.h" 3 4
typedef __blkcnt64_t blkcnt64_t;
typedef __fsblkcnt64_t fsblkcnt64_t;
typedef __fsfilcnt64_t fsfilcnt64_t;





# 1 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 1 3 4
# 44 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h" 1 3 4
# 21 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes-arch.h" 2 3 4
# 45 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h" 1 3 4
# 25 "/usr/include/x86_64-linux-gnu/bits/atomic_wide_counter.h" 3 4
typedef union
{
  __extension__ unsigned long long int __value64;
  struct
  {
    unsigned int __low;
    unsigned int __high;
  } __value32;
} __atomic_wide_counter;
# 47 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 2 3 4




typedef struct __pthread_internal_list
{
  struct __pthread_internal_list *__prev;
  struct __pthread_internal_list *__next;
} __pthread_list_t;

typedef struct __pthread_internal_slist
{
  struct __pthread_internal_slist *__next;
} __pthread_slist_t;
# 76 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/struct_mutex.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/struct_mutex.h" 3 4
struct __pthread_mutex_s
{
  int __lock;
  unsigned int __count;
  int __owner;

  unsigned int __nusers;



  int __kind;

  short __spins;
  short __elision;
  __pthread_list_t __list;
# 53 "/usr/include/x86_64-linux-gnu/bits/struct_mutex.h" 3 4
};
# 77 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 2 3 4
# 89 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/struct_rwlock.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/struct_rwlock.h" 3 4
struct __pthread_rwlock_arch_t
{
  unsigned int __readers;
  unsigned int __writers;
  unsigned int __wrphase_futex;
  unsigned int __writers_futex;
  unsigned int __pad3;
  unsigned int __pad4;

  int __cur_writer;
  int __shared;
  signed char __rwelision;




  unsigned char __pad1[7];


  unsigned long int __pad2;


  unsigned int __flags;
# 55 "/usr/include/x86_64-linux-gnu/bits/struct_rwlock.h" 3 4
};
# 90 "/usr/include/x86_64-linux-gnu/bits/thread-shared-types.h" 2 3 4




struct __pthread_cond_s
{
  __atomic_wide_counter __wseq;
  __atomic_wide_counter __g1_start;
  unsigned int __g_refs[2] ;
  unsigned int __g_size[2];
  unsigned int __g1_orig_size;
  unsigned int __wrefs;
  unsigned int __g_signals[2];
};

typedef unsigned int __tss_t;
typedef unsigned long int __thrd_t;

typedef struct
{
  int __data ;
} __once_flag;
# 24 "/usr/include/x86_64-linux-gnu/bits/pthreadtypes.h" 2 3 4



typedef unsigned long int pthread_t;




typedef union
{
  char __size[4];
  int __align;
} pthread_mutexattr_t;




typedef union
{
  char __size[4];
  int __align;
} pthread_condattr_t;



typedef unsigned int pthread_key_t;



typedef int pthread_once_t;


union pthread_attr_t
{
  char __size[56];
  long int __align;
};

typedef union pthread_attr_t pthread_attr_t;




typedef union
{
  struct __pthread_mutex_s __data;
  char __size[40];
  long int __align;
} pthread_mutex_t;


typedef union
{
  struct __pthread_cond_s __data;
  char __size[48];
  __extension__ long long int __align;
} pthread_cond_t;





typedef union
{
  struct __pthread_rwlock_arch_t __data;
  char __size[56];
  long int __align;
} pthread_rwlock_t;

typedef union
{
  char __size[8];
  long int __align;
} pthread_rwlockattr_t;





typedef volatile int pthread_spinlock_t;




typedef union
{
  char __size[32];
  long int __align;
} pthread_barrier_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_barrierattr_t;
# 228 "/usr/include/x86_64-linux-gnu/sys/types.h" 2 3 4


}
# 396 "/usr/include/stdlib.h" 2 3 4






extern long int random (void) noexcept (true);


extern void srandom (unsigned int __seed) noexcept (true);





extern char *initstate (unsigned int __seed, char *__statebuf,
   size_t __statelen) noexcept (true) __attribute__ ((__nonnull__ (2)));



extern char *setstate (char *__statebuf) noexcept (true) __attribute__ ((__nonnull__ (1)));







struct random_data
  {
    int32_t *fptr;
    int32_t *rptr;
    int32_t *state;
    int rand_type;
    int rand_deg;
    int rand_sep;
    int32_t *end_ptr;
  };

extern int random_r (struct random_data *__restrict __buf,
       int32_t *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));

extern int srandom_r (unsigned int __seed, struct random_data *__buf)
     noexcept (true) __attribute__ ((__nonnull__ (2)));

extern int initstate_r (unsigned int __seed, char *__restrict __statebuf,
   size_t __statelen,
   struct random_data *__restrict __buf)
     noexcept (true) __attribute__ ((__nonnull__ (2, 4)));

extern int setstate_r (char *__restrict __statebuf,
         struct random_data *__restrict __buf)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));





extern int rand (void) noexcept (true);

extern void srand (unsigned int __seed) noexcept (true);



extern int rand_r (unsigned int *__seed) noexcept (true);







extern double drand48 (void) noexcept (true);
extern double erand48 (unsigned short int __xsubi[3]) noexcept (true) __attribute__ ((__nonnull__ (1)));


extern long int lrand48 (void) noexcept (true);
extern long int nrand48 (unsigned short int __xsubi[3])
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern long int mrand48 (void) noexcept (true);
extern long int jrand48 (unsigned short int __xsubi[3])
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern void srand48 (long int __seedval) noexcept (true);
extern unsigned short int *seed48 (unsigned short int __seed16v[3])
     noexcept (true) __attribute__ ((__nonnull__ (1)));
extern void lcong48 (unsigned short int __param[7]) noexcept (true) __attribute__ ((__nonnull__ (1)));





struct drand48_data
  {
    unsigned short int __x[3];
    unsigned short int __old_x[3];
    unsigned short int __c;
    unsigned short int __init;
    __extension__ unsigned long long int __a;

  };


extern int drand48_r (struct drand48_data *__restrict __buffer,
        double *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
extern int erand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        double *__restrict __result) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int lrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
extern int nrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int mrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
extern int jrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int srand48_r (long int __seedval, struct drand48_data *__buffer)
     noexcept (true) __attribute__ ((__nonnull__ (2)));

extern int seed48_r (unsigned short int __seed16v[3],
       struct drand48_data *__buffer) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));

extern int lcong48_r (unsigned short int __param[7],
        struct drand48_data *__buffer)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern __uint32_t arc4random (void)
     noexcept (true) ;


extern void arc4random_buf (void *__buf, size_t __size)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern __uint32_t arc4random_uniform (__uint32_t __upper_bound)
     noexcept (true) ;




extern void *malloc (size_t __size) noexcept (true) __attribute__ ((__malloc__))
                                         ;

extern void *calloc (size_t __nmemb, size_t __size)
     noexcept (true) __attribute__ ((__malloc__)) ;






extern void *realloc (void *__ptr, size_t __size)
     noexcept (true) __attribute__ ((__warn_unused_result__)) ;


extern void free (void *__ptr) noexcept (true);







extern void *reallocarray (void *__ptr, size_t __nmemb, size_t __size)
     noexcept (true) __attribute__ ((__warn_unused_result__))

                       ;


extern void *reallocarray (void *__ptr, size_t __nmemb, size_t __size)
     noexcept (true) ;



# 1 "/usr/include/alloca.h" 1 3 4
# 24 "/usr/include/alloca.h" 3 4
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 25 "/usr/include/alloca.h" 2 3 4

extern "C" {





extern void *alloca (size_t __size) noexcept (true);





}
# 588 "/usr/include/stdlib.h" 2 3 4





extern void *valloc (size_t __size) noexcept (true) __attribute__ ((__malloc__))
                                         ;




extern int posix_memalign (void **__memptr, size_t __alignment, size_t __size)
     noexcept (true) __attribute__ ((__nonnull__ (1))) ;




extern void *aligned_alloc (size_t __alignment, size_t __size)
     noexcept (true) __attribute__ ((__malloc__)) __attribute__ ((__alloc_align__ (1)))
                                         ;



extern void abort (void) noexcept (true) __attribute__ ((__noreturn__));



extern int atexit (void (*__func) (void)) noexcept (true) __attribute__ ((__nonnull__ (1)));




extern "C++" int at_quick_exit (void (*__func) (void))
     noexcept (true) __asm ("at_quick_exit") __attribute__ ((__nonnull__ (1)));
# 630 "/usr/include/stdlib.h" 3 4
extern int on_exit (void (*__func) (int __status, void *__arg), void *__arg)
     noexcept (true) __attribute__ ((__nonnull__ (1)));





extern void exit (int __status) noexcept (true) __attribute__ ((__noreturn__));





extern void quick_exit (int __status) noexcept (true) __attribute__ ((__noreturn__));





extern void _Exit (int __status) noexcept (true) __attribute__ ((__noreturn__));




extern char *getenv (const char *__name) noexcept (true) __attribute__ ((__nonnull__ (1))) ;




extern char *secure_getenv (const char *__name)
     noexcept (true) __attribute__ ((__nonnull__ (1))) ;






extern int putenv (char *__string) noexcept (true) __attribute__ ((__nonnull__ (1)));





extern int setenv (const char *__name, const char *__value, int __replace)
     noexcept (true) __attribute__ ((__nonnull__ (2)));


extern int unsetenv (const char *__name) noexcept (true) __attribute__ ((__nonnull__ (1)));






extern int clearenv (void) noexcept (true);
# 695 "/usr/include/stdlib.h" 3 4
extern char *mktemp (char *__template) noexcept (true) __attribute__ ((__nonnull__ (1)));
# 708 "/usr/include/stdlib.h" 3 4
extern int mkstemp (char *__template) __attribute__ ((__nonnull__ (1))) ;
# 718 "/usr/include/stdlib.h" 3 4
extern int mkstemp64 (char *__template) __attribute__ ((__nonnull__ (1))) ;
# 730 "/usr/include/stdlib.h" 3 4
extern int mkstemps (char *__template, int __suffixlen) __attribute__ ((__nonnull__ (1))) ;
# 740 "/usr/include/stdlib.h" 3 4
extern int mkstemps64 (char *__template, int __suffixlen)
     __attribute__ ((__nonnull__ (1))) ;
# 751 "/usr/include/stdlib.h" 3 4
extern char *mkdtemp (char *__template) noexcept (true) __attribute__ ((__nonnull__ (1))) ;
# 762 "/usr/include/stdlib.h" 3 4
extern int mkostemp (char *__template, int __flags) __attribute__ ((__nonnull__ (1))) ;
# 772 "/usr/include/stdlib.h" 3 4
extern int mkostemp64 (char *__template, int __flags) __attribute__ ((__nonnull__ (1))) ;
# 782 "/usr/include/stdlib.h" 3 4
extern int mkostemps (char *__template, int __suffixlen, int __flags)
     __attribute__ ((__nonnull__ (1))) ;
# 794 "/usr/include/stdlib.h" 3 4
extern int mkostemps64 (char *__template, int __suffixlen, int __flags)
     __attribute__ ((__nonnull__ (1))) ;
# 804 "/usr/include/stdlib.h" 3 4
extern int system (const char *__command) ;





extern char *canonicalize_file_name (const char *__name)
     noexcept (true) __attribute__ ((__nonnull__ (1))) __attribute__ ((__malloc__))
                              ;
# 821 "/usr/include/stdlib.h" 3 4
extern char *realpath (const char *__restrict __name,
         char *__restrict __resolved) noexcept (true) ;






typedef int (*__compar_fn_t) (const void *, const void *);


typedef __compar_fn_t comparison_fn_t;



typedef int (*__compar_d_fn_t) (const void *, const void *, void *);




extern void *bsearch (const void *__key, const void *__base,
        size_t __nmemb, size_t __size, __compar_fn_t __compar)
     __attribute__ ((__nonnull__ (1, 2, 5))) ;







extern void qsort (void *__base, size_t __nmemb, size_t __size,
     __compar_fn_t __compar) __attribute__ ((__nonnull__ (1, 4)));

extern void qsort_r (void *__base, size_t __nmemb, size_t __size,
       __compar_d_fn_t __compar, void *__arg)
  __attribute__ ((__nonnull__ (1, 4)));




extern int abs (int __x) noexcept (true) __attribute__ ((__const__)) ;
extern long int labs (long int __x) noexcept (true) __attribute__ ((__const__)) ;


__extension__ extern long long int llabs (long long int __x)
     noexcept (true) __attribute__ ((__const__)) ;






extern div_t div (int __numer, int __denom)
     noexcept (true) __attribute__ ((__const__)) ;
extern ldiv_t ldiv (long int __numer, long int __denom)
     noexcept (true) __attribute__ ((__const__)) ;


__extension__ extern lldiv_t lldiv (long long int __numer,
        long long int __denom)
     noexcept (true) __attribute__ ((__const__)) ;
# 893 "/usr/include/stdlib.h" 3 4
extern char *ecvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;




extern char *fcvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;




extern char *gcvt (double __value, int __ndigit, char *__buf)
     noexcept (true) __attribute__ ((__nonnull__ (3))) ;




extern char *qecvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qfcvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     noexcept (true) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qgcvt (long double __value, int __ndigit, char *__buf)
     noexcept (true) __attribute__ ((__nonnull__ (3))) ;




extern int ecvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
extern int fcvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));

extern int qecvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));
extern int qfcvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     noexcept (true) __attribute__ ((__nonnull__ (3, 4, 5)));





extern int mblen (const char *__s, size_t __n) noexcept (true);


extern int mbtowc (wchar_t *__restrict __pwc,
     const char *__restrict __s, size_t __n) noexcept (true);


extern int wctomb (char *__s, wchar_t __wchar) noexcept (true);



extern size_t mbstowcs (wchar_t *__restrict __pwcs,
   const char *__restrict __s, size_t __n) noexcept (true)
                                      ;

extern size_t wcstombs (char *__restrict __s,
   const wchar_t *__restrict __pwcs, size_t __n)
     noexcept (true)

                                    ;






extern int rpmatch (const char *__response) noexcept (true) __attribute__ ((__nonnull__ (1))) ;
# 980 "/usr/include/stdlib.h" 3 4
extern int getsubopt (char **__restrict __optionp,
        char *const *__restrict __tokens,
        char **__restrict __valuep)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2, 3))) ;







extern int posix_openpt (int __oflag) ;







extern int grantpt (int __fd) noexcept (true);



extern int unlockpt (int __fd) noexcept (true);




extern char *ptsname (int __fd) noexcept (true) ;






extern int ptsname_r (int __fd, char *__buf, size_t __buflen)
     noexcept (true) __attribute__ ((__nonnull__ (2))) ;


extern int getpt (void);






extern int getloadavg (double __loadavg[], int __nelem)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 1036 "/usr/include/stdlib.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/stdlib-float.h" 1 3 4
# 1037 "/usr/include/stdlib.h" 2 3 4
# 1048 "/usr/include/stdlib.h" 3 4
}
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/std_abs.h" 2 3







extern "C++"
{
namespace std __attribute__ ((__visibility__ ("default")))
{


  using ::abs;


  inline long
  abs(long __i) { return __builtin_labs(__i); }



  inline long long
  abs(long long __x) { return __builtin_llabs (__x); }
# 70 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/std_abs.h" 3
  inline constexpr double
  abs(double __x)
  { return __builtin_fabs(__x); }

  inline constexpr float
  abs(float __x)
  { return __builtin_fabsf(__x); }

  inline constexpr long double
  abs(long double __x)
  { return __builtin_fabsl(__x); }
# 108 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/std_abs.h" 3
}
}
# 48 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 2 3
# 77 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
extern "C++"
{
namespace std __attribute__ ((__visibility__ ("default")))
{


  using ::acos;


  inline constexpr float
  acos(float __x)
  { return __builtin_acosf(__x); }

  inline constexpr long double
  acos(long double __x)
  { return __builtin_acosl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    acos(_Tp __x)
    { return __builtin_acos(__x); }

  using ::asin;


  inline constexpr float
  asin(float __x)
  { return __builtin_asinf(__x); }

  inline constexpr long double
  asin(long double __x)
  { return __builtin_asinl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    asin(_Tp __x)
    { return __builtin_asin(__x); }

  using ::atan;


  inline constexpr float
  atan(float __x)
  { return __builtin_atanf(__x); }

  inline constexpr long double
  atan(long double __x)
  { return __builtin_atanl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    atan(_Tp __x)
    { return __builtin_atan(__x); }

  using ::atan2;


  inline constexpr float
  atan2(float __y, float __x)
  { return __builtin_atan2f(__y, __x); }

  inline constexpr long double
  atan2(long double __y, long double __x)
  { return __builtin_atan2l(__y, __x); }


  template<typename _Tp, typename _Up>
    inline constexpr
    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    atan2(_Tp __y, _Up __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return atan2(__type(__y), __type(__x));
    }

  using ::ceil;


  inline constexpr float
  ceil(float __x)
  { return __builtin_ceilf(__x); }

  inline constexpr long double
  ceil(long double __x)
  { return __builtin_ceill(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    ceil(_Tp __x)
    { return __builtin_ceil(__x); }

  using ::cos;


  inline constexpr float
  cos(float __x)
  { return __builtin_cosf(__x); }

  inline constexpr long double
  cos(long double __x)
  { return __builtin_cosl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    cos(_Tp __x)
    { return __builtin_cos(__x); }

  using ::cosh;


  inline constexpr float
  cosh(float __x)
  { return __builtin_coshf(__x); }

  inline constexpr long double
  cosh(long double __x)
  { return __builtin_coshl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    cosh(_Tp __x)
    { return __builtin_cosh(__x); }

  using ::exp;


  inline constexpr float
  exp(float __x)
  { return __builtin_expf(__x); }

  inline constexpr long double
  exp(long double __x)
  { return __builtin_expl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    exp(_Tp __x)
    { return __builtin_exp(__x); }

  using ::fabs;


  inline constexpr float
  fabs(float __x)
  { return __builtin_fabsf(__x); }

  inline constexpr long double
  fabs(long double __x)
  { return __builtin_fabsl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    fabs(_Tp __x)
    { return __builtin_fabs(__x); }

  using ::floor;


  inline constexpr float
  floor(float __x)
  { return __builtin_floorf(__x); }

  inline constexpr long double
  floor(long double __x)
  { return __builtin_floorl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    floor(_Tp __x)
    { return __builtin_floor(__x); }

  using ::fmod;


  inline constexpr float
  fmod(float __x, float __y)
  { return __builtin_fmodf(__x, __y); }

  inline constexpr long double
  fmod(long double __x, long double __y)
  { return __builtin_fmodl(__x, __y); }


  template<typename _Tp, typename _Up>
    inline constexpr
    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fmod(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fmod(__type(__x), __type(__y));
    }

  using ::frexp;


  inline float
  frexp(float __x, int* __exp)
  { return __builtin_frexpf(__x, __exp); }

  inline long double
  frexp(long double __x, int* __exp)
  { return __builtin_frexpl(__x, __exp); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    frexp(_Tp __x, int* __exp)
    { return __builtin_frexp(__x, __exp); }

  using ::ldexp;


  inline constexpr float
  ldexp(float __x, int __exp)
  { return __builtin_ldexpf(__x, __exp); }

  inline constexpr long double
  ldexp(long double __x, int __exp)
  { return __builtin_ldexpl(__x, __exp); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    ldexp(_Tp __x, int __exp)
    { return __builtin_ldexp(__x, __exp); }

  using ::log;


  inline constexpr float
  log(float __x)
  { return __builtin_logf(__x); }

  inline constexpr long double
  log(long double __x)
  { return __builtin_logl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    log(_Tp __x)
    { return __builtin_log(__x); }

  using ::log10;


  inline constexpr float
  log10(float __x)
  { return __builtin_log10f(__x); }

  inline constexpr long double
  log10(long double __x)
  { return __builtin_log10l(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    log10(_Tp __x)
    { return __builtin_log10(__x); }

  using ::modf;


  inline float
  modf(float __x, float* __iptr)
  { return __builtin_modff(__x, __iptr); }

  inline long double
  modf(long double __x, long double* __iptr)
  { return __builtin_modfl(__x, __iptr); }


  using ::pow;


  inline constexpr float
  pow(float __x, float __y)
  { return __builtin_powf(__x, __y); }

  inline constexpr long double
  pow(long double __x, long double __y)
  { return __builtin_powl(__x, __y); }
# 412 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
  template<typename _Tp, typename _Up>
    inline constexpr
    typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    pow(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return pow(__type(__x), __type(__y));
    }

  using ::sin;


  inline constexpr float
  sin(float __x)
  { return __builtin_sinf(__x); }

  inline constexpr long double
  sin(long double __x)
  { return __builtin_sinl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    sin(_Tp __x)
    { return __builtin_sin(__x); }

  using ::sinh;


  inline constexpr float
  sinh(float __x)
  { return __builtin_sinhf(__x); }

  inline constexpr long double
  sinh(long double __x)
  { return __builtin_sinhl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    sinh(_Tp __x)
    { return __builtin_sinh(__x); }

  using ::sqrt;


  inline constexpr float
  sqrt(float __x)
  { return __builtin_sqrtf(__x); }

  inline constexpr long double
  sqrt(long double __x)
  { return __builtin_sqrtl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    sqrt(_Tp __x)
    { return __builtin_sqrt(__x); }

  using ::tan;


  inline constexpr float
  tan(float __x)
  { return __builtin_tanf(__x); }

  inline constexpr long double
  tan(long double __x)
  { return __builtin_tanl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    tan(_Tp __x)
    { return __builtin_tan(__x); }

  using ::tanh;


  inline constexpr float
  tanh(float __x)
  { return __builtin_tanhf(__x); }

  inline constexpr long double
  tanh(long double __x)
  { return __builtin_tanhl(__x); }


  template<typename _Tp>
    inline constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    double>::__type
    tanh(_Tp __x)
    { return __builtin_tanh(__x); }
# 536 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
  constexpr int
  fpclassify(float __x)
  { return __builtin_fpclassify(0, 1, 4,
    3, 2, __x); }

  constexpr int
  fpclassify(double __x)
  { return __builtin_fpclassify(0, 1, 4,
    3, 2, __x); }

  constexpr int
  fpclassify(long double __x)
  { return __builtin_fpclassify(0, 1, 4,
    3, 2, __x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              int>::__type
    fpclassify(_Tp __x)
    { return __x != 0 ? 4 : 2; }



  constexpr bool
  isfinite(float __x)
  { return __builtin_isfinite(__x); }

  constexpr bool
  isfinite(double __x)
  { return __builtin_isfinite(__x); }

  constexpr bool
  isfinite(long double __x)
  { return __builtin_isfinite(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              bool>::__type
    isfinite(_Tp __x)
    { return true; }



  constexpr bool
  isinf(float __x)
  { return __builtin_isinf(__x); }





  constexpr bool
  isinf(double __x)
  { return __builtin_isinf(__x); }


  constexpr bool
  isinf(long double __x)
  { return __builtin_isinf(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              bool>::__type
    isinf(_Tp __x)
    { return false; }



  constexpr bool
  isnan(float __x)
  { return __builtin_isnan(__x); }





  constexpr bool
  isnan(double __x)
  { return __builtin_isnan(__x); }


  constexpr bool
  isnan(long double __x)
  { return __builtin_isnan(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              bool>::__type
    isnan(_Tp __x)
    { return false; }



  constexpr bool
  isnormal(float __x)
  { return __builtin_isnormal(__x); }

  constexpr bool
  isnormal(double __x)
  { return __builtin_isnormal(__x); }

  constexpr bool
  isnormal(long double __x)
  { return __builtin_isnormal(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              bool>::__type
    isnormal(_Tp __x)
    { return __x != 0 ? true : false; }




  constexpr bool
  signbit(float __x)
  { return __builtin_signbit(__x); }

  constexpr bool
  signbit(double __x)
  { return __builtin_signbit(__x); }

  constexpr bool
  signbit(long double __x)
  { return __builtin_signbit(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              bool>::__type
    signbit(_Tp __x)
    { return __x < 0 ? true : false; }



  constexpr bool
  isgreater(float __x, float __y)
  { return __builtin_isgreater(__x, __y); }

  constexpr bool
  isgreater(double __x, double __y)
  { return __builtin_isgreater(__x, __y); }

  constexpr bool
  isgreater(long double __x, long double __y)
  { return __builtin_isgreater(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    isgreater(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_isgreater(__type(__x), __type(__y));
    }



  constexpr bool
  isgreaterequal(float __x, float __y)
  { return __builtin_isgreaterequal(__x, __y); }

  constexpr bool
  isgreaterequal(double __x, double __y)
  { return __builtin_isgreaterequal(__x, __y); }

  constexpr bool
  isgreaterequal(long double __x, long double __y)
  { return __builtin_isgreaterequal(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    isgreaterequal(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_isgreaterequal(__type(__x), __type(__y));
    }



  constexpr bool
  isless(float __x, float __y)
  { return __builtin_isless(__x, __y); }

  constexpr bool
  isless(double __x, double __y)
  { return __builtin_isless(__x, __y); }

  constexpr bool
  isless(long double __x, long double __y)
  { return __builtin_isless(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    isless(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_isless(__type(__x), __type(__y));
    }



  constexpr bool
  islessequal(float __x, float __y)
  { return __builtin_islessequal(__x, __y); }

  constexpr bool
  islessequal(double __x, double __y)
  { return __builtin_islessequal(__x, __y); }

  constexpr bool
  islessequal(long double __x, long double __y)
  { return __builtin_islessequal(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    islessequal(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_islessequal(__type(__x), __type(__y));
    }



  constexpr bool
  islessgreater(float __x, float __y)
  { return __builtin_islessgreater(__x, __y); }

  constexpr bool
  islessgreater(double __x, double __y)
  { return __builtin_islessgreater(__x, __y); }

  constexpr bool
  islessgreater(long double __x, long double __y)
  { return __builtin_islessgreater(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    islessgreater(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_islessgreater(__type(__x), __type(__y));
    }



  constexpr bool
  isunordered(float __x, float __y)
  { return __builtin_isunordered(__x, __y); }

  constexpr bool
  isunordered(double __x, double __y)
  { return __builtin_isunordered(__x, __y); }

  constexpr bool
  isunordered(long double __x, long double __y)
  { return __builtin_isunordered(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename
    __gnu_cxx::__enable_if<(__is_arithmetic<_Tp>::__value
       && __is_arithmetic<_Up>::__value), bool>::__type
    isunordered(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return __builtin_isunordered(__type(__x), __type(__y));
    }
# 1065 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
  using ::double_t;
  using ::float_t;


  using ::acosh;
  using ::acoshf;
  using ::acoshl;

  using ::asinh;
  using ::asinhf;
  using ::asinhl;

  using ::atanh;
  using ::atanhf;
  using ::atanhl;

  using ::cbrt;
  using ::cbrtf;
  using ::cbrtl;

  using ::copysign;
  using ::copysignf;
  using ::copysignl;

  using ::erf;
  using ::erff;
  using ::erfl;

  using ::erfc;
  using ::erfcf;
  using ::erfcl;

  using ::exp2;
  using ::exp2f;
  using ::exp2l;

  using ::expm1;
  using ::expm1f;
  using ::expm1l;

  using ::fdim;
  using ::fdimf;
  using ::fdiml;

  using ::fma;
  using ::fmaf;
  using ::fmal;

  using ::fmax;
  using ::fmaxf;
  using ::fmaxl;

  using ::fmin;
  using ::fminf;
  using ::fminl;

  using ::hypot;
  using ::hypotf;
  using ::hypotl;

  using ::ilogb;
  using ::ilogbf;
  using ::ilogbl;

  using ::lgamma;
  using ::lgammaf;
  using ::lgammal;


  using ::llrint;
  using ::llrintf;
  using ::llrintl;

  using ::llround;
  using ::llroundf;
  using ::llroundl;


  using ::log1p;
  using ::log1pf;
  using ::log1pl;

  using ::log2;
  using ::log2f;
  using ::log2l;

  using ::logb;
  using ::logbf;
  using ::logbl;

  using ::lrint;
  using ::lrintf;
  using ::lrintl;

  using ::lround;
  using ::lroundf;
  using ::lroundl;

  using ::nan;
  using ::nanf;
  using ::nanl;

  using ::nearbyint;
  using ::nearbyintf;
  using ::nearbyintl;

  using ::nextafter;
  using ::nextafterf;
  using ::nextafterl;

  using ::nexttoward;
  using ::nexttowardf;
  using ::nexttowardl;

  using ::remainder;
  using ::remainderf;
  using ::remainderl;

  using ::remquo;
  using ::remquof;
  using ::remquol;

  using ::rint;
  using ::rintf;
  using ::rintl;

  using ::round;
  using ::roundf;
  using ::roundl;

  using ::scalbln;
  using ::scalblnf;
  using ::scalblnl;

  using ::scalbn;
  using ::scalbnf;
  using ::scalbnl;

  using ::tgamma;
  using ::tgammaf;
  using ::tgammal;

  using ::trunc;
  using ::truncf;
  using ::truncl;



  constexpr float
  acosh(float __x)
  { return __builtin_acoshf(__x); }

  constexpr long double
  acosh(long double __x)
  { return __builtin_acoshl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    acosh(_Tp __x)
    { return __builtin_acosh(__x); }



  constexpr float
  asinh(float __x)
  { return __builtin_asinhf(__x); }

  constexpr long double
  asinh(long double __x)
  { return __builtin_asinhl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    asinh(_Tp __x)
    { return __builtin_asinh(__x); }



  constexpr float
  atanh(float __x)
  { return __builtin_atanhf(__x); }

  constexpr long double
  atanh(long double __x)
  { return __builtin_atanhl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    atanh(_Tp __x)
    { return __builtin_atanh(__x); }



  constexpr float
  cbrt(float __x)
  { return __builtin_cbrtf(__x); }

  constexpr long double
  cbrt(long double __x)
  { return __builtin_cbrtl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    cbrt(_Tp __x)
    { return __builtin_cbrt(__x); }



  constexpr float
  copysign(float __x, float __y)
  { return __builtin_copysignf(__x, __y); }

  constexpr long double
  copysign(long double __x, long double __y)
  { return __builtin_copysignl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    copysign(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return copysign(__type(__x), __type(__y));
    }



  constexpr float
  erf(float __x)
  { return __builtin_erff(__x); }

  constexpr long double
  erf(long double __x)
  { return __builtin_erfl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    erf(_Tp __x)
    { return __builtin_erf(__x); }



  constexpr float
  erfc(float __x)
  { return __builtin_erfcf(__x); }

  constexpr long double
  erfc(long double __x)
  { return __builtin_erfcl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    erfc(_Tp __x)
    { return __builtin_erfc(__x); }



  constexpr float
  exp2(float __x)
  { return __builtin_exp2f(__x); }

  constexpr long double
  exp2(long double __x)
  { return __builtin_exp2l(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    exp2(_Tp __x)
    { return __builtin_exp2(__x); }



  constexpr float
  expm1(float __x)
  { return __builtin_expm1f(__x); }

  constexpr long double
  expm1(long double __x)
  { return __builtin_expm1l(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    expm1(_Tp __x)
    { return __builtin_expm1(__x); }



  constexpr float
  fdim(float __x, float __y)
  { return __builtin_fdimf(__x, __y); }

  constexpr long double
  fdim(long double __x, long double __y)
  { return __builtin_fdiml(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fdim(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fdim(__type(__x), __type(__y));
    }



  constexpr float
  fma(float __x, float __y, float __z)
  { return __builtin_fmaf(__x, __y, __z); }

  constexpr long double
  fma(long double __x, long double __y, long double __z)
  { return __builtin_fmal(__x, __y, __z); }



  template<typename _Tp, typename _Up, typename _Vp>
    constexpr typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type
    fma(_Tp __x, _Up __y, _Vp __z)
    {
      typedef typename __gnu_cxx::__promote_3<_Tp, _Up, _Vp>::__type __type;
      return fma(__type(__x), __type(__y), __type(__z));
    }



  constexpr float
  fmax(float __x, float __y)
  { return __builtin_fmaxf(__x, __y); }

  constexpr long double
  fmax(long double __x, long double __y)
  { return __builtin_fmaxl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fmax(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fmax(__type(__x), __type(__y));
    }



  constexpr float
  fmin(float __x, float __y)
  { return __builtin_fminf(__x, __y); }

  constexpr long double
  fmin(long double __x, long double __y)
  { return __builtin_fminl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    fmin(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return fmin(__type(__x), __type(__y));
    }



  constexpr float
  hypot(float __x, float __y)
  { return __builtin_hypotf(__x, __y); }

  constexpr long double
  hypot(long double __x, long double __y)
  { return __builtin_hypotl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    hypot(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return hypot(__type(__x), __type(__y));
    }



  constexpr int
  ilogb(float __x)
  { return __builtin_ilogbf(__x); }

  constexpr int
  ilogb(long double __x)
  { return __builtin_ilogbl(__x); }



  template<typename _Tp>
    constexpr
    typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                    int>::__type
    ilogb(_Tp __x)
    { return __builtin_ilogb(__x); }



  constexpr float
  lgamma(float __x)
  { return __builtin_lgammaf(__x); }

  constexpr long double
  lgamma(long double __x)
  { return __builtin_lgammal(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    lgamma(_Tp __x)
    { return __builtin_lgamma(__x); }



  constexpr long long
  llrint(float __x)
  { return __builtin_llrintf(__x); }

  constexpr long long
  llrint(long double __x)
  { return __builtin_llrintl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              long long>::__type
    llrint(_Tp __x)
    { return __builtin_llrint(__x); }



  constexpr long long
  llround(float __x)
  { return __builtin_llroundf(__x); }

  constexpr long long
  llround(long double __x)
  { return __builtin_llroundl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              long long>::__type
    llround(_Tp __x)
    { return __builtin_llround(__x); }



  constexpr float
  log1p(float __x)
  { return __builtin_log1pf(__x); }

  constexpr long double
  log1p(long double __x)
  { return __builtin_log1pl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    log1p(_Tp __x)
    { return __builtin_log1p(__x); }




  constexpr float
  log2(float __x)
  { return __builtin_log2f(__x); }

  constexpr long double
  log2(long double __x)
  { return __builtin_log2l(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    log2(_Tp __x)
    { return __builtin_log2(__x); }



  constexpr float
  logb(float __x)
  { return __builtin_logbf(__x); }

  constexpr long double
  logb(long double __x)
  { return __builtin_logbl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    logb(_Tp __x)
    { return __builtin_logb(__x); }



  constexpr long
  lrint(float __x)
  { return __builtin_lrintf(__x); }

  constexpr long
  lrint(long double __x)
  { return __builtin_lrintl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              long>::__type
    lrint(_Tp __x)
    { return __builtin_lrint(__x); }



  constexpr long
  lround(float __x)
  { return __builtin_lroundf(__x); }

  constexpr long
  lround(long double __x)
  { return __builtin_lroundl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              long>::__type
    lround(_Tp __x)
    { return __builtin_lround(__x); }



  constexpr float
  nearbyint(float __x)
  { return __builtin_nearbyintf(__x); }

  constexpr long double
  nearbyint(long double __x)
  { return __builtin_nearbyintl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    nearbyint(_Tp __x)
    { return __builtin_nearbyint(__x); }



  constexpr float
  nextafter(float __x, float __y)
  { return __builtin_nextafterf(__x, __y); }

  constexpr long double
  nextafter(long double __x, long double __y)
  { return __builtin_nextafterl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    nextafter(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return nextafter(__type(__x), __type(__y));
    }



  constexpr float
  nexttoward(float __x, long double __y)
  { return __builtin_nexttowardf(__x, __y); }

  constexpr long double
  nexttoward(long double __x, long double __y)
  { return __builtin_nexttowardl(__x, __y); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    nexttoward(_Tp __x, long double __y)
    { return __builtin_nexttoward(__x, __y); }



  constexpr float
  remainder(float __x, float __y)
  { return __builtin_remainderf(__x, __y); }

  constexpr long double
  remainder(long double __x, long double __y)
  { return __builtin_remainderl(__x, __y); }



  template<typename _Tp, typename _Up>
    constexpr typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    remainder(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return remainder(__type(__x), __type(__y));
    }



  inline float
  remquo(float __x, float __y, int* __pquo)
  { return __builtin_remquof(__x, __y, __pquo); }

  inline long double
  remquo(long double __x, long double __y, int* __pquo)
  { return __builtin_remquol(__x, __y, __pquo); }



  template<typename _Tp, typename _Up>
    inline typename __gnu_cxx::__promote_2<_Tp, _Up>::__type
    remquo(_Tp __x, _Up __y, int* __pquo)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return remquo(__type(__x), __type(__y), __pquo);
    }



  constexpr float
  rint(float __x)
  { return __builtin_rintf(__x); }

  constexpr long double
  rint(long double __x)
  { return __builtin_rintl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    rint(_Tp __x)
    { return __builtin_rint(__x); }



  constexpr float
  round(float __x)
  { return __builtin_roundf(__x); }

  constexpr long double
  round(long double __x)
  { return __builtin_roundl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    round(_Tp __x)
    { return __builtin_round(__x); }



  constexpr float
  scalbln(float __x, long __ex)
  { return __builtin_scalblnf(__x, __ex); }

  constexpr long double
  scalbln(long double __x, long __ex)
  { return __builtin_scalblnl(__x, __ex); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    scalbln(_Tp __x, long __ex)
    { return __builtin_scalbln(__x, __ex); }



  constexpr float
  scalbn(float __x, int __ex)
  { return __builtin_scalbnf(__x, __ex); }

  constexpr long double
  scalbn(long double __x, int __ex)
  { return __builtin_scalbnl(__x, __ex); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    scalbn(_Tp __x, int __ex)
    { return __builtin_scalbn(__x, __ex); }



  constexpr float
  tgamma(float __x)
  { return __builtin_tgammaf(__x); }

  constexpr long double
  tgamma(long double __x)
  { return __builtin_tgammal(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    tgamma(_Tp __x)
    { return __builtin_tgamma(__x); }



  constexpr float
  trunc(float __x)
  { return __builtin_truncf(__x); }

  constexpr long double
  trunc(long double __x)
  { return __builtin_truncl(__x); }



  template<typename _Tp>
    constexpr typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
                                              double>::__type
    trunc(_Tp __x)
    { return __builtin_trunc(__x); }
# 1932 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
}





}
# 51 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
# 121 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
extern "C++"
{
namespace std __attribute__ ((__visibility__ ("default")))
{


  using ::div_t;
  using ::ldiv_t;

  using ::abort;



  using ::atexit;


  using ::at_quick_exit;


  using ::atof;
  using ::atoi;
  using ::atol;
  using ::bsearch;
  using ::calloc;
  using ::div;
  using ::exit;
  using ::free;
  using ::getenv;
  using ::labs;
  using ::ldiv;
  using ::malloc;

  using ::mblen;
  using ::mbstowcs;
  using ::mbtowc;

  using ::qsort;


  using ::quick_exit;


  using ::rand;
  using ::realloc;
  using ::srand;
  using ::strtod;
  using ::strtol;
  using ::strtoul;
  using ::system;

  using ::wcstombs;
  using ::wctomb;



  inline ldiv_t
  div(long __i, long __j) { return ldiv(__i, __j); }




}
# 195 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{



  using ::lldiv_t;





  using ::_Exit;



  using ::llabs;

  inline lldiv_t
  div(long long __n, long long __d)
  { lldiv_t __q; __q.quot = __n / __d; __q.rem = __n % __d; return __q; }

  using ::lldiv;
# 227 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
  using ::atoll;
  using ::strtoll;
  using ::strtoull;

  using ::strtof;
  using ::strtold;


}

namespace std
{

  using ::__gnu_cxx::lldiv_t;

  using ::__gnu_cxx::_Exit;

  using ::__gnu_cxx::llabs;
  using ::__gnu_cxx::div;
  using ::__gnu_cxx::lldiv;

  using ::__gnu_cxx::atoll;
  using ::__gnu_cxx::strtof;
  using ::__gnu_cxx::strtoll;
  using ::__gnu_cxx::strtoull;
  using ::__gnu_cxx::strtold;
}



}
# 52 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdlib.h" 1 3
# 36 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdlib.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdlib.h" 2 3

using std::abort;
using std::atexit;
using std::exit;


  using std::at_quick_exit;


  using std::quick_exit;




using std::div_t;
using std::ldiv_t;

using std::abs;
using std::atof;
using std::atoi;
using std::atol;
using std::bsearch;
using std::calloc;
using std::div;
using std::free;
using std::getenv;
using std::labs;
using std::ldiv;
using std::malloc;

using std::mblen;
using std::mbstowcs;
using std::mbtowc;

using std::qsort;
using std::rand;
using std::realloc;
using std::srand;
using std::strtod;
using std::strtol;
using std::strtoul;
using std::system;

using std::wcstombs;
using std::wctomb;
# 53 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3

# 1 "/usr/include/hip/hip_version.h" 1 3 4
# 55 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 74 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 3
typedef long unsigned int __hip_size_t;


extern "C" {



extern "C" __attribute__((device)) unsigned long long __ockl_dm_alloc(unsigned long long __size);
extern "C" __attribute__((device)) void __ockl_dm_dealloc(unsigned long long __addr);
__attribute__((weak)) inline __attribute__((device)) void *malloc(__hip_size_t __size) {
  return (void *) __ockl_dm_alloc(__size);
}
__attribute__((weak)) inline __attribute__((device)) void free(void *__ptr) {
  __ockl_dm_dealloc((unsigned long long)__ptr);
}
# 111 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 3
}


# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_libdevice_declares.h" 1 3
# 14 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_libdevice_declares.h" 3
extern "C" {



__attribute__((device)) __attribute__((const)) float __ocml_acos_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_acosh_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_asin_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_asinh_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_atan2_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_atan_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_atanh_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_cbrt_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_ceil_f32(float);
__attribute__((device)) __attribute__((const)) __attribute__((device)) float __ocml_copysign_f32(float,
                                                                       float);
__attribute__((device)) float __ocml_cos_f32(float);
__attribute__((device)) float __ocml_native_cos_f32(float);
__attribute__((device)) __attribute__((pure)) __attribute__((device)) float __ocml_cosh_f32(float);
__attribute__((device)) float __ocml_cospi_f32(float);
__attribute__((device)) float __ocml_i0_f32(float);
__attribute__((device)) float __ocml_i1_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_erfc_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_erfcinv_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_erfcx_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_erf_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_erfinv_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_exp10_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_native_exp10_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_exp2_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_exp_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_native_exp_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_expm1_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_fabs_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_fdim_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_floor_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_fma_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_fmax_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_fmin_f32(float, float);
__attribute__((device)) __attribute__((const)) __attribute__((device)) float __ocml_fmod_f32(float,
                                                                   float);
__attribute__((device)) float __ocml_frexp_f32(float,
                                  __attribute__((address_space(5))) int *);
__attribute__((device)) __attribute__((const)) float __ocml_hypot_f32(float, float);
__attribute__((device)) __attribute__((const)) int __ocml_ilogb_f32(float);
__attribute__((device)) __attribute__((const)) int __ocml_isfinite_f32(float);
__attribute__((device)) __attribute__((const)) int __ocml_isinf_f32(float);
__attribute__((device)) __attribute__((const)) int __ocml_isnan_f32(float);
__attribute__((device)) float __ocml_j0_f32(float);
__attribute__((device)) float __ocml_j1_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_ldexp_f32(float, int);
__attribute__((device)) float __ocml_lgamma_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_log10_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_native_log10_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_log1p_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_log2_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_native_log2_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_logb_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_log_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_native_log_f32(float);
__attribute__((device)) float __ocml_modf_f32(float,
                                 __attribute__((address_space(5))) float *);
__attribute__((device)) __attribute__((const)) float __ocml_nearbyint_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_nextafter_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_len3_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_len4_f32(float, float, float,
                                                        float);
__attribute__((device)) __attribute__((pure)) float __ocml_ncdf_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_ncdfinv_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_pow_f32(float, float);
__attribute__((device)) __attribute__((pure)) float __ocml_pown_f32(float, int);
__attribute__((device)) __attribute__((pure)) float __ocml_rcbrt_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_remainder_f32(float, float);
__attribute__((device)) float __ocml_remquo_f32(float, float,
                                   __attribute__((address_space(5))) int *);
__attribute__((device)) __attribute__((const)) float __ocml_rhypot_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_rint_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_rlen3_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_rlen4_f32(float, float, float,
                                                         float);
__attribute__((device)) __attribute__((const)) float __ocml_round_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_rsqrt_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_scalb_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_scalbn_f32(float, int);
__attribute__((device)) __attribute__((const)) int __ocml_signbit_f32(float);
__attribute__((device)) float __ocml_sincos_f32(float,
                                   __attribute__((address_space(5))) float *);
__attribute__((device)) float __ocml_sincospi_f32(float,
                                     __attribute__((address_space(5))) float *);
__attribute__((device)) float __ocml_sin_f32(float);
__attribute__((device)) float __ocml_native_sin_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_sinh_f32(float);
__attribute__((device)) float __ocml_sinpi_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_sqrt_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_native_sqrt_f32(float);
__attribute__((device)) float __ocml_tan_f32(float);
__attribute__((device)) __attribute__((pure)) float __ocml_tanh_f32(float);
__attribute__((device)) float __ocml_tgamma_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_trunc_f32(float);
__attribute__((device)) float __ocml_y0_f32(float);
__attribute__((device)) float __ocml_y1_f32(float);


__attribute__((device)) __attribute__((const)) float __ocml_add_rte_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_add_rtn_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_add_rtp_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_add_rtz_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_sub_rte_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_sub_rtn_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_sub_rtp_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_sub_rtz_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_mul_rte_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_mul_rtn_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_mul_rtp_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_mul_rtz_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_div_rte_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_div_rtn_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_div_rtp_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_div_rtz_f32(float, float);
__attribute__((device)) __attribute__((const)) float __ocml_sqrt_rte_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_sqrt_rtn_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_sqrt_rtp_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_sqrt_rtz_f32(float);
__attribute__((device)) __attribute__((const)) float __ocml_fma_rte_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_fma_rtn_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_fma_rtp_f32(float, float, float);
__attribute__((device)) __attribute__((const)) float __ocml_fma_rtz_f32(float, float, float);

__attribute__((device)) inline __attribute__((const)) float
__llvm_amdgcn_cos_f32(float __x) {
  return __builtin_amdgcn_cosf(__x);
}
__attribute__((device)) inline __attribute__((const)) float
__llvm_amdgcn_rcp_f32(float __x) {
  return __builtin_amdgcn_rcpf(__x);
}
__attribute__((device)) inline __attribute__((const)) float
__llvm_amdgcn_rsq_f32(float __x) {
  return __builtin_amdgcn_rsqf(__x);
}
__attribute__((device)) inline __attribute__((const)) float
__llvm_amdgcn_sin_f32(float __x) {
  return __builtin_amdgcn_sinf(__x);
}




__attribute__((device)) __attribute__((const)) double __ocml_acos_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_acosh_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_asin_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_asinh_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_atan2_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_atan_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_atanh_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_cbrt_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_ceil_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_copysign_f64(double, double);
__attribute__((device)) double __ocml_cos_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_cosh_f64(double);
__attribute__((device)) double __ocml_cospi_f64(double);
__attribute__((device)) double __ocml_i0_f64(double);
__attribute__((device)) double __ocml_i1_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_erfc_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_erfcinv_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_erfcx_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_erf_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_erfinv_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_exp10_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_exp2_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_exp_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_expm1_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_fabs_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_fdim_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_floor_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_fma_f64(double, double, double);
__attribute__((device)) __attribute__((const)) double __ocml_fmax_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_fmin_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_fmod_f64(double, double);
__attribute__((device)) double __ocml_frexp_f64(double,
                                   __attribute__((address_space(5))) int *);
__attribute__((device)) __attribute__((const)) double __ocml_hypot_f64(double, double);
__attribute__((device)) __attribute__((const)) int __ocml_ilogb_f64(double);
__attribute__((device)) __attribute__((const)) int __ocml_isfinite_f64(double);
__attribute__((device)) __attribute__((const)) int __ocml_isinf_f64(double);
__attribute__((device)) __attribute__((const)) int __ocml_isnan_f64(double);
__attribute__((device)) double __ocml_j0_f64(double);
__attribute__((device)) double __ocml_j1_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_ldexp_f64(double, int);
__attribute__((device)) double __ocml_lgamma_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_log10_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_log1p_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_log2_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_logb_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_log_f64(double);
__attribute__((device)) double __ocml_modf_f64(double,
                                  __attribute__((address_space(5))) double *);
__attribute__((device)) __attribute__((const)) double __ocml_nearbyint_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_nextafter_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_len3_f64(double, double,
                                                         double);
__attribute__((device)) __attribute__((const)) double __ocml_len4_f64(double, double, double,
                                                         double);
__attribute__((device)) __attribute__((pure)) double __ocml_ncdf_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_ncdfinv_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_pow_f64(double, double);
__attribute__((device)) __attribute__((pure)) double __ocml_pown_f64(double, int);
__attribute__((device)) __attribute__((pure)) double __ocml_rcbrt_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_remainder_f64(double, double);
__attribute__((device)) double __ocml_remquo_f64(double, double,
                                    __attribute__((address_space(5))) int *);
__attribute__((device)) __attribute__((const)) double __ocml_rhypot_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_rint_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_rlen3_f64(double, double,
                                                          double);
__attribute__((device)) __attribute__((const)) double __ocml_rlen4_f64(double, double,
                                                          double, double);
__attribute__((device)) __attribute__((const)) double __ocml_round_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_rsqrt_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_scalb_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_scalbn_f64(double, int);
__attribute__((device)) __attribute__((const)) int __ocml_signbit_f64(double);
__attribute__((device)) double __ocml_sincos_f64(double,
                                    __attribute__((address_space(5))) double *);
__attribute__((device)) double
__ocml_sincospi_f64(double, __attribute__((address_space(5))) double *);
__attribute__((device)) double __ocml_sin_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_sinh_f64(double);
__attribute__((device)) double __ocml_sinpi_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_sqrt_f64(double);
__attribute__((device)) double __ocml_tan_f64(double);
__attribute__((device)) __attribute__((pure)) double __ocml_tanh_f64(double);
__attribute__((device)) double __ocml_tgamma_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_trunc_f64(double);
__attribute__((device)) double __ocml_y0_f64(double);
__attribute__((device)) double __ocml_y1_f64(double);


__attribute__((device)) __attribute__((const)) double __ocml_add_rte_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_add_rtn_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_add_rtp_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_add_rtz_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_sub_rte_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_sub_rtn_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_sub_rtp_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_sub_rtz_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_mul_rte_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_mul_rtn_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_mul_rtp_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_mul_rtz_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_div_rte_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_div_rtn_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_div_rtp_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_div_rtz_f64(double, double);
__attribute__((device)) __attribute__((const)) double __ocml_sqrt_rte_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_sqrt_rtn_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_sqrt_rtp_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_sqrt_rtz_f64(double);
__attribute__((device)) __attribute__((const)) double __ocml_fma_rte_f64(double, double,
                                                            double);
__attribute__((device)) __attribute__((const)) double __ocml_fma_rtn_f64(double, double,
                                                            double);
__attribute__((device)) __attribute__((const)) double __ocml_fma_rtp_f64(double, double,
                                                            double);
__attribute__((device)) __attribute__((const)) double __ocml_fma_rtz_f64(double, double,
                                                            double);

__attribute__((device)) inline __attribute__((const)) double
__llvm_amdgcn_rcp_f64(double __x) {
  return __builtin_amdgcn_rcp(__x);
}
__attribute__((device)) inline __attribute__((const)) double
__llvm_amdgcn_rsq_f64(double __x) {
  return __builtin_amdgcn_rsq(__x);
}

__attribute__((device)) __attribute__((const)) _Float16 __ocml_ceil_f16(_Float16);
__attribute__((device)) _Float16 __ocml_cos_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_exp_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_exp10_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_exp2_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_floor_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_fma_f16(_Float16, _Float16,
                                                          _Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_fabs_f16(_Float16);
__attribute__((device)) __attribute__((const)) int __ocml_isinf_f16(_Float16);
__attribute__((device)) __attribute__((const)) int __ocml_isnan_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_log_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_log10_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_log2_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __llvm_amdgcn_rcp_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_rint_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_rsqrt_f16(_Float16);
__attribute__((device)) _Float16 __ocml_sin_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_sqrt_f16(_Float16);
__attribute__((device)) __attribute__((const)) _Float16 __ocml_trunc_f16(_Float16);
__attribute__((device)) __attribute__((pure)) _Float16 __ocml_pown_f16(_Float16, int);

typedef _Float16 __2f16 __attribute__((ext_vector_type(2)));
typedef short __2i16 __attribute__((ext_vector_type(2)));

__attribute__((device)) __attribute__((const)) float __ockl_fdot2(__2f16 a, __2f16 b,
                                                     float c, bool s);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_ceil_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_fabs_2f16(__2f16);
__attribute__((device)) __2f16 __ocml_cos_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_exp_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_exp10_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_exp2_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_floor_2f16(__2f16);
__attribute__((device)) __attribute__((const))
__2f16 __ocml_fma_2f16(__2f16, __2f16, __2f16);
__attribute__((device)) __attribute__((const)) __2i16 __ocml_isinf_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2i16 __ocml_isnan_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_log_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_log10_2f16(__2f16);
__attribute__((device)) __attribute__((pure)) __2f16 __ocml_log2_2f16(__2f16);
__attribute__((device)) inline __2f16
__llvm_amdgcn_rcp_2f16(__2f16 __x)
{
  return (__2f16)(__llvm_amdgcn_rcp_f16(__x.x), __llvm_amdgcn_rcp_f16(__x.y));
}
__attribute__((device)) __attribute__((const)) __2f16 __ocml_rint_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_rsqrt_2f16(__2f16);
__attribute__((device)) __2f16 __ocml_sin_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_sqrt_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_trunc_2f16(__2f16);
__attribute__((device)) __attribute__((const)) __2f16 __ocml_pown_2f16(__2f16, __2i16);


}
# 115 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 1 3
# 18 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/algorithm" 1 3
# 55 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/algorithm" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/algorithm" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/algorithm" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 1 3
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functexcept.h" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functexcept.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_defines.h" 1 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functexcept.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{



  void
  __throw_bad_exception(void) __attribute__((__noreturn__));


  void
  __throw_bad_alloc(void) __attribute__((__noreturn__));

  void
  __throw_bad_array_new_length(void) __attribute__((__noreturn__));


  void
  __throw_bad_cast(void) __attribute__((__noreturn__));

  void
  __throw_bad_typeid(void) __attribute__((__noreturn__));


  void
  __throw_logic_error(const char*) __attribute__((__noreturn__));

  void
  __throw_domain_error(const char*) __attribute__((__noreturn__));

  void
  __throw_invalid_argument(const char*) __attribute__((__noreturn__));

  void
  __throw_length_error(const char*) __attribute__((__noreturn__));

  void
  __throw_out_of_range(const char*) __attribute__((__noreturn__));

  void
  __throw_out_of_range_fmt(const char*, ...) __attribute__((__noreturn__))
    __attribute__((__format__(__gnu_printf__, 1, 2)));

  void
  __throw_runtime_error(const char*) __attribute__((__noreturn__));

  void
  __throw_range_error(const char*) __attribute__((__noreturn__));

  void
  __throw_overflow_error(const char*) __attribute__((__noreturn__));

  void
  __throw_underflow_error(const char*) __attribute__((__noreturn__));


  void
  __throw_ios_failure(const char*) __attribute__((__noreturn__));

  void
  __throw_ios_failure(const char*, int) __attribute__((__noreturn__));


  void
  __throw_system_error(int) __attribute__((__noreturn__));


  void
  __throw_future_error(int) __attribute__((__noreturn__));


  void
  __throw_bad_function_call() __attribute__((__noreturn__));


}
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 3




namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{
# 50 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 3
  template<typename _Tp>
    struct __is_integer_nonstrict
    : public std::__is_integer<_Tp>
    {
      using std::__is_integer<_Tp>::__value;


      enum { __width = __value ? sizeof(_Tp) * 8 : 0 };
    };

  template<typename _Value>
    struct __numeric_traits_integer
    {

      static_assert(__is_integer_nonstrict<_Value>::__value,
      "invalid specialization");




      static const bool __is_signed = (_Value)(-1) < 0;
      static const int __digits
 = __is_integer_nonstrict<_Value>::__width - __is_signed;


      static const _Value __max = __is_signed
 ? (((((_Value)1 << (__digits - 1)) - 1) << 1) + 1)
 : ~(_Value)0;
      static const _Value __min = __is_signed ? -__max - 1 : (_Value)0;
    };

  template<typename _Value>
    const _Value __numeric_traits_integer<_Value>::__min;

  template<typename _Value>
    const _Value __numeric_traits_integer<_Value>::__max;

  template<typename _Value>
    const bool __numeric_traits_integer<_Value>::__is_signed;

  template<typename _Value>
    const int __numeric_traits_integer<_Value>::__digits;
# 130 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 3
  __extension__ template<> struct __is_integer_nonstrict<__int128> { enum { __value = 1 }; typedef std::__true_type __type; enum { __width = 128 }; }; __extension__ template<> struct __is_integer_nonstrict<unsigned __int128> { enum { __value = 1 }; typedef std::__true_type __type; enum { __width = 128 }; };






  template<typename _Tp>
    using __int_traits = __numeric_traits_integer<_Tp>;
# 157 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 3
  template<typename _Value>
    struct __numeric_traits_floating
    {

      static const int __max_digits10 = (2 + (std::__are_same<_Value, float>::__value ? 24 : std::__are_same<_Value, double>::__value ? 53 : 64) * 643L / 2136);


      static const bool __is_signed = true;
      static const int __digits10 = (std::__are_same<_Value, float>::__value ? 6 : std::__are_same<_Value, double>::__value ? 15 : 18);
      static const int __max_exponent10 = (std::__are_same<_Value, float>::__value ? 38 : std::__are_same<_Value, double>::__value ? 308 : 4932);
    };

  template<typename _Value>
    const int __numeric_traits_floating<_Value>::__max_digits10;

  template<typename _Value>
    const bool __numeric_traits_floating<_Value>::__is_signed;

  template<typename _Value>
    const int __numeric_traits_floating<_Value>::__digits10;

  template<typename _Value>
    const int __numeric_traits_floating<_Value>::__max_exponent10;






  template<typename _Value>
    struct __numeric_traits
    : public __numeric_traits_integer<_Value>
    { };

  template<>
    struct __numeric_traits<float>
    : public __numeric_traits_floating<float>
    { };

  template<>
    struct __numeric_traits<double>
    : public __numeric_traits_floating<double>
    { };

  template<>
    struct __numeric_traits<long double>
    : public __numeric_traits_floating<long double>
    { };
# 239 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/numeric_traits.h" 3
}
# 64 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 1 3
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3







namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _Tp>
    class reference_wrapper;
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp, _Tp __v>
    struct integral_constant
    {
      static constexpr _Tp value = __v;
      typedef _Tp value_type;
      typedef integral_constant<_Tp, __v> type;
      constexpr operator value_type() const noexcept { return value; }






    };


  template<typename _Tp, _Tp __v>
    constexpr _Tp integral_constant<_Tp, __v>::value;



  using true_type = integral_constant<bool, true>;


  using false_type = integral_constant<bool, false>;



  template<bool __v>
    using __bool_constant = integral_constant<bool, __v>;
# 103 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<bool>
    struct __conditional
    {
      template<typename _Tp, typename>
 using type = _Tp;
    };

  template<>
    struct __conditional<false>
    {
      template<typename, typename _Up>
 using type = _Up;
    };


  template<bool _Cond, typename _If, typename _Else>
    using __conditional_t
      = typename __conditional<_Cond>::template type<_If, _Else>;


  template <typename _Type>
    struct __type_identity
    { using type = _Type; };

  template<typename _Tp>
    using __type_identity_t = typename __type_identity<_Tp>::type;

  template<typename...>
    struct __or_;

  template<>
    struct __or_<>
    : public false_type
    { };

  template<typename _B1>
    struct __or_<_B1>
    : public _B1
    { };

  template<typename _B1, typename _B2>
    struct __or_<_B1, _B2>
    : public __conditional_t<_B1::value, _B1, _B2>
    { };

  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
    struct __or_<_B1, _B2, _B3, _Bn...>
    : public __conditional_t<_B1::value, _B1, __or_<_B2, _B3, _Bn...>>
    { };

  template<typename...>
    struct __and_;

  template<>
    struct __and_<>
    : public true_type
    { };

  template<typename _B1>
    struct __and_<_B1>
    : public _B1
    { };

  template<typename _B1, typename _B2>
    struct __and_<_B1, _B2>
    : public __conditional_t<_B1::value, _B2, _B1>
    { };

  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
    struct __and_<_B1, _B2, _B3, _Bn...>
    : public __conditional_t<_B1::value, __and_<_B2, _B3, _Bn...>, _B1>
    { };

  template<typename _Pp>
    struct __not_
    : public __bool_constant<!bool(_Pp::value)>
    { };
# 224 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename>
    struct is_reference;
  template<typename>
    struct is_function;
  template<typename>
    struct is_void;
  template<typename>
    struct remove_cv;
  template<typename>
    struct is_const;


  template<typename>
    struct __is_array_unknown_bounds;




  template <typename _Tp, size_t = sizeof(_Tp)>
    constexpr true_type __is_complete_or_unbounded(__type_identity<_Tp>)
    { return {}; }

  template <typename _TypeIdentity,
      typename _NestedType = typename _TypeIdentity::type>
    constexpr typename __or_<
      is_reference<_NestedType>,
      is_function<_NestedType>,
      is_void<_NestedType>,
      __is_array_unknown_bounds<_NestedType>
    >::type __is_complete_or_unbounded(_TypeIdentity)
    { return {}; }






  template<typename _Tp>
    struct __success_type
    { typedef _Tp type; };

  struct __failure_type
  { };


  template<typename _Tp>
    using __remove_cv_t = typename remove_cv<_Tp>::type;



  template<typename>
    struct __is_void_helper
    : public false_type { };

  template<>
    struct __is_void_helper<void>
    : public true_type { };



  template<typename _Tp>
    struct is_void
    : public __is_void_helper<__remove_cv_t<_Tp>>::type
    { };


  template<typename>
    struct __is_integral_helper
    : public false_type { };

  template<>
    struct __is_integral_helper<bool>
    : public true_type { };

  template<>
    struct __is_integral_helper<char>
    : public true_type { };

  template<>
    struct __is_integral_helper<signed char>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned char>
    : public true_type { };




  template<>
    struct __is_integral_helper<wchar_t>
    : public true_type { };







  template<>
    struct __is_integral_helper<char16_t>
    : public true_type { };

  template<>
    struct __is_integral_helper<char32_t>
    : public true_type { };

  template<>
    struct __is_integral_helper<short>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned short>
    : public true_type { };

  template<>
    struct __is_integral_helper<int>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned int>
    : public true_type { };

  template<>
    struct __is_integral_helper<long>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned long>
    : public true_type { };

  template<>
    struct __is_integral_helper<long long>
    : public true_type { };

  template<>
    struct __is_integral_helper<unsigned long long>
    : public true_type { };
# 412 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct is_integral
    : public __is_integral_helper<__remove_cv_t<_Tp>>::type
    { };


  template<typename>
    struct __is_floating_point_helper
    : public false_type { };

  template<>
    struct __is_floating_point_helper<float>
    : public true_type { };

  template<>
    struct __is_floating_point_helper<double>
    : public true_type { };

  template<>
    struct __is_floating_point_helper<long double>
    : public true_type { };
# 442 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct is_floating_point
    : public __is_floating_point_helper<__remove_cv_t<_Tp>>::type
    { };


  template<typename>
    struct is_array
    : public false_type { };

  template<typename _Tp, std::size_t _Size>
    struct is_array<_Tp[_Size]>
    : public true_type { };

  template<typename _Tp>
    struct is_array<_Tp[]>
    : public true_type { };

  template<typename>
    struct __is_pointer_helper
    : public false_type { };

  template<typename _Tp>
    struct __is_pointer_helper<_Tp*>
    : public true_type { };


  template<typename _Tp>
    struct is_pointer
    : public __is_pointer_helper<__remove_cv_t<_Tp>>::type
    { };


  template<typename>
    struct is_lvalue_reference
    : public false_type { };

  template<typename _Tp>
    struct is_lvalue_reference<_Tp&>
    : public true_type { };


  template<typename>
    struct is_rvalue_reference
    : public false_type { };

  template<typename _Tp>
    struct is_rvalue_reference<_Tp&&>
    : public true_type { };

  template<typename>
    struct __is_member_object_pointer_helper
    : public false_type { };

  template<typename _Tp, typename _Cp>
    struct __is_member_object_pointer_helper<_Tp _Cp::*>
    : public __not_<is_function<_Tp>>::type { };


  template<typename _Tp>
    struct is_member_object_pointer
    : public __is_member_object_pointer_helper<__remove_cv_t<_Tp>>::type
    { };

  template<typename>
    struct __is_member_function_pointer_helper
    : public false_type { };

  template<typename _Tp, typename _Cp>
    struct __is_member_function_pointer_helper<_Tp _Cp::*>
    : public is_function<_Tp>::type { };


  template<typename _Tp>
    struct is_member_function_pointer
    : public __is_member_function_pointer_helper<__remove_cv_t<_Tp>>::type
    { };


  template<typename _Tp>
    struct is_enum
    : public integral_constant<bool, __is_enum(_Tp)>
    { };


  template<typename _Tp>
    struct is_union
    : public integral_constant<bool, __is_union(_Tp)>
    { };


  template<typename _Tp>
    struct is_class
    : public integral_constant<bool, __is_class(_Tp)>
    { };


  template<typename _Tp>
    struct is_function
    : public __bool_constant<!is_const<const _Tp>::value> { };

  template<typename _Tp>
    struct is_function<_Tp&>
    : public false_type { };

  template<typename _Tp>
    struct is_function<_Tp&&>
    : public false_type { };



  template<typename>
    struct __is_null_pointer_helper
    : public false_type { };

  template<>
    struct __is_null_pointer_helper<std::nullptr_t>
    : public true_type { };


  template<typename _Tp>
    struct is_null_pointer
    : public __is_null_pointer_helper<__remove_cv_t<_Tp>>::type
    { };



  template<typename _Tp>
    struct __is_nullptr_t
    : public is_null_pointer<_Tp>
    { } __attribute__ ((__deprecated__ ("use '" "std::is_null_pointer" "' instead")));




  template<typename _Tp>
    struct is_reference
    : public __or_<is_lvalue_reference<_Tp>,
                   is_rvalue_reference<_Tp>>::type
    { };


  template<typename _Tp>
    struct is_arithmetic
    : public __or_<is_integral<_Tp>, is_floating_point<_Tp>>::type
    { };


  template<typename _Tp>
    struct is_fundamental
    : public __or_<is_arithmetic<_Tp>, is_void<_Tp>,
     is_null_pointer<_Tp>>::type
    { };


  template<typename _Tp>
    struct is_object
    : public __not_<__or_<is_function<_Tp>, is_reference<_Tp>,
                          is_void<_Tp>>>::type
    { };

  template<typename>
    struct is_member_pointer;


  template<typename _Tp>
    struct is_scalar
    : public __or_<is_arithmetic<_Tp>, is_enum<_Tp>, is_pointer<_Tp>,
                   is_member_pointer<_Tp>, is_null_pointer<_Tp>>::type
    { };


  template<typename _Tp>
    struct is_compound
    : public __not_<is_fundamental<_Tp>>::type { };


  template<typename _Tp>
    struct __is_member_pointer_helper
    : public false_type { };

  template<typename _Tp, typename _Cp>
    struct __is_member_pointer_helper<_Tp _Cp::*>
    : public true_type { };



  template<typename _Tp>
    struct is_member_pointer
    : public __is_member_pointer_helper<__remove_cv_t<_Tp>>::type
    { };

  template<typename, typename>
    struct is_same;


  template<typename _Tp, typename... _Types>
    using __is_one_of = __or_<is_same<_Tp, _Types>...>;


  __extension__
  template<typename _Tp>
    using __is_signed_integer = __is_one_of<__remove_cv_t<_Tp>,
   signed char, signed short, signed int, signed long,
   signed long long
# 659 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
   >;


  __extension__
  template<typename _Tp>
    using __is_unsigned_integer = __is_one_of<__remove_cv_t<_Tp>,
   unsigned char, unsigned short, unsigned int, unsigned long,
   unsigned long long
# 679 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
   >;


  template<typename _Tp>
    using __is_standard_integer
      = __or_<__is_signed_integer<_Tp>, __is_unsigned_integer<_Tp>>;


  template<typename...> using __void_t = void;



  template<typename _Tp, typename = void>
    struct __is_referenceable
    : public false_type
    { };

  template<typename _Tp>
    struct __is_referenceable<_Tp, __void_t<_Tp&>>
    : public true_type
    { };





  template<typename>
    struct is_const
    : public false_type { };

  template<typename _Tp>
    struct is_const<_Tp const>
    : public true_type { };


  template<typename>
    struct is_volatile
    : public false_type { };

  template<typename _Tp>
    struct is_volatile<_Tp volatile>
    : public true_type { };


  template<typename _Tp>
    struct is_trivial
    : public integral_constant<bool, __is_trivial(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_trivially_copyable
    : public integral_constant<bool, __is_trivially_copyable(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_standard_layout
    : public integral_constant<bool, __is_standard_layout(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };






  template<typename _Tp>
    struct

    is_pod
    : public integral_constant<bool, __is_pod(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };





  template<typename _Tp>
    struct

    is_literal_type
    : public integral_constant<bool, __is_literal_type(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_empty
    : public integral_constant<bool, __is_empty(_Tp)>
    { };


  template<typename _Tp>
    struct is_polymorphic
    : public integral_constant<bool, __is_polymorphic(_Tp)>
    { };
# 801 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct is_abstract
    : public integral_constant<bool, __is_abstract(_Tp)>
    { };


  template<typename _Tp,
    bool = is_arithmetic<_Tp>::value>
    struct __is_signed_helper
    : public false_type { };

  template<typename _Tp>
    struct __is_signed_helper<_Tp, true>
    : public integral_constant<bool, _Tp(-1) < _Tp(0)>
    { };



  template<typename _Tp>
    struct is_signed
    : public __is_signed_helper<_Tp>::type
    { };


  template<typename _Tp>
    struct is_unsigned
    : public __and_<is_arithmetic<_Tp>, __not_<is_signed<_Tp>>>
    { };


  template<typename _Tp, typename _Up = _Tp&&>
    _Up
    __declval(int);

  template<typename _Tp>
    _Tp
    __declval(long);


  template<typename _Tp>
    auto declval() noexcept -> decltype(__declval<_Tp>(0));

  template<typename, unsigned = 0>
    struct extent;

  template<typename>
    struct remove_all_extents;


  template<typename _Tp>
    struct __is_array_known_bounds
    : public integral_constant<bool, (extent<_Tp>::value > 0)>
    { };

  template<typename _Tp>
    struct __is_array_unknown_bounds
    : public __and_<is_array<_Tp>, __not_<extent<_Tp>>>
    { };
# 867 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  struct __do_is_destructible_impl
  {
    template<typename _Tp, typename = decltype(declval<_Tp&>().~_Tp())>
      static true_type __test(int);

    template<typename>
      static false_type __test(...);
  };

  template<typename _Tp>
    struct __is_destructible_impl
    : public __do_is_destructible_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };

  template<typename _Tp,
           bool = __or_<is_void<_Tp>,
                        __is_array_unknown_bounds<_Tp>,
                        is_function<_Tp>>::value,
           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
    struct __is_destructible_safe;

  template<typename _Tp>
    struct __is_destructible_safe<_Tp, false, false>
    : public __is_destructible_impl<typename
               remove_all_extents<_Tp>::type>::type
    { };

  template<typename _Tp>
    struct __is_destructible_safe<_Tp, true, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_destructible_safe<_Tp, false, true>
    : public true_type { };



  template<typename _Tp>
    struct is_destructible
    : public __is_destructible_safe<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };







  struct __do_is_nt_destructible_impl
  {
    template<typename _Tp>
      static __bool_constant<noexcept(declval<_Tp&>().~_Tp())>
      __test(int);

    template<typename>
      static false_type __test(...);
  };

  template<typename _Tp>
    struct __is_nt_destructible_impl
    : public __do_is_nt_destructible_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };

  template<typename _Tp,
           bool = __or_<is_void<_Tp>,
                        __is_array_unknown_bounds<_Tp>,
                        is_function<_Tp>>::value,
           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
    struct __is_nt_destructible_safe;

  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, false, false>
    : public __is_nt_destructible_impl<typename
               remove_all_extents<_Tp>::type>::type
    { };

  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, true, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nt_destructible_safe<_Tp, false, true>
    : public true_type { };



  template<typename _Tp>
    struct is_nothrow_destructible
    : public __is_nt_destructible_safe<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, typename... _Args>
    struct __is_constructible_impl
    : public __bool_constant<__is_constructible(_Tp, _Args...)>
    { };



  template<typename _Tp, typename... _Args>
    struct is_constructible
      : public __is_constructible_impl<_Tp, _Args...>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_default_constructible
    : public __is_constructible_impl<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_copy_constructible_impl;

  template<typename _Tp>
    struct __is_copy_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_copy_constructible_impl<_Tp, true>
    : public __is_constructible_impl<_Tp, const _Tp&>
    { };



  template<typename _Tp>
    struct is_copy_constructible
    : public __is_copy_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_move_constructible_impl;

  template<typename _Tp>
    struct __is_move_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_move_constructible_impl<_Tp, true>
    : public __is_constructible_impl<_Tp, _Tp&&>
    { };



  template<typename _Tp>
    struct is_move_constructible
    : public __is_move_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, typename... _Args>
    using __is_nothrow_constructible_impl
      = __bool_constant<__is_nothrow_constructible(_Tp, _Args...)>;



  template<typename _Tp, typename... _Args>
    struct is_nothrow_constructible
    : public __is_nothrow_constructible_impl<_Tp, _Args...>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_nothrow_default_constructible
    : public __bool_constant<__is_nothrow_constructible(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nothrow_copy_constructible_impl;

  template<typename _Tp>
    struct __is_nothrow_copy_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nothrow_copy_constructible_impl<_Tp, true>
    : public __is_nothrow_constructible_impl<_Tp, const _Tp&>
    { };



  template<typename _Tp>
    struct is_nothrow_copy_constructible
    : public __is_nothrow_copy_constructible_impl<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nothrow_move_constructible_impl;

  template<typename _Tp>
    struct __is_nothrow_move_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nothrow_move_constructible_impl<_Tp, true>
    : public __is_nothrow_constructible_impl<_Tp, _Tp&&>
    { };



  template<typename _Tp>
    struct is_nothrow_move_constructible
    : public __is_nothrow_move_constructible_impl<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, typename _Up>
    struct is_assignable
    : public __bool_constant<__is_assignable(_Tp, _Up)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_copy_assignable_impl;

  template<typename _Tp>
    struct __is_copy_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_copy_assignable_impl<_Tp, true>
    : public __bool_constant<__is_assignable(_Tp&, const _Tp&)>
    { };


  template<typename _Tp>
    struct is_copy_assignable
    : public __is_copy_assignable_impl<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_move_assignable_impl;

  template<typename _Tp>
    struct __is_move_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_move_assignable_impl<_Tp, true>
    : public __bool_constant<__is_assignable(_Tp&, _Tp&&)>
    { };


  template<typename _Tp>
    struct is_move_assignable
    : public __is_move_assignable_impl<_Tp>::type
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, typename _Up>
    using __is_nothrow_assignable_impl
      = __bool_constant<__is_nothrow_assignable(_Tp, _Up)>;


  template<typename _Tp, typename _Up>
    struct is_nothrow_assignable
    : public __is_nothrow_assignable_impl<_Tp, _Up>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nt_copy_assignable_impl;

  template<typename _Tp>
    struct __is_nt_copy_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nt_copy_assignable_impl<_Tp, true>
    : public __is_nothrow_assignable_impl<_Tp&, const _Tp&>
    { };


  template<typename _Tp>
    struct is_nothrow_copy_assignable
    : public __is_nt_copy_assignable_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_nt_move_assignable_impl;

  template<typename _Tp>
    struct __is_nt_move_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_nt_move_assignable_impl<_Tp, true>
    : public __is_nothrow_assignable_impl<_Tp&, _Tp&&>
    { };


  template<typename _Tp>
    struct is_nothrow_move_assignable
    : public __is_nt_move_assignable_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, typename... _Args>
    struct is_trivially_constructible
    : public __bool_constant<__is_trivially_constructible(_Tp, _Args...)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_trivially_default_constructible
    : public __bool_constant<__is_trivially_constructible(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  struct __do_is_implicitly_default_constructible_impl
  {
    template <typename _Tp>
    static void __helper(const _Tp&);

    template <typename _Tp>
    static true_type __test(const _Tp&,
                            decltype(__helper<const _Tp&>({}))* = 0);

    static false_type __test(...);
  };

  template<typename _Tp>
    struct __is_implicitly_default_constructible_impl
    : public __do_is_implicitly_default_constructible_impl
    {
      typedef decltype(__test(declval<_Tp>())) type;
    };

  template<typename _Tp>
    struct __is_implicitly_default_constructible_safe
    : public __is_implicitly_default_constructible_impl<_Tp>::type
    { };

  template <typename _Tp>
    struct __is_implicitly_default_constructible
    : public __and_<__is_constructible_impl<_Tp>,
      __is_implicitly_default_constructible_safe<_Tp>>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_trivially_copy_constructible_impl;

  template<typename _Tp>
    struct __is_trivially_copy_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_trivially_copy_constructible_impl<_Tp, true>
    : public __and_<__is_copy_constructible_impl<_Tp>,
      integral_constant<bool,
   __is_trivially_constructible(_Tp, const _Tp&)>>
    { };


  template<typename _Tp>
    struct is_trivially_copy_constructible
    : public __is_trivially_copy_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_trivially_move_constructible_impl;

  template<typename _Tp>
    struct __is_trivially_move_constructible_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_trivially_move_constructible_impl<_Tp, true>
    : public __and_<__is_move_constructible_impl<_Tp>,
      integral_constant<bool,
   __is_trivially_constructible(_Tp, _Tp&&)>>
    { };


  template<typename _Tp>
    struct is_trivially_move_constructible
    : public __is_trivially_move_constructible_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp, typename _Up>
    struct is_trivially_assignable
    : public __bool_constant<__is_trivially_assignable(_Tp, _Up)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_trivially_copy_assignable_impl;

  template<typename _Tp>
    struct __is_trivially_copy_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_trivially_copy_assignable_impl<_Tp, true>
    : public __bool_constant<__is_trivially_assignable(_Tp&, const _Tp&)>
    { };


  template<typename _Tp>
    struct is_trivially_copy_assignable
    : public __is_trivially_copy_assignable_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __is_trivially_move_assignable_impl;

  template<typename _Tp>
    struct __is_trivially_move_assignable_impl<_Tp, false>
    : public false_type { };

  template<typename _Tp>
    struct __is_trivially_move_assignable_impl<_Tp, true>
    : public __bool_constant<__is_trivially_assignable(_Tp&, _Tp&&)>
    { };


  template<typename _Tp>
    struct is_trivially_move_assignable
    : public __is_trivially_move_assignable_impl<_Tp>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename _Tp>
    struct is_trivially_destructible
    : public __and_<__is_destructible_safe<_Tp>,
      __bool_constant<__has_trivial_destructor(_Tp)>>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };



  template<typename _Tp>
    struct has_virtual_destructor
    : public integral_constant<bool, __has_virtual_destructor(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };





  template<typename _Tp>
    struct alignment_of
    : public integral_constant<std::size_t, alignof(_Tp)>
    {
      static_assert(std::__is_complete_or_unbounded(__type_identity<_Tp>{}),
 "template argument must be a complete class or an unbounded array");
    };


  template<typename>
    struct rank
    : public integral_constant<std::size_t, 0> { };

  template<typename _Tp, std::size_t _Size>
    struct rank<_Tp[_Size]>
    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };

  template<typename _Tp>
    struct rank<_Tp[]>
    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };


  template<typename, unsigned _Uint>
    struct extent
    : public integral_constant<std::size_t, 0> { };

  template<typename _Tp, unsigned _Uint, std::size_t _Size>
    struct extent<_Tp[_Size], _Uint>
    : public integral_constant<std::size_t,
          _Uint == 0 ? _Size : extent<_Tp,
          _Uint - 1>::value>
    { };

  template<typename _Tp, unsigned _Uint>
    struct extent<_Tp[], _Uint>
    : public integral_constant<std::size_t,
          _Uint == 0 ? 0 : extent<_Tp,
             _Uint - 1>::value>
    { };





  template<typename _Tp, typename _Up>
    struct is_same

    : public integral_constant<bool, __is_same(_Tp, _Up)>



    { };
# 1445 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Base, typename _Derived>
    struct is_base_of
    : public integral_constant<bool, __is_base_of(_Base, _Derived)>
    { };

  template<typename _From, typename _To,
           bool = __or_<is_void<_From>, is_function<_To>,
                        is_array<_To>>::value>
    struct __is_convertible_helper
    {
      typedef typename is_void<_To>::type type;
    };

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
  template<typename _From, typename _To>
    class __is_convertible_helper<_From, _To, false>
    {
      template<typename _To1>
 static void __test_aux(_To1) noexcept;

      template<typename _From1, typename _To1,
        typename = decltype(__test_aux<_To1>(std::declval<_From1>()))>
 static true_type
 __test(int);

      template<typename, typename>
 static false_type
 __test(...);

    public:
      typedef decltype(__test<_From, _To>(0)) type;
    };
#pragma GCC diagnostic pop


  template<typename _From, typename _To>
    struct is_convertible
    : public __is_convertible_helper<_From, _To>::type
    { };


  template<typename _ToElementType, typename _FromElementType>
    using __is_array_convertible
      = is_convertible<_FromElementType(*)[], _ToElementType(*)[]>;

  template<typename _From, typename _To,
           bool = __or_<is_void<_From>, is_function<_To>,
                        is_array<_To>>::value>
    struct __is_nt_convertible_helper
    : is_void<_To>
    { };

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
  template<typename _From, typename _To>
    class __is_nt_convertible_helper<_From, _To, false>
    {
      template<typename _To1>
 static void __test_aux(_To1) noexcept;

      template<typename _From1, typename _To1>
 static
 __bool_constant<noexcept(__test_aux<_To1>(std::declval<_From1>()))>
 __test(int);

      template<typename, typename>
 static false_type
 __test(...);

    public:
      using type = decltype(__test<_From, _To>(0));
    };
#pragma GCC diagnostic pop


  template<typename _From, typename _To>
    struct __is_nothrow_convertible
    : public __is_nt_convertible_helper<_From, _To>::type
    { };
# 1543 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct remove_const
    { typedef _Tp type; };

  template<typename _Tp>
    struct remove_const<_Tp const>
    { typedef _Tp type; };


  template<typename _Tp>
    struct remove_volatile
    { typedef _Tp type; };

  template<typename _Tp>
    struct remove_volatile<_Tp volatile>
    { typedef _Tp type; };


  template<typename _Tp>
    struct remove_cv
    { using type = _Tp; };

  template<typename _Tp>
    struct remove_cv<const _Tp>
    { using type = _Tp; };

  template<typename _Tp>
    struct remove_cv<volatile _Tp>
    { using type = _Tp; };

  template<typename _Tp>
    struct remove_cv<const volatile _Tp>
    { using type = _Tp; };


  template<typename _Tp>
    struct add_const
    { typedef _Tp const type; };


  template<typename _Tp>
    struct add_volatile
    { typedef _Tp volatile type; };


  template<typename _Tp>
    struct add_cv
    {
      typedef typename
      add_const<typename add_volatile<_Tp>::type>::type type;
    };
# 1627 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct remove_reference
    { typedef _Tp type; };

  template<typename _Tp>
    struct remove_reference<_Tp&>
    { typedef _Tp type; };

  template<typename _Tp>
    struct remove_reference<_Tp&&>
    { typedef _Tp type; };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __add_lvalue_reference_helper
    { typedef _Tp type; };

  template<typename _Tp>
    struct __add_lvalue_reference_helper<_Tp, true>
    { typedef _Tp& type; };


  template<typename _Tp>
    struct add_lvalue_reference
    : public __add_lvalue_reference_helper<_Tp>
    { };

  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
    struct __add_rvalue_reference_helper
    { typedef _Tp type; };

  template<typename _Tp>
    struct __add_rvalue_reference_helper<_Tp, true>
    { typedef _Tp&& type; };


  template<typename _Tp>
    struct add_rvalue_reference
    : public __add_rvalue_reference_helper<_Tp>
    { };
# 1686 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Unqualified, bool _IsConst, bool _IsVol>
    struct __cv_selector;

  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, false, false>
    { typedef _Unqualified __type; };

  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, false, true>
    { typedef volatile _Unqualified __type; };

  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, true, false>
    { typedef const _Unqualified __type; };

  template<typename _Unqualified>
    struct __cv_selector<_Unqualified, true, true>
    { typedef const volatile _Unqualified __type; };

  template<typename _Qualified, typename _Unqualified,
    bool _IsConst = is_const<_Qualified>::value,
    bool _IsVol = is_volatile<_Qualified>::value>
    class __match_cv_qualifiers
    {
      typedef __cv_selector<_Unqualified, _IsConst, _IsVol> __match;

    public:
      typedef typename __match::__type __type;
    };


  template<typename _Tp>
    struct __make_unsigned
    { typedef _Tp __type; };

  template<>
    struct __make_unsigned<char>
    { typedef unsigned char __type; };

  template<>
    struct __make_unsigned<signed char>
    { typedef unsigned char __type; };

  template<>
    struct __make_unsigned<short>
    { typedef unsigned short __type; };

  template<>
    struct __make_unsigned<int>
    { typedef unsigned int __type; };

  template<>
    struct __make_unsigned<long>
    { typedef unsigned long __type; };

  template<>
    struct __make_unsigned<long long>
    { typedef unsigned long long __type; };
# 1771 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp,
    bool _IsInt = is_integral<_Tp>::value,
    bool _IsEnum = is_enum<_Tp>::value>
    class __make_unsigned_selector;

  template<typename _Tp>
    class __make_unsigned_selector<_Tp, true, false>
    {
      using __unsigned_type
 = typename __make_unsigned<__remove_cv_t<_Tp>>::__type;

    public:
      using __type
 = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
    };

  class __make_unsigned_selector_base
  {
  protected:
    template<typename...> struct _List { };

    template<typename _Tp, typename... _Up>
      struct _List<_Tp, _Up...> : _List<_Up...>
      { static constexpr size_t __size = sizeof(_Tp); };

    template<size_t _Sz, typename _Tp, bool = (_Sz <= _Tp::__size)>
      struct __select;

    template<size_t _Sz, typename _Uint, typename... _UInts>
      struct __select<_Sz, _List<_Uint, _UInts...>, true>
      { using __type = _Uint; };

    template<size_t _Sz, typename _Uint, typename... _UInts>
      struct __select<_Sz, _List<_Uint, _UInts...>, false>
      : __select<_Sz, _List<_UInts...>>
      { };
  };


  template<typename _Tp>
    class __make_unsigned_selector<_Tp, false, true>
    : __make_unsigned_selector_base
    {

      using _UInts = _List<unsigned char, unsigned short, unsigned int,
      unsigned long, unsigned long long>;

      using __unsigned_type = typename __select<sizeof(_Tp), _UInts>::__type;

    public:
      using __type
 = typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
    };





  template<>
    struct __make_unsigned<wchar_t>
    {
      using __type
 = typename __make_unsigned_selector<wchar_t, false, true>::__type;
    };
# 1845 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<>
    struct __make_unsigned<char16_t>
    {
      using __type
 = typename __make_unsigned_selector<char16_t, false, true>::__type;
    };

  template<>
    struct __make_unsigned<char32_t>
    {
      using __type
 = typename __make_unsigned_selector<char32_t, false, true>::__type;
    };






  template<typename _Tp>
    struct make_unsigned
    { typedef typename __make_unsigned_selector<_Tp>::__type type; };


  template<>
    struct make_unsigned<bool>;




  template<typename _Tp>
    struct __make_signed
    { typedef _Tp __type; };

  template<>
    struct __make_signed<char>
    { typedef signed char __type; };

  template<>
    struct __make_signed<unsigned char>
    { typedef signed char __type; };

  template<>
    struct __make_signed<unsigned short>
    { typedef signed short __type; };

  template<>
    struct __make_signed<unsigned int>
    { typedef signed int __type; };

  template<>
    struct __make_signed<unsigned long>
    { typedef signed long __type; };

  template<>
    struct __make_signed<unsigned long long>
    { typedef signed long long __type; };
# 1929 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp,
    bool _IsInt = is_integral<_Tp>::value,
    bool _IsEnum = is_enum<_Tp>::value>
    class __make_signed_selector;

  template<typename _Tp>
    class __make_signed_selector<_Tp, true, false>
    {
      using __signed_type
 = typename __make_signed<__remove_cv_t<_Tp>>::__type;

    public:
      using __type
 = typename __match_cv_qualifiers<_Tp, __signed_type>::__type;
    };


  template<typename _Tp>
    class __make_signed_selector<_Tp, false, true>
    {
      typedef typename __make_unsigned_selector<_Tp>::__type __unsigned_type;

    public:
      typedef typename __make_signed_selector<__unsigned_type>::__type __type;
    };





  template<>
    struct __make_signed<wchar_t>
    {
      using __type
 = typename __make_signed_selector<wchar_t, false, true>::__type;
    };
# 1975 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<>
    struct __make_signed<char16_t>
    {
      using __type
 = typename __make_signed_selector<char16_t, false, true>::__type;
    };

  template<>
    struct __make_signed<char32_t>
    {
      using __type
 = typename __make_signed_selector<char32_t, false, true>::__type;
    };






  template<typename _Tp>
    struct make_signed
    { typedef typename __make_signed_selector<_Tp>::__type type; };


  template<>
    struct make_signed<bool>;
# 2015 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp>
    struct remove_extent
    { typedef _Tp type; };

  template<typename _Tp, std::size_t _Size>
    struct remove_extent<_Tp[_Size]>
    { typedef _Tp type; };

  template<typename _Tp>
    struct remove_extent<_Tp[]>
    { typedef _Tp type; };


  template<typename _Tp>
    struct remove_all_extents
    { typedef _Tp type; };

  template<typename _Tp, std::size_t _Size>
    struct remove_all_extents<_Tp[_Size]>
    { typedef typename remove_all_extents<_Tp>::type type; };

  template<typename _Tp>
    struct remove_all_extents<_Tp[]>
    { typedef typename remove_all_extents<_Tp>::type type; };
# 2052 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Tp, typename>
    struct __remove_pointer_helper
    { typedef _Tp type; };

  template<typename _Tp, typename _Up>
    struct __remove_pointer_helper<_Tp, _Up*>
    { typedef _Up type; };


  template<typename _Tp>
    struct remove_pointer
    : public __remove_pointer_helper<_Tp, __remove_cv_t<_Tp>>
    { };

  template<typename _Tp, bool = __or_<__is_referenceable<_Tp>,
          is_void<_Tp>>::value>
    struct __add_pointer_helper
    { typedef _Tp type; };

  template<typename _Tp>
    struct __add_pointer_helper<_Tp, true>
    { typedef typename remove_reference<_Tp>::type* type; };


  template<typename _Tp>
    struct add_pointer
    : public __add_pointer_helper<_Tp>
    { };
# 2091 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<std::size_t _Len>
    struct __aligned_storage_msa
    {
      union __type
      {
 unsigned char __data[_Len];
 struct __attribute__((__aligned__)) { } __align;
      };
    };
# 2111 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<std::size_t _Len, std::size_t _Align =
    __alignof__(typename __aligned_storage_msa<_Len>::__type)>
    struct aligned_storage
    {
      union type
      {
 unsigned char __data[_Len];
 struct __attribute__((__aligned__((_Align)))) { } __align;
      };
    };

  template <typename... _Types>
    struct __strictest_alignment
    {
      static const size_t _S_alignment = 0;
      static const size_t _S_size = 0;
    };

  template <typename _Tp, typename... _Types>
    struct __strictest_alignment<_Tp, _Types...>
    {
      static const size_t _S_alignment =
        alignof(_Tp) > __strictest_alignment<_Types...>::_S_alignment
 ? alignof(_Tp) : __strictest_alignment<_Types...>::_S_alignment;
      static const size_t _S_size =
        sizeof(_Tp) > __strictest_alignment<_Types...>::_S_size
 ? sizeof(_Tp) : __strictest_alignment<_Types...>::_S_size;
    };
# 2150 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template <size_t _Len, typename... _Types>
    struct aligned_union
    {
    private:
      static_assert(sizeof...(_Types) != 0, "At least one type is required");

      using __strictest = __strictest_alignment<_Types...>;
      static const size_t _S_len = _Len > __strictest::_S_size
 ? _Len : __strictest::_S_size;
    public:

      static const size_t alignment_value = __strictest::_S_alignment;

      typedef typename aligned_storage<_S_len, alignment_value>::type type;
    };

  template <size_t _Len, typename... _Types>
    const size_t aligned_union<_Len, _Types...>::alignment_value;





  template<typename _Up,
    bool _IsArray = is_array<_Up>::value,
    bool _IsFunction = is_function<_Up>::value>
    struct __decay_selector;


  template<typename _Up>
    struct __decay_selector<_Up, false, false>
    { typedef __remove_cv_t<_Up> __type; };

  template<typename _Up>
    struct __decay_selector<_Up, true, false>
    { typedef typename remove_extent<_Up>::type* __type; };

  template<typename _Up>
    struct __decay_selector<_Up, false, true>
    { typedef typename add_pointer<_Up>::type __type; };



  template<typename _Tp>
    class decay
    {
      typedef typename remove_reference<_Tp>::type __remove_type;

    public:
      typedef typename __decay_selector<__remove_type>::__type type;
    };




  template<typename _Tp>
    struct __strip_reference_wrapper
    {
      typedef _Tp __type;
    };

  template<typename _Tp>
    struct __strip_reference_wrapper<reference_wrapper<_Tp> >
    {
      typedef _Tp& __type;
    };


  template<typename _Tp>
    using __decay_t = typename decay<_Tp>::type;

  template<typename _Tp>
    using __decay_and_strip = __strip_reference_wrapper<__decay_t<_Tp>>;




  template<bool, typename _Tp = void>
    struct enable_if
    { };


  template<typename _Tp>
    struct enable_if<true, _Tp>
    { typedef _Tp type; };




  template<bool _Cond, typename _Tp = void>
    using __enable_if_t = typename enable_if<_Cond, _Tp>::type;


  template<typename... _Cond>
    using _Require = __enable_if_t<__and_<_Cond...>::value>;


  template<typename _Tp>
    using __remove_cvref_t
     = typename remove_cv<typename remove_reference<_Tp>::type>::type;




  template<bool _Cond, typename _Iftrue, typename _Iffalse>
    struct conditional
    { typedef _Iftrue type; };


  template<typename _Iftrue, typename _Iffalse>
    struct conditional<false, _Iftrue, _Iffalse>
    { typedef _Iffalse type; };


  template<typename... _Tp>
    struct common_type;




  struct __do_common_type_impl
  {
    template<typename _Tp, typename _Up>
      using __cond_t
 = decltype(true ? std::declval<_Tp>() : std::declval<_Up>());



    template<typename _Tp, typename _Up>
      static __success_type<__decay_t<__cond_t<_Tp, _Up>>>
      _S_test(int);
# 2290 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
    template<typename, typename>
      static __failure_type
      _S_test_2(...);

    template<typename _Tp, typename _Up>
      static decltype(_S_test_2<_Tp, _Up>(0))
      _S_test(...);
  };


  template<>
    struct common_type<>
    { };


  template<typename _Tp0>
    struct common_type<_Tp0>
    : public common_type<_Tp0, _Tp0>
    { };


  template<typename _Tp1, typename _Tp2,
    typename _Dp1 = __decay_t<_Tp1>, typename _Dp2 = __decay_t<_Tp2>>
    struct __common_type_impl
    {


      using type = common_type<_Dp1, _Dp2>;
    };

  template<typename _Tp1, typename _Tp2>
    struct __common_type_impl<_Tp1, _Tp2, _Tp1, _Tp2>
    : private __do_common_type_impl
    {


      using type = decltype(_S_test<_Tp1, _Tp2>(0));
    };


  template<typename _Tp1, typename _Tp2>
    struct common_type<_Tp1, _Tp2>
    : public __common_type_impl<_Tp1, _Tp2>::type
    { };

  template<typename...>
    struct __common_type_pack
    { };

  template<typename, typename, typename = void>
    struct __common_type_fold;


  template<typename _Tp1, typename _Tp2, typename... _Rp>
    struct common_type<_Tp1, _Tp2, _Rp...>
    : public __common_type_fold<common_type<_Tp1, _Tp2>,
    __common_type_pack<_Rp...>>
    { };




  template<typename _CTp, typename... _Rp>
    struct __common_type_fold<_CTp, __common_type_pack<_Rp...>,
         __void_t<typename _CTp::type>>
    : public common_type<typename _CTp::type, _Rp...>
    { };


  template<typename _CTp, typename _Rp>
    struct __common_type_fold<_CTp, _Rp, void>
    { };

  template<typename _Tp, bool = is_enum<_Tp>::value>
    struct __underlying_type_impl
    {
      using type = __underlying_type(_Tp);
    };

  template<typename _Tp>
    struct __underlying_type_impl<_Tp, false>
    { };



  template<typename _Tp>
    struct underlying_type
    : public __underlying_type_impl<_Tp>
    { };


  template<typename _Tp>
    struct __declval_protector
    {
      static const bool __stop = false;
    };






  template<typename _Tp>
    auto declval() noexcept -> decltype(__declval<_Tp>(0))
    {
      static_assert(__declval_protector<_Tp>::__stop,
      "declval() must not be used!");
      return __declval<_Tp>(0);
    }


  template<typename _Signature>
    struct result_of;






  struct __invoke_memfun_ref { };
  struct __invoke_memfun_deref { };
  struct __invoke_memobj_ref { };
  struct __invoke_memobj_deref { };
  struct __invoke_other { };


  template<typename _Tp, typename _Tag>
    struct __result_of_success : __success_type<_Tp>
    { using __invoke_type = _Tag; };


  struct __result_of_memfun_ref_impl
  {
    template<typename _Fp, typename _Tp1, typename... _Args>
      static __result_of_success<decltype(
      (std::declval<_Tp1>().*std::declval<_Fp>())(std::declval<_Args>()...)
      ), __invoke_memfun_ref> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun_ref
    : private __result_of_memfun_ref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
    };


  struct __result_of_memfun_deref_impl
  {
    template<typename _Fp, typename _Tp1, typename... _Args>
      static __result_of_success<decltype(
      ((*std::declval<_Tp1>()).*std::declval<_Fp>())(std::declval<_Args>()...)
      ), __invoke_memfun_deref> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun_deref
    : private __result_of_memfun_deref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
    };


  struct __result_of_memobj_ref_impl
  {
    template<typename _Fp, typename _Tp1>
      static __result_of_success<decltype(
      std::declval<_Tp1>().*std::declval<_Fp>()
      ), __invoke_memobj_ref> _S_test(int);

    template<typename, typename>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj_ref
    : private __result_of_memobj_ref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
    };


  struct __result_of_memobj_deref_impl
  {
    template<typename _Fp, typename _Tp1>
      static __result_of_success<decltype(
      (*std::declval<_Tp1>()).*std::declval<_Fp>()
      ), __invoke_memobj_deref> _S_test(int);

    template<typename, typename>
      static __failure_type _S_test(...);
  };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj_deref
    : private __result_of_memobj_deref_impl
    {
      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
    };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_memobj;

  template<typename _Res, typename _Class, typename _Arg>
    struct __result_of_memobj<_Res _Class::*, _Arg>
    {
      typedef __remove_cvref_t<_Arg> _Argval;
      typedef _Res _Class::* _MemPtr;
      typedef typename __conditional_t<__or_<is_same<_Argval, _Class>,
        is_base_of<_Class, _Argval>>::value,
        __result_of_memobj_ref<_MemPtr, _Arg>,
        __result_of_memobj_deref<_MemPtr, _Arg>
      >::type type;
    };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_memfun;

  template<typename _Res, typename _Class, typename _Arg, typename... _Args>
    struct __result_of_memfun<_Res _Class::*, _Arg, _Args...>
    {
      typedef typename remove_reference<_Arg>::type _Argval;
      typedef _Res _Class::* _MemPtr;
      typedef typename __conditional_t<is_base_of<_Class, _Argval>::value,
        __result_of_memfun_ref<_MemPtr, _Arg, _Args...>,
        __result_of_memfun_deref<_MemPtr, _Arg, _Args...>
      >::type type;
    };






  template<typename _Tp, typename _Up = __remove_cvref_t<_Tp>>
    struct __inv_unwrap
    {
      using type = _Tp;
    };

  template<typename _Tp, typename _Up>
    struct __inv_unwrap<_Tp, reference_wrapper<_Up>>
    {
      using type = _Up&;
    };

  template<bool, bool, typename _Functor, typename... _ArgTypes>
    struct __result_of_impl
    {
      typedef __failure_type type;
    };

  template<typename _MemPtr, typename _Arg>
    struct __result_of_impl<true, false, _MemPtr, _Arg>
    : public __result_of_memobj<__decay_t<_MemPtr>,
    typename __inv_unwrap<_Arg>::type>
    { };

  template<typename _MemPtr, typename _Arg, typename... _Args>
    struct __result_of_impl<false, true, _MemPtr, _Arg, _Args...>
    : public __result_of_memfun<__decay_t<_MemPtr>,
    typename __inv_unwrap<_Arg>::type, _Args...>
    { };


  struct __result_of_other_impl
  {
    template<typename _Fn, typename... _Args>
      static __result_of_success<decltype(
      std::declval<_Fn>()(std::declval<_Args>()...)
      ), __invoke_other> _S_test(int);

    template<typename...>
      static __failure_type _S_test(...);
  };

  template<typename _Functor, typename... _ArgTypes>
    struct __result_of_impl<false, false, _Functor, _ArgTypes...>
    : private __result_of_other_impl
    {
      typedef decltype(_S_test<_Functor, _ArgTypes...>(0)) type;
    };


  template<typename _Functor, typename... _ArgTypes>
    struct __invoke_result
    : public __result_of_impl<
        is_member_object_pointer<
          typename remove_reference<_Functor>::type
        >::value,
        is_member_function_pointer<
          typename remove_reference<_Functor>::type
        >::value,
 _Functor, _ArgTypes...
      >::type
    { };


  template<typename _Functor, typename... _ArgTypes>
    struct result_of<_Functor(_ArgTypes...)>
    : public __invoke_result<_Functor, _ArgTypes...>
    { } ;
# 2642 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Default, typename _AlwaysVoid,
    template<typename...> class _Op, typename... _Args>
    struct __detector
    {
      using value_t = false_type;
      using type = _Default;
    };


  template<typename _Default, template<typename...> class _Op,
     typename... _Args>
    struct __detector<_Default, __void_t<_Op<_Args...>>, _Op, _Args...>
    {
      using value_t = true_type;
      using type = _Op<_Args...>;
    };


  template<typename _Default, template<typename...> class _Op,
    typename... _Args>
    using __detected_or = __detector<_Default, void, _Op, _Args...>;


  template<typename _Default, template<typename...> class _Op,
    typename... _Args>
    using __detected_or_t
      = typename __detected_or<_Default, _Op, _Args...>::type;
# 2684 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template <typename _Tp>
    struct __is_swappable;

  template <typename _Tp>
    struct __is_nothrow_swappable;

  template<typename>
    struct __is_tuple_like_impl : false_type
    { };


  template<typename _Tp>
    struct __is_tuple_like
    : public __is_tuple_like_impl<__remove_cvref_t<_Tp>>::type
    { };


  template<typename _Tp>

    inline
    _Require<__not_<__is_tuple_like<_Tp>>,
      is_move_constructible<_Tp>,
      is_move_assignable<_Tp>>
    swap(_Tp&, _Tp&)
    noexcept(__and_<is_nothrow_move_constructible<_Tp>,
             is_nothrow_move_assignable<_Tp>>::value);

  template<typename _Tp, size_t _Nm>

    inline
    __enable_if_t<__is_swappable<_Tp>::value>
    swap(_Tp (&__a)[_Nm], _Tp (&__b)[_Nm])
    noexcept(__is_nothrow_swappable<_Tp>::value);


  namespace __swappable_details {
    using std::swap;

    struct __do_is_swappable_impl
    {
      template<typename _Tp, typename
               = decltype(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))>
        static true_type __test(int);

      template<typename>
        static false_type __test(...);
    };

    struct __do_is_nothrow_swappable_impl
    {
      template<typename _Tp>
        static __bool_constant<
          noexcept(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))
        > __test(int);

      template<typename>
        static false_type __test(...);
    };

  }

  template<typename _Tp>
    struct __is_swappable_impl
    : public __swappable_details::__do_is_swappable_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };

  template<typename _Tp>
    struct __is_nothrow_swappable_impl
    : public __swappable_details::__do_is_nothrow_swappable_impl
    {
      typedef decltype(__test<_Tp>(0)) type;
    };

  template<typename _Tp>
    struct __is_swappable
    : public __is_swappable_impl<_Tp>::type
    { };

  template<typename _Tp>
    struct __is_nothrow_swappable
    : public __is_nothrow_swappable_impl<_Tp>::type
    { };
# 2907 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
  template<typename _Result, typename _Ret,
    bool = is_void<_Ret>::value, typename = void>
    struct __is_invocable_impl : false_type { };


  template<typename _Result, typename _Ret>
    struct __is_invocable_impl<_Result, _Ret,
                                true,
          __void_t<typename _Result::type>>
    : true_type
    { };

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"

  template<typename _Result, typename _Ret>
    struct __is_invocable_impl<_Result, _Ret,
                                false,
          __void_t<typename _Result::type>>
    {
    private:


      static typename _Result::type _S_get();

      template<typename _Tp>
 static void _S_conv(_Tp);


      template<typename _Tp, typename = decltype(_S_conv<_Tp>(_S_get()))>
 static true_type
 _S_test(int);

      template<typename _Tp>
 static false_type
 _S_test(...);

    public:
      using type = decltype(_S_test<_Ret>(1));
    };
#pragma GCC diagnostic pop

  template<typename _Fn, typename... _ArgTypes>
    struct __is_invocable
    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>::type
    { };

  template<typename _Fn, typename _Tp, typename... _Args>
    constexpr bool __call_is_nt(__invoke_memfun_ref)
    {
      using _Up = typename __inv_unwrap<_Tp>::type;
      return noexcept((std::declval<_Up>().*std::declval<_Fn>())(
     std::declval<_Args>()...));
    }

  template<typename _Fn, typename _Tp, typename... _Args>
    constexpr bool __call_is_nt(__invoke_memfun_deref)
    {
      return noexcept(((*std::declval<_Tp>()).*std::declval<_Fn>())(
     std::declval<_Args>()...));
    }

  template<typename _Fn, typename _Tp>
    constexpr bool __call_is_nt(__invoke_memobj_ref)
    {
      using _Up = typename __inv_unwrap<_Tp>::type;
      return noexcept(std::declval<_Up>().*std::declval<_Fn>());
    }

  template<typename _Fn, typename _Tp>
    constexpr bool __call_is_nt(__invoke_memobj_deref)
    {
      return noexcept((*std::declval<_Tp>()).*std::declval<_Fn>());
    }

  template<typename _Fn, typename... _Args>
    constexpr bool __call_is_nt(__invoke_other)
    {
      return noexcept(std::declval<_Fn>()(std::declval<_Args>()...));
    }

  template<typename _Result, typename _Fn, typename... _Args>
    struct __call_is_nothrow
    : __bool_constant<
 std::__call_is_nt<_Fn, _Args...>(typename _Result::__invoke_type{})
      >
    { };

  template<typename _Fn, typename... _Args>
    using __call_is_nothrow_
      = __call_is_nothrow<__invoke_result<_Fn, _Args...>, _Fn, _Args...>;


  template<typename _Fn, typename... _Args>
    struct __is_nothrow_invocable
    : __and_<__is_invocable<_Fn, _Args...>,
             __call_is_nothrow_<_Fn, _Args...>>::type
    { };

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wctor-dtor-privacy"
  struct __nonesuchbase {};
  struct __nonesuch : private __nonesuchbase {
    ~__nonesuch() = delete;
    __nonesuch(__nonesuch const&) = delete;
    void operator=(__nonesuch const&) = delete;
  };
#pragma GCC diagnostic pop
# 3704 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/type_traits" 3
}
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{







  template<typename _Tp>
    inline constexpr _Tp*
    __addressof(_Tp& __r) noexcept
    { return __builtin_addressof(__r); }




}



namespace std __attribute__ ((__visibility__ ("default")))
{
# 74 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 3
  template<typename _Tp>

    constexpr _Tp&&
    forward(typename std::remove_reference<_Tp>::type& __t) noexcept
    { return static_cast<_Tp&&>(__t); }







  template<typename _Tp>

    constexpr _Tp&&
    forward(typename std::remove_reference<_Tp>::type&& __t) noexcept
    {
      static_assert(!std::is_lvalue_reference<_Tp>::value,
   "std::forward must not be used to convert an rvalue to an lvalue");
      return static_cast<_Tp&&>(__t);
    }






  template<typename _Tp>

    constexpr typename std::remove_reference<_Tp>::type&&
    move(_Tp&& __t) noexcept
    { return static_cast<typename std::remove_reference<_Tp>::type&&>(__t); }


  template<typename _Tp>
    struct __move_if_noexcept_cond
    : public __and_<__not_<is_nothrow_move_constructible<_Tp>>,
                    is_copy_constructible<_Tp>>::type { };
# 121 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 3
  template<typename _Tp>

    constexpr
    __conditional_t<__move_if_noexcept_cond<_Tp>::value, const _Tp&, _Tp&&>
    move_if_noexcept(_Tp& __x) noexcept
    { return std::move(__x); }
# 142 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 3
  template<typename _Tp>

    inline _Tp*
    addressof(_Tp& __r) noexcept
    { return std::__addressof(__r); }



  template<typename _Tp>
    const _Tp* addressof(const _Tp&&) = delete;


  template <typename _Tp, typename _Up = _Tp>

    inline _Tp
    __exchange(_Tp& __obj, _Up&& __new_val)
    {
      _Tp __old_val = std::move(__obj);
      __obj = std::forward<_Up>(__new_val);
      return __old_val;
    }
# 186 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/move.h" 3
  template<typename _Tp>

    inline

    typename enable_if<__and_<__not_<__is_tuple_like<_Tp>>,
         is_move_constructible<_Tp>,
         is_move_assignable<_Tp>>::value>::type



    swap(_Tp& __a, _Tp& __b)
    noexcept(__and_<is_nothrow_move_constructible<_Tp>, is_nothrow_move_assignable<_Tp>>::value)

    {




      _Tp __tmp = std::move(__a);
      __a = std::move(__b);
      __b = std::move(__tmp);
    }




  template<typename _Tp, size_t _Nm>

    inline

    typename enable_if<__is_swappable<_Tp>::value>::type



    swap(_Tp (&__a)[_Nm], _Tp (&__b)[_Nm])
    noexcept(__is_nothrow_swappable<_Tp>::value)
    {
      for (size_t __n = 0; __n < _Nm; ++__n)
 swap(__a[__n], __b[__n]);
    }



}
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/utility.h" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/utility.h" 3






namespace std __attribute__ ((__visibility__ ("default")))
{



  template<typename _Tp>
    struct tuple_size;





  template<typename _Tp,
    typename _Up = typename remove_cv<_Tp>::type,
    typename = typename enable_if<is_same<_Tp, _Up>::value>::type,
    size_t = tuple_size<_Tp>::value>
    using __enable_if_has_tuple_size = _Tp;

  template<typename _Tp>
    struct tuple_size<const __enable_if_has_tuple_size<_Tp>>
    : public tuple_size<_Tp> { };

  template<typename _Tp>
    struct tuple_size<volatile __enable_if_has_tuple_size<_Tp>>
    : public tuple_size<_Tp> { };

  template<typename _Tp>
    struct tuple_size<const volatile __enable_if_has_tuple_size<_Tp>>
    : public tuple_size<_Tp> { };







  template<size_t __i, typename _Tp>
    struct tuple_element;


  template<size_t __i, typename _Tp>
    using __tuple_element_t = typename tuple_element<__i, _Tp>::type;

  template<size_t __i, typename _Tp>
    struct tuple_element<__i, const _Tp>
    {
      typedef typename add_const<__tuple_element_t<__i, _Tp>>::type type;
    };

  template<size_t __i, typename _Tp>
    struct tuple_element<__i, volatile _Tp>
    {
      typedef typename add_volatile<__tuple_element_t<__i, _Tp>>::type type;
    };

  template<size_t __i, typename _Tp>
    struct tuple_element<__i, const volatile _Tp>
    {
      typedef typename add_cv<__tuple_element_t<__i, _Tp>>::type type;
    };
# 140 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/utility.h" 3
  template<size_t... _Indexes> struct _Index_tuple { };


  template<size_t _Num>
    struct _Build_index_tuple
    {

      template<typename, size_t... _Indices>
 using _IdxTuple = _Index_tuple<_Indices...>;


      using __type = __make_integer_seq<_IdxTuple, size_t, _Num>;




    };
# 227 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/utility.h" 3
  template<size_t _Np, typename... _Types>
    struct _Nth_type
    { };

  template<typename _Tp0, typename... _Rest>
    struct _Nth_type<0, _Tp0, _Rest...>
    { using type = _Tp0; };

  template<typename _Tp0, typename _Tp1, typename... _Rest>
    struct _Nth_type<1, _Tp0, _Tp1, _Rest...>
    { using type = _Tp1; };

  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
    struct _Nth_type<2, _Tp0, _Tp1, _Tp2, _Rest...>
    { using type = _Tp2; };

  template<size_t _Np, typename _Tp0, typename _Tp1, typename _Tp2,
    typename... _Rest>



    struct _Nth_type<_Np, _Tp0, _Tp1, _Tp2, _Rest...>
    : _Nth_type<_Np - 3, _Rest...>
    { };


  template<typename _Tp0, typename _Tp1, typename... _Rest>
    struct _Nth_type<0, _Tp0, _Tp1, _Rest...>
    { using type = _Tp0; };

  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
    struct _Nth_type<0, _Tp0, _Tp1, _Tp2, _Rest...>
    { using type = _Tp0; };

  template<typename _Tp0, typename _Tp1, typename _Tp2, typename... _Rest>
    struct _Nth_type<1, _Tp0, _Tp1, _Tp2, _Rest...>
    { using type = _Tp1; };



}
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 2 3






namespace std __attribute__ ((__visibility__ ("default")))
{
# 80 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  struct piecewise_construct_t { explicit piecewise_construct_t() = default; };


                    constexpr piecewise_construct_t piecewise_construct =
    piecewise_construct_t();




  template<typename...>
    class tuple;

  template<size_t...>
    struct _Index_tuple;







  template <bool, typename _T1, typename _T2>
    struct _PCC
    {
      template <typename _U1, typename _U2>
      static constexpr bool _ConstructiblePair()
      {
 return __and_<is_constructible<_T1, const _U1&>,
        is_constructible<_T2, const _U2&>>::value;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _ImplicitlyConvertiblePair()
      {
 return __and_<is_convertible<const _U1&, _T1>,
        is_convertible<const _U2&, _T2>>::value;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _MoveConstructiblePair()
      {
 return __and_<is_constructible<_T1, _U1&&>,
        is_constructible<_T2, _U2&&>>::value;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _ImplicitlyMoveConvertiblePair()
      {
 return __and_<is_convertible<_U1&&, _T1>,
        is_convertible<_U2&&, _T2>>::value;
      }
    };

  template <typename _T1, typename _T2>
    struct _PCC<false, _T1, _T2>
    {
      template <typename _U1, typename _U2>
      static constexpr bool _ConstructiblePair()
      {
 return false;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _ImplicitlyConvertiblePair()
      {
 return false;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _MoveConstructiblePair()
      {
 return false;
      }

      template <typename _U1, typename _U2>
      static constexpr bool _ImplicitlyMoveConvertiblePair()
      {
 return false;
      }
    };



  template<typename _U1, typename _U2> class __pair_base
  {

    template<typename _T1, typename _T2> friend struct pair;
    __pair_base() = default;
    ~__pair_base() = default;
    __pair_base(const __pair_base&) = default;
    __pair_base& operator=(const __pair_base&) = delete;

  };
# 184 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
    struct pair
    : public __pair_base<_T1, _T2>
    {
      typedef _T1 first_type;
      typedef _T2 second_type;

      _T1 first;
      _T2 second;


      constexpr pair(const pair&) = default;
      constexpr pair(pair&&) = default;

      template<typename... _Args1, typename... _Args2>

 pair(piecewise_construct_t, tuple<_Args1...>, tuple<_Args2...>);


                           void
      swap(pair& __p)
      noexcept(__and_<__is_nothrow_swappable<_T1>,
        __is_nothrow_swappable<_T2>>::value)
      {
 using std::swap;
 swap(first, __p.first);
 swap(second, __p.second);
      }

    private:
      template<typename... _Args1, size_t... _Indexes1,
        typename... _Args2, size_t... _Indexes2>

 pair(tuple<_Args1...>&, tuple<_Args2...>&,
      _Index_tuple<_Indexes1...>, _Index_tuple<_Indexes2...>);
    public:
# 378 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
      template <typename _U1 = _T1,
                typename _U2 = _T2,
                typename enable_if<__and_<
                                     __is_implicitly_default_constructible<_U1>,
                                     __is_implicitly_default_constructible<_U2>>
                                   ::value, bool>::type = true>
      constexpr pair()
      : first(), second() { }

      template <typename _U1 = _T1,
                typename _U2 = _T2,
                typename enable_if<__and_<
                       is_default_constructible<_U1>,
                       is_default_constructible<_U2>,
                       __not_<
                         __and_<__is_implicitly_default_constructible<_U1>,
                                __is_implicitly_default_constructible<_U2>>>>
                                   ::value, bool>::type = false>
      explicit constexpr pair()
      : first(), second() { }



      using _PCCP = _PCC<true, _T1, _T2>;



      template<typename _U1 = _T1, typename _U2=_T2, typename
        enable_if<_PCCP::template
      _ConstructiblePair<_U1, _U2>()
                  && _PCCP::template
      _ImplicitlyConvertiblePair<_U1, _U2>(),
                         bool>::type=true>
      constexpr pair(const _T1& __a, const _T2& __b)
      : first(__a), second(__b) { }


       template<typename _U1 = _T1, typename _U2=_T2, typename
  enable_if<_PCCP::template
       _ConstructiblePair<_U1, _U2>()
                   && !_PCCP::template
       _ImplicitlyConvertiblePair<_U1, _U2>(),
                         bool>::type=false>
      explicit constexpr pair(const _T1& __a, const _T2& __b)
      : first(__a), second(__b) { }



      template <typename _U1, typename _U2>
        using _PCCFP = _PCC<!is_same<_T1, _U1>::value
       || !is_same<_T2, _U2>::value,
       _T1, _T2>;


      template<typename _U1, typename _U2, typename
        enable_if<_PCCFP<_U1, _U2>::template
      _ConstructiblePair<_U1, _U2>()
                  && _PCCFP<_U1, _U2>::template
      _ImplicitlyConvertiblePair<_U1, _U2>(),
     bool>::type=true>
        constexpr pair(const pair<_U1, _U2>& __p)
        : first(__p.first), second(__p.second) { }

      template<typename _U1, typename _U2, typename
        enable_if<_PCCFP<_U1, _U2>::template
      _ConstructiblePair<_U1, _U2>()
    && !_PCCFP<_U1, _U2>::template
      _ImplicitlyConvertiblePair<_U1, _U2>(),
                         bool>::type=false>
 explicit constexpr pair(const pair<_U1, _U2>& __p)
 : first(__p.first), second(__p.second) { }
# 460 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
    private:



      struct __zero_as_null_pointer_constant
      {
 __zero_as_null_pointer_constant(int __zero_as_null_pointer_constant::*)
 { }
 template<typename _Tp,
   typename = __enable_if_t<is_null_pointer<_Tp>::value>>
 __zero_as_null_pointer_constant(_Tp) = delete;
      };

    public:




      template<typename _U1,
        __enable_if_t<__and_<__not_<is_reference<_U1>>,
        is_pointer<_T2>,
        is_constructible<_T1, _U1>,
        __not_<is_constructible<_T1, const _U1&>>,
        is_convertible<_U1, _T1>>::value,
        bool> = true>
 __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
 constexpr
 pair(_U1&& __x, __zero_as_null_pointer_constant, ...)
 : first(std::forward<_U1>(__x)), second(nullptr) { }

      template<typename _U1,
        __enable_if_t<__and_<__not_<is_reference<_U1>>,
        is_pointer<_T2>,
        is_constructible<_T1, _U1>,
        __not_<is_constructible<_T1, const _U1&>>,
        __not_<is_convertible<_U1, _T1>>>::value,
        bool> = false>
 __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
 explicit constexpr
 pair(_U1&& __x, __zero_as_null_pointer_constant, ...)
 : first(std::forward<_U1>(__x)), second(nullptr) { }

      template<typename _U2,
        __enable_if_t<__and_<is_pointer<_T1>,
        __not_<is_reference<_U2>>,
        is_constructible<_T2, _U2>,
        __not_<is_constructible<_T2, const _U2&>>,
        is_convertible<_U2, _T2>>::value,
        bool> = true>
 __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
 constexpr
 pair(__zero_as_null_pointer_constant, _U2&& __y, ...)
 : first(nullptr), second(std::forward<_U2>(__y)) { }

      template<typename _U2,
        __enable_if_t<__and_<is_pointer<_T1>,
        __not_<is_reference<_U2>>,
        is_constructible<_T2, _U2>,
        __not_<is_constructible<_T2, const _U2&>>,
        __not_<is_convertible<_U2, _T2>>>::value,
        bool> = false>
 __attribute__ ((__deprecated__ ("use 'nullptr' instead of '0' to " "initialize std::pair of move-only " "type and pointer")))
 explicit constexpr
 pair(__zero_as_null_pointer_constant, _U2&& __y, ...)
 : first(nullptr), second(std::forward<_U2>(__y)) { }



      template<typename _U1, typename _U2, typename
        enable_if<_PCCP::template
      _MoveConstructiblePair<_U1, _U2>()
     && _PCCP::template
      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
                         bool>::type=true>
 constexpr pair(_U1&& __x, _U2&& __y)
 : first(std::forward<_U1>(__x)), second(std::forward<_U2>(__y)) { }

      template<typename _U1, typename _U2, typename
        enable_if<_PCCP::template
      _MoveConstructiblePair<_U1, _U2>()
     && !_PCCP::template
      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
                         bool>::type=false>
 explicit constexpr pair(_U1&& __x, _U2&& __y)
 : first(std::forward<_U1>(__x)), second(std::forward<_U2>(__y)) { }


      template<typename _U1, typename _U2, typename
        enable_if<_PCCFP<_U1, _U2>::template
      _MoveConstructiblePair<_U1, _U2>()
     && _PCCFP<_U1, _U2>::template
      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
                         bool>::type=true>
 constexpr pair(pair<_U1, _U2>&& __p)
 : first(std::forward<_U1>(__p.first)),
   second(std::forward<_U2>(__p.second)) { }

      template<typename _U1, typename _U2, typename
        enable_if<_PCCFP<_U1, _U2>::template
      _MoveConstructiblePair<_U1, _U2>()
     && !_PCCFP<_U1, _U2>::template
      _ImplicitlyMoveConvertiblePair<_U1, _U2>(),
                         bool>::type=false>
 explicit constexpr pair(pair<_U1, _U2>&& __p)
 : first(std::forward<_U1>(__p.first)),
   second(std::forward<_U2>(__p.second)) { }

      pair&
      operator=(__conditional_t<__and_<is_copy_assignable<_T1>,
           is_copy_assignable<_T2>>::value,
    const pair&, const __nonesuch&> __p)
      {
 first = __p.first;
 second = __p.second;
 return *this;
      }

      pair&
      operator=(__conditional_t<__and_<is_move_assignable<_T1>,
           is_move_assignable<_T2>>::value,
    pair&&, __nonesuch&&> __p)
      noexcept(__and_<is_nothrow_move_assignable<_T1>,
        is_nothrow_move_assignable<_T2>>::value)
      {
 first = std::forward<first_type>(__p.first);
 second = std::forward<second_type>(__p.second);
 return *this;
      }

      template<typename _U1, typename _U2>
 typename enable_if<__and_<is_assignable<_T1&, const _U1&>,
      is_assignable<_T2&, const _U2&>>::value,
      pair&>::type
 operator=(const pair<_U1, _U2>& __p)
 {
   first = __p.first;
   second = __p.second;
   return *this;
 }

      template<typename _U1, typename _U2>
 typename enable_if<__and_<is_assignable<_T1&, _U1&&>,
      is_assignable<_T2&, _U2&&>>::value,
      pair&>::type
 operator=(pair<_U1, _U2>&& __p)
 {
   first = std::forward<_U1>(__p.first);
   second = std::forward<_U2>(__p.second);
   return *this;
 }
# 629 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
    };
# 638 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
    inline constexpr bool
    operator==(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return __x.first == __y.first && __x.second == __y.second; }
# 661 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
    inline constexpr bool
    operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return __x.first < __y.first
      || (!(__y.first < __x.first) && __x.second < __y.second); }


  template<typename _T1, typename _T2>
    inline constexpr bool
    operator!=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return !(__x == __y); }


  template<typename _T1, typename _T2>
    inline constexpr bool
    operator>(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return __y < __x; }


  template<typename _T1, typename _T2>
    inline constexpr bool
    operator<=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return !(__y < __x); }


  template<typename _T1, typename _T2>
    inline constexpr bool
    operator>=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
    { return !(__x < __y); }
# 698 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
                         inline





    void

    swap(pair<_T1, _T2>& __x, pair<_T1, _T2>& __y)
    noexcept(noexcept(__x.swap(__y)))
    { __x.swap(__y); }
# 738 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
    constexpr pair<typename __decay_and_strip<_T1>::__type,
                   typename __decay_and_strip<_T2>::__type>
    make_pair(_T1&& __x, _T2&& __y)
    {
      typedef typename __decay_and_strip<_T1>::__type __ds_type1;
      typedef typename __decay_and_strip<_T2>::__type __ds_type2;
      typedef pair<__ds_type1, __ds_type2> __pair_type;
      return __pair_type(std::forward<_T1>(__x), std::forward<_T2>(__y));
    }
# 760 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<typename _T1, typename _T2>
    struct __is_tuple_like_impl<pair<_T1, _T2>> : true_type
    { };


  template<class _Tp1, class _Tp2>
    struct tuple_size<pair<_Tp1, _Tp2>>
    : public integral_constant<size_t, 2> { };


  template<class _Tp1, class _Tp2>
    struct tuple_element<0, pair<_Tp1, _Tp2>>
    { typedef _Tp1 type; };


  template<class _Tp1, class _Tp2>
    struct tuple_element<1, pair<_Tp1, _Tp2>>
    { typedef _Tp2 type; };
# 797 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
  template<size_t _Int>
    struct __pair_get;

  template<>
    struct __pair_get<0>
    {
      template<typename _Tp1, typename _Tp2>
 static constexpr _Tp1&
 __get(pair<_Tp1, _Tp2>& __pair) noexcept
 { return __pair.first; }

      template<typename _Tp1, typename _Tp2>
 static constexpr _Tp1&&
 __move_get(pair<_Tp1, _Tp2>&& __pair) noexcept
 { return std::forward<_Tp1>(__pair.first); }

      template<typename _Tp1, typename _Tp2>
 static constexpr const _Tp1&
 __const_get(const pair<_Tp1, _Tp2>& __pair) noexcept
 { return __pair.first; }

      template<typename _Tp1, typename _Tp2>
 static constexpr const _Tp1&&
 __const_move_get(const pair<_Tp1, _Tp2>&& __pair) noexcept
 { return std::forward<const _Tp1>(__pair.first); }
    };

  template<>
    struct __pair_get<1>
    {
      template<typename _Tp1, typename _Tp2>
 static constexpr _Tp2&
 __get(pair<_Tp1, _Tp2>& __pair) noexcept
 { return __pair.second; }

      template<typename _Tp1, typename _Tp2>
 static constexpr _Tp2&&
 __move_get(pair<_Tp1, _Tp2>&& __pair) noexcept
 { return std::forward<_Tp2>(__pair.second); }

      template<typename _Tp1, typename _Tp2>
 static constexpr const _Tp2&
 __const_get(const pair<_Tp1, _Tp2>& __pair) noexcept
 { return __pair.second; }

      template<typename _Tp1, typename _Tp2>
 static constexpr const _Tp2&&
 __const_move_get(const pair<_Tp1, _Tp2>&& __pair) noexcept
 { return std::forward<const _Tp2>(__pair.second); }
    };






  template<size_t _Int, class _Tp1, class _Tp2>
    constexpr typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&
    get(pair<_Tp1, _Tp2>& __in) noexcept
    { return __pair_get<_Int>::__get(__in); }

  template<size_t _Int, class _Tp1, class _Tp2>
    constexpr typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&&
    get(pair<_Tp1, _Tp2>&& __in) noexcept
    { return __pair_get<_Int>::__move_get(std::move(__in)); }

  template<size_t _Int, class _Tp1, class _Tp2>
    constexpr const typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&
    get(const pair<_Tp1, _Tp2>& __in) noexcept
    { return __pair_get<_Int>::__const_get(__in); }

  template<size_t _Int, class _Tp1, class _Tp2>
    constexpr const typename tuple_element<_Int, pair<_Tp1, _Tp2>>::type&&
    get(const pair<_Tp1, _Tp2>&& __in) noexcept
    { return __pair_get<_Int>::__const_move_get(std::move(__in)); }
# 922 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_pair.h" 3
}
# 65 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 1 3
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
# 74 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 93 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
  struct input_iterator_tag { };


  struct output_iterator_tag { };


  struct forward_iterator_tag : public input_iterator_tag { };



  struct bidirectional_iterator_tag : public forward_iterator_tag { };



  struct random_access_iterator_tag : public bidirectional_iterator_tag { };
# 125 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
  template<typename _Category, typename _Tp, typename _Distance = ptrdiff_t,
           typename _Pointer = _Tp*, typename _Reference = _Tp&>
    struct iterator
    {

      typedef _Category iterator_category;

      typedef _Tp value_type;

      typedef _Distance difference_type;

      typedef _Pointer pointer;

      typedef _Reference reference;
    };
# 149 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
  template<typename _Iterator>
    struct iterator_traits;




  template<typename _Iterator, typename = __void_t<>>
    struct __iterator_traits { };



  template<typename _Iterator>
    struct __iterator_traits<_Iterator,
        __void_t<typename _Iterator::iterator_category,
          typename _Iterator::value_type,
          typename _Iterator::difference_type,
          typename _Iterator::pointer,
          typename _Iterator::reference>>
    {
      typedef typename _Iterator::iterator_category iterator_category;
      typedef typename _Iterator::value_type value_type;
      typedef typename _Iterator::difference_type difference_type;
      typedef typename _Iterator::pointer pointer;
      typedef typename _Iterator::reference reference;
    };


  template<typename _Iterator>
    struct iterator_traits
    : public __iterator_traits<_Iterator> { };
# 209 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
  template<typename _Tp>
    struct iterator_traits<_Tp*>
    {
      typedef random_access_iterator_tag iterator_category;
      typedef _Tp value_type;
      typedef ptrdiff_t difference_type;
      typedef _Tp* pointer;
      typedef _Tp& reference;
    };


  template<typename _Tp>
    struct iterator_traits<const _Tp*>
    {
      typedef random_access_iterator_tag iterator_category;
      typedef _Tp value_type;
      typedef ptrdiff_t difference_type;
      typedef const _Tp* pointer;
      typedef const _Tp& reference;
    };






  template<typename _Iter>
    inline constexpr
    typename iterator_traits<_Iter>::iterator_category
    __iterator_category(const _Iter&)
    { return typename iterator_traits<_Iter>::iterator_category(); }




  template<typename _Iter>
    using __iterator_category_t
      = typename iterator_traits<_Iter>::iterator_category;

  template<typename _InIter>
    using _RequireInputIter =
      __enable_if_t<is_convertible<__iterator_category_t<_InIter>,
       input_iterator_tag>::value>;

  template<typename _It,
    typename _Cat = __iterator_category_t<_It>>
    struct __is_random_access_iter
      : is_base_of<random_access_iterator_tag, _Cat>
    {
      typedef is_base_of<random_access_iterator_tag, _Cat> _Base;
      enum { __value = _Base::value };
    };
# 269 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_types.h" 3
}
# 66 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 1 3
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/concept_check.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/concept_check.h" 3
# 65 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/debug/assertions.h" 1 3
# 66 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 2 3


namespace std __attribute__ ((__visibility__ ("default")))
{




  template <typename> struct _List_iterator;
  template <typename> struct _List_const_iterator;


  template<typename _InputIterator>
    inline
    typename iterator_traits<_InputIterator>::difference_type
    __distance(_InputIterator __first, _InputIterator __last,
               input_iterator_tag)
    {



      typename iterator_traits<_InputIterator>::difference_type __n = 0;
      while (__first != __last)
 {
   ++__first;
   ++__n;
 }
      return __n;
    }

  template<typename _RandomAccessIterator>
    inline
    typename iterator_traits<_RandomAccessIterator>::difference_type
    __distance(_RandomAccessIterator __first, _RandomAccessIterator __last,
               random_access_iterator_tag)
    {



      return __last - __first;
    }



  template<typename _Tp>
    ptrdiff_t
    __distance(std::_List_iterator<_Tp>,
        std::_List_iterator<_Tp>,
        input_iterator_tag);

  template<typename _Tp>
    ptrdiff_t
    __distance(std::_List_const_iterator<_Tp>,
        std::_List_const_iterator<_Tp>,
        input_iterator_tag);




  template<typename _OutputIterator>
    void
    __distance(_OutputIterator, _OutputIterator, output_iterator_tag) = delete;
# 143 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 3
  template<typename _InputIterator>

    inline
    typename iterator_traits<_InputIterator>::difference_type
    distance(_InputIterator __first, _InputIterator __last)
    {

      return std::__distance(__first, __last,
        std::__iterator_category(__first));
    }

  template<typename _InputIterator, typename _Distance>
    inline void
    __advance(_InputIterator& __i, _Distance __n, input_iterator_tag)
    {


      do { if (std::__is_constant_evaluated() && !bool(__n >= 0)) __builtin_unreachable(); } while (false);
      while (__n--)
 ++__i;
    }

  template<typename _BidirectionalIterator, typename _Distance>
    inline void
    __advance(_BidirectionalIterator& __i, _Distance __n,
       bidirectional_iterator_tag)
    {



      if (__n > 0)
        while (__n--)
   ++__i;
      else
        while (__n++)
   --__i;
    }

  template<typename _RandomAccessIterator, typename _Distance>
    inline void
    __advance(_RandomAccessIterator& __i, _Distance __n,
              random_access_iterator_tag)
    {



      if (__builtin_constant_p(__n) && __n == 1)
 ++__i;
      else if (__builtin_constant_p(__n) && __n == -1)
 --__i;
      else
 __i += __n;
    }



  template<typename _OutputIterator, typename _Distance>
    void
    __advance(_OutputIterator&, _Distance, output_iterator_tag) = delete;
# 216 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator_base_funcs.h" 3
  template<typename _InputIterator, typename _Distance>
    inline void
    advance(_InputIterator& __i, _Distance __n)
    {

      typename iterator_traits<_InputIterator>::difference_type __d = __n;
      std::__advance(__i, __d, std::__iterator_category(__i));
    }



  template<typename _InputIterator>

    inline _InputIterator
    next(_InputIterator __x, typename
  iterator_traits<_InputIterator>::difference_type __n = 1)
    {


      std::advance(__x, __n);
      return __x;
    }

  template<typename _BidirectionalIterator>

    inline _BidirectionalIterator
    prev(_BidirectionalIterator __x, typename
  iterator_traits<_BidirectionalIterator>::difference_type __n = 1)
    {



      std::advance(__x, -__n);
      return __x;
    }




}
# 67 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 1 3
# 67 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ptr_traits.h" 1 3
# 46 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ptr_traits.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{


  class __undefined;



  template<typename _Tp>
    struct __get_first_arg
    { using type = __undefined; };

  template<template<typename, typename...> class _SomeTemplate, typename _Tp,
           typename... _Types>
    struct __get_first_arg<_SomeTemplate<_Tp, _Types...>>
    { using type = _Tp; };



  template<typename _Tp, typename _Up>
    struct __replace_first_arg
    { };

  template<template<typename, typename...> class _SomeTemplate, typename _Up,
           typename _Tp, typename... _Types>
    struct __replace_first_arg<_SomeTemplate<_Tp, _Types...>, _Up>
    { using type = _SomeTemplate<_Up, _Types...>; };
# 81 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ptr_traits.h" 3
  template<typename _Ptr, typename = void>
    struct __ptr_traits_elem : __get_first_arg<_Ptr>
    { };


  template<typename _Ptr>
    struct __ptr_traits_elem<_Ptr, __void_t<typename _Ptr::element_type>>
    { using type = typename _Ptr::element_type; };

  template<typename _Ptr>
    using __ptr_traits_elem_t = typename __ptr_traits_elem<_Ptr>::type;



  template<typename _Ptr, typename _Elt, bool = is_void<_Elt>::value>
    struct __ptr_traits_ptr_to
    {
      using pointer = _Ptr;
      using element_type = _Elt;







      static pointer
      pointer_to(element_type& __e)





      { return pointer::pointer_to(__e); }
    };


  template<typename _Ptr, typename _Elt>
    struct __ptr_traits_ptr_to<_Ptr, _Elt, true>
    { };


  template<typename _Tp>
    struct __ptr_traits_ptr_to<_Tp*, _Tp, false>
    {
      using pointer = _Tp*;
      using element_type = _Tp;






      static pointer
      pointer_to(element_type& __r) noexcept
      { return std::addressof(__r); }
    };

  template<typename _Ptr, typename _Elt>
    struct __ptr_traits_impl : __ptr_traits_ptr_to<_Ptr, _Elt>
    {
    private:
      template<typename _Tp, typename = void>
 struct __difference { using type = ptrdiff_t; };

      template<typename _Tp>




 struct __difference<_Tp, __void_t<typename _Tp::difference_type>>

 { using type = typename _Tp::difference_type; };

      template<typename _Tp, typename _Up, typename = void>
 struct __rebind : __replace_first_arg<_Tp, _Up> { };

      template<typename _Tp, typename _Up>




 struct __rebind<_Tp, _Up, __void_t<typename _Tp::template rebind<_Up>>>

 { using type = typename _Tp::template rebind<_Up>; };

    public:

      using pointer = _Ptr;


      using element_type = _Elt;


      using difference_type = typename __difference<_Ptr>::type;


      template<typename _Up>
        using rebind = typename __rebind<_Ptr, _Up>::type;
    };



  template<typename _Ptr>
    struct __ptr_traits_impl<_Ptr, __undefined>
    { };






  template<typename _Ptr>
    struct pointer_traits : __ptr_traits_impl<_Ptr, __ptr_traits_elem_t<_Ptr>>
    { };
# 209 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ptr_traits.h" 3
  template<typename _Tp>
    struct pointer_traits<_Tp*> : __ptr_traits_ptr_to<_Tp*, _Tp>
    {

      typedef _Tp* pointer;

      typedef _Tp element_type;

      typedef ptrdiff_t difference_type;

      template<typename _Up> using rebind = _Up*;
    };


  template<typename _Ptr, typename _Tp>
    using __ptr_rebind = typename pointer_traits<_Ptr>::template rebind<_Tp>;

  template<typename _Tp>
    constexpr _Tp*
    __to_address(_Tp* __ptr) noexcept
    {
      static_assert(!std::is_function<_Tp>::value, "not a function pointer");
      return __ptr;
    }


  template<typename _Ptr>
    constexpr typename std::pointer_traits<_Ptr>::element_type*
    __to_address(const _Ptr& __ptr)
    { return std::__to_address(__ptr.operator->()); }
# 283 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ptr_traits.h" 3
}
# 68 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 2 3
# 88 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 109 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
# 131 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>
    class reverse_iterator
    : public iterator<typename iterator_traits<_Iterator>::iterator_category,
        typename iterator_traits<_Iterator>::value_type,
        typename iterator_traits<_Iterator>::difference_type,
        typename iterator_traits<_Iterator>::pointer,
                      typename iterator_traits<_Iterator>::reference>
    {
      template<typename _Iter>
 friend class reverse_iterator;
# 150 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
    protected:
      _Iterator current;

      typedef iterator_traits<_Iterator> __traits_type;

    public:
      typedef _Iterator iterator_type;
      typedef typename __traits_type::pointer pointer;

      typedef typename __traits_type::difference_type difference_type;
      typedef typename __traits_type::reference reference;
# 182 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      reverse_iterator()
      noexcept(noexcept(_Iterator()))
      : current()
      { }




      explicit
      reverse_iterator(iterator_type __x)
      noexcept(noexcept(_Iterator(__x)))
      : current(__x)
      { }





      reverse_iterator(const reverse_iterator& __x)
      noexcept(noexcept(_Iterator(__x.current)))
      : current(__x.current)
      { }


      reverse_iterator& operator=(const reverse_iterator&) = default;






      template<typename _Iter>




        reverse_iterator(const reverse_iterator<_Iter>& __x)
 noexcept(noexcept(_Iterator(__x.current)))
 : current(__x.current)
 { }


      template<typename _Iter>





 reverse_iterator&
 operator=(const reverse_iterator<_Iter>& __x)
 noexcept(noexcept(current = __x.current))
 {
   current = __x.current;
   return *this;
 }






                           iterator_type
      base() const
      noexcept(noexcept(_Iterator(current)))
      { return current; }
# 259 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
                           reference
      operator*() const
      {
 _Iterator __tmp = current;
 return *--__tmp;
      }







                           pointer
      operator->() const




      {


 _Iterator __tmp = current;
 --__tmp;
 return _S_to_pointer(__tmp);
      }






                           reverse_iterator&
      operator++()
      {
 --current;
 return *this;
      }






                           reverse_iterator
      operator++(int)
      {
 reverse_iterator __tmp = *this;
 --current;
 return __tmp;
      }






                           reverse_iterator&
      operator--()
      {
 ++current;
 return *this;
      }






                           reverse_iterator
      operator--(int)
      {
 reverse_iterator __tmp = *this;
 ++current;
 return __tmp;
      }







                           reverse_iterator
      operator+(difference_type __n) const
      { return reverse_iterator(current - __n); }







                           reverse_iterator&
      operator+=(difference_type __n)
      {
 current -= __n;
 return *this;
      }







                           reverse_iterator
      operator-(difference_type __n) const
      { return reverse_iterator(current + __n); }







                           reverse_iterator&
      operator-=(difference_type __n)
      {
 current += __n;
 return *this;
      }







                           reference
      operator[](difference_type __n) const
      { return *(*this + __n); }
# 418 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
    private:
      template<typename _Tp>
 static _Tp*
 _S_to_pointer(_Tp* __p)
        { return __p; }

      template<typename _Tp>
 static pointer
 _S_to_pointer(_Tp __t)
        { return __t.operator->(); }
    };
# 441 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>

    inline bool
    operator==(const reverse_iterator<_Iterator>& __x,
        const reverse_iterator<_Iterator>& __y)
    { return __x.base() == __y.base(); }

  template<typename _Iterator>

    inline bool
    operator<(const reverse_iterator<_Iterator>& __x,
       const reverse_iterator<_Iterator>& __y)
    { return __y.base() < __x.base(); }

  template<typename _Iterator>

    inline bool
    operator!=(const reverse_iterator<_Iterator>& __x,
        const reverse_iterator<_Iterator>& __y)
    { return !(__x == __y); }

  template<typename _Iterator>

    inline bool
    operator>(const reverse_iterator<_Iterator>& __x,
       const reverse_iterator<_Iterator>& __y)
    { return __y < __x; }

  template<typename _Iterator>

    inline bool
    operator<=(const reverse_iterator<_Iterator>& __x,
        const reverse_iterator<_Iterator>& __y)
    { return !(__y < __x); }

  template<typename _Iterator>

    inline bool
    operator>=(const reverse_iterator<_Iterator>& __x,
        const reverse_iterator<_Iterator>& __y)
    { return !(__x < __y); }




  template<typename _IteratorL, typename _IteratorR>

    inline bool
    operator==(const reverse_iterator<_IteratorL>& __x,
        const reverse_iterator<_IteratorR>& __y)
    { return __x.base() == __y.base(); }

  template<typename _IteratorL, typename _IteratorR>

    inline bool
    operator<(const reverse_iterator<_IteratorL>& __x,
       const reverse_iterator<_IteratorR>& __y)
    { return __x.base() > __y.base(); }

  template<typename _IteratorL, typename _IteratorR>

    inline bool
    operator!=(const reverse_iterator<_IteratorL>& __x,
        const reverse_iterator<_IteratorR>& __y)
    { return __x.base() != __y.base(); }

  template<typename _IteratorL, typename _IteratorR>

    inline bool
    operator>(const reverse_iterator<_IteratorL>& __x,
       const reverse_iterator<_IteratorR>& __y)
    { return __x.base() < __y.base(); }

  template<typename _IteratorL, typename _IteratorR>
    inline bool
    operator<=(const reverse_iterator<_IteratorL>& __x,
        const reverse_iterator<_IteratorR>& __y)
    { return __x.base() >= __y.base(); }

  template<typename _IteratorL, typename _IteratorR>

    inline bool
    operator>=(const reverse_iterator<_IteratorL>& __x,
        const reverse_iterator<_IteratorR>& __y)
    { return __x.base() <= __y.base(); }
# 618 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline auto
    operator-(const reverse_iterator<_IteratorL>& __x,
       const reverse_iterator<_IteratorR>& __y)
    -> decltype(__y.base() - __x.base())
    { return __y.base() - __x.base(); }


  template<typename _Iterator>

    inline reverse_iterator<_Iterator>
    operator+(typename reverse_iterator<_Iterator>::difference_type __n,
       const reverse_iterator<_Iterator>& __x)
    { return reverse_iterator<_Iterator>(__x.base() - __n); }



  template<typename _Iterator>
    inline reverse_iterator<_Iterator>
    __make_reverse_iterator(_Iterator __i)
    { return reverse_iterator<_Iterator>(__i); }
# 662 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>

    auto
    __niter_base(reverse_iterator<_Iterator> __it)
    -> decltype(__make_reverse_iterator(__niter_base(__it.base())))
    { return __make_reverse_iterator(__niter_base(__it.base())); }

  template<typename _Iterator>
    struct __is_move_iterator<reverse_iterator<_Iterator> >
      : __is_move_iterator<_Iterator>
    { };

  template<typename _Iterator>

    auto
    __miter_base(reverse_iterator<_Iterator> __it)
    -> decltype(__make_reverse_iterator(__miter_base(__it.base())))
    { return __make_reverse_iterator(__miter_base(__it.base())); }
# 693 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>
    class back_insert_iterator
    : public iterator<output_iterator_tag, void, void, void, void>
    {
    protected:
      _Container* container;

    public:

      typedef _Container container_type;





      explicit
      back_insert_iterator(_Container& __x)
      : container(std::__addressof(__x)) { }
# 732 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      back_insert_iterator&
      operator=(const typename _Container::value_type& __value)
      {
 container->push_back(__value);
 return *this;
      }


      back_insert_iterator&
      operator=(typename _Container::value_type&& __value)
      {
 container->push_back(std::move(__value));
 return *this;
      }




      back_insert_iterator&
      operator*()
      { return *this; }



      back_insert_iterator&
      operator++()
      { return *this; }



      back_insert_iterator
      operator++(int)
      { return *this; }
    };
# 778 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>

    inline back_insert_iterator<_Container>
    back_inserter(_Container& __x)
    { return back_insert_iterator<_Container>(__x); }
# 794 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>
    class front_insert_iterator
    : public iterator<output_iterator_tag, void, void, void, void>
    {
    protected:
      _Container* container;

    public:

      typedef _Container container_type;





      explicit
      front_insert_iterator(_Container& __x)
      : container(std::__addressof(__x)) { }
# 833 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      front_insert_iterator&
      operator=(const typename _Container::value_type& __value)
      {
 container->push_front(__value);
 return *this;
      }


      front_insert_iterator&
      operator=(typename _Container::value_type&& __value)
      {
 container->push_front(std::move(__value));
 return *this;
      }




      front_insert_iterator&
      operator*()
      { return *this; }



      front_insert_iterator&
      operator++()
      { return *this; }



      front_insert_iterator
      operator++(int)
      { return *this; }
    };
# 879 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>

    inline front_insert_iterator<_Container>
    front_inserter(_Container& __x)
    { return front_insert_iterator<_Container>(__x); }
# 899 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>
    class insert_iterator
    : public iterator<output_iterator_tag, void, void, void, void>
    {



      typedef typename _Container::iterator _Iter;

    protected:
      _Container* container;
      _Iter iter;

    public:

      typedef _Container container_type;
# 925 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      insert_iterator(_Container& __x, _Iter __i)
      : container(std::__addressof(__x)), iter(__i) {}
# 961 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      insert_iterator&
      operator=(const typename _Container::value_type& __value)
      {
 iter = container->insert(iter, __value);
 ++iter;
 return *this;
      }


      insert_iterator&
      operator=(typename _Container::value_type&& __value)
      {
 iter = container->insert(iter, std::move(__value));
 ++iter;
 return *this;
      }




      insert_iterator&
      operator*()
      { return *this; }



      insert_iterator&
      operator++()
      { return *this; }



      insert_iterator&
      operator++(int)
      { return *this; }
    };

#pragma GCC diagnostic pop
# 1019 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Container>

    inline insert_iterator<_Container>
    inserter(_Container& __x, typename _Container::iterator __i)
    { return insert_iterator<_Container>(__x, __i); }





}

namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{
# 1042 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator, typename _Container>
    class __normal_iterator
    {
    protected:
      _Iterator _M_current;

      typedef std::iterator_traits<_Iterator> __traits_type;


      template<typename _Iter>
 using __convertible_from
   = std::__enable_if_t<std::is_convertible<_Iter, _Iterator>::value>;


    public:
      typedef _Iterator iterator_type;
      typedef typename __traits_type::iterator_category iterator_category;
      typedef typename __traits_type::value_type value_type;
      typedef typename __traits_type::difference_type difference_type;
      typedef typename __traits_type::reference reference;
      typedef typename __traits_type::pointer pointer;





      constexpr __normal_iterator() noexcept
      : _M_current(_Iterator()) { }

      explicit
      __normal_iterator(const _Iterator& __i) noexcept
      : _M_current(__i) { }



      template<typename _Iter, typename = __convertible_from<_Iter>>

 __normal_iterator(const __normal_iterator<_Iter, _Container>& __i)
 noexcept
# 1090 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
        : _M_current(__i.base()) { }



      reference
      operator*() const noexcept
      { return *_M_current; }


      pointer
      operator->() const noexcept
      { return _M_current; }


      __normal_iterator&
      operator++() noexcept
      {
 ++_M_current;
 return *this;
      }


      __normal_iterator
      operator++(int) noexcept
      { return __normal_iterator(_M_current++); }



      __normal_iterator&
      operator--() noexcept
      {
 --_M_current;
 return *this;
      }


      __normal_iterator
      operator--(int) noexcept
      { return __normal_iterator(_M_current--); }



      reference
      operator[](difference_type __n) const noexcept
      { return _M_current[__n]; }


      __normal_iterator&
      operator+=(difference_type __n) noexcept
      { _M_current += __n; return *this; }


      __normal_iterator
      operator+(difference_type __n) const noexcept
      { return __normal_iterator(_M_current + __n); }


      __normal_iterator&
      operator-=(difference_type __n) noexcept
      { _M_current -= __n; return *this; }


      __normal_iterator
      operator-(difference_type __n) const noexcept
      { return __normal_iterator(_M_current - __n); }


      const _Iterator&
      base() const noexcept
      { return _M_current; }
    };
# 1210 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator==(const __normal_iterator<_IteratorL, _Container>& __lhs,
        const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() == __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator==(const __normal_iterator<_Iterator, _Container>& __lhs,
        const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() == __rhs.base(); }

  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator!=(const __normal_iterator<_IteratorL, _Container>& __lhs,
        const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() != __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator!=(const __normal_iterator<_Iterator, _Container>& __lhs,
        const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() != __rhs.base(); }


  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator<(const __normal_iterator<_IteratorL, _Container>& __lhs,
       const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() < __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator<(const __normal_iterator<_Iterator, _Container>& __lhs,
       const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() < __rhs.base(); }

  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator>(const __normal_iterator<_IteratorL, _Container>& __lhs,
       const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() > __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator>(const __normal_iterator<_Iterator, _Container>& __lhs,
       const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() > __rhs.base(); }

  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator<=(const __normal_iterator<_IteratorL, _Container>& __lhs,
        const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() <= __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator<=(const __normal_iterator<_Iterator, _Container>& __lhs,
        const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() <= __rhs.base(); }

  template<typename _IteratorL, typename _IteratorR, typename _Container>

    inline bool
    operator>=(const __normal_iterator<_IteratorL, _Container>& __lhs,
        const __normal_iterator<_IteratorR, _Container>& __rhs)
    noexcept
    { return __lhs.base() >= __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline bool
    operator>=(const __normal_iterator<_Iterator, _Container>& __lhs,
        const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() >= __rhs.base(); }






  template<typename _IteratorL, typename _IteratorR, typename _Container>


    [[__nodiscard__]]
    inline auto
    operator-(const __normal_iterator<_IteratorL, _Container>& __lhs,
       const __normal_iterator<_IteratorR, _Container>& __rhs) noexcept
    -> decltype(__lhs.base() - __rhs.base())





    { return __lhs.base() - __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline typename __normal_iterator<_Iterator, _Container>::difference_type
    operator-(const __normal_iterator<_Iterator, _Container>& __lhs,
       const __normal_iterator<_Iterator, _Container>& __rhs)
    noexcept
    { return __lhs.base() - __rhs.base(); }

  template<typename _Iterator, typename _Container>

    inline __normal_iterator<_Iterator, _Container>
    operator+(typename __normal_iterator<_Iterator, _Container>::difference_type
       __n, const __normal_iterator<_Iterator, _Container>& __i)
    noexcept
    { return __normal_iterator<_Iterator, _Container>(__i.base() + __n); }


}

namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _Iterator, typename _Container>

    _Iterator
    __niter_base(__gnu_cxx::__normal_iterator<_Iterator, _Container> __it)
    noexcept(std::is_nothrow_copy_constructible<_Iterator>::value)
    { return __it.base(); }






  template<typename _Iterator, typename _Container>
    constexpr auto
    __to_address(const __gnu_cxx::__normal_iterator<_Iterator,
          _Container>& __it) noexcept
    -> decltype(std::__to_address(__it.base()))
    { return std::__to_address(__it.base()); }
# 1417 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  namespace __detail
  {
# 1433 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  }
# 1444 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>
    class move_iterator



    {
      _Iterator _M_current;

      using __traits_type = iterator_traits<_Iterator>;

      using __base_ref = typename __traits_type::reference;


      template<typename _Iter2>
 friend class move_iterator;
# 1468 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
    public:
      using iterator_type = _Iterator;
# 1479 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      typedef typename __traits_type::iterator_category iterator_category;
      typedef typename __traits_type::value_type value_type;
      typedef typename __traits_type::difference_type difference_type;

      typedef _Iterator pointer;


      using reference
 = __conditional_t<is_reference<__base_ref>::value,
     typename remove_reference<__base_ref>::type&&,
     __base_ref>;



      move_iterator()
      : _M_current() { }

      explicit
      move_iterator(iterator_type __i)
      : _M_current(std::move(__i)) { }

      template<typename _Iter>




 move_iterator(const move_iterator<_Iter>& __i)
 : _M_current(__i._M_current) { }

      template<typename _Iter>





 move_iterator& operator=(const move_iterator<_Iter>& __i)
 {
   _M_current = __i._M_current;
   return *this;
 }


      [[__nodiscard__]]
                           iterator_type
      base() const
      { return _M_current; }
# 1537 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
      [[__nodiscard__]]
                           reference
      operator*() const



      { return static_cast<reference>(*_M_current); }


      [[__nodiscard__]]
                           pointer
      operator->() const
      { return _M_current; }

                           move_iterator&
      operator++()
      {
 ++_M_current;
 return *this;
      }

                           move_iterator
      operator++(int)
      {
 move_iterator __tmp = *this;
 ++_M_current;
 return __tmp;
      }







                           move_iterator&
      operator--()
      {
 --_M_current;
 return *this;
      }

                           move_iterator
      operator--(int)
      {
 move_iterator __tmp = *this;
 --_M_current;
 return __tmp;
      }

      [[__nodiscard__]]
                           move_iterator
      operator+(difference_type __n) const
      { return move_iterator(_M_current + __n); }

                           move_iterator&
      operator+=(difference_type __n)
      {
 _M_current += __n;
 return *this;
      }

      [[__nodiscard__]]
                           move_iterator
      operator-(difference_type __n) const
      { return move_iterator(_M_current - __n); }

                           move_iterator&
      operator-=(difference_type __n)
      {
 _M_current -= __n;
 return *this;
      }

      [[__nodiscard__]]
                           reference
      operator[](difference_type __n) const



      { return std::move(_M_current[__n]); }
# 1651 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
    };

  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator==(const move_iterator<_IteratorL>& __x,
        const move_iterator<_IteratorR>& __y)



    { return __x.base() == __y.base(); }
# 1672 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator!=(const move_iterator<_IteratorL>& __x,
        const move_iterator<_IteratorR>& __y)
    { return !(__x == __y); }


  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator<(const move_iterator<_IteratorL>& __x,
       const move_iterator<_IteratorR>& __y)



    { return __x.base() < __y.base(); }

  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator<=(const move_iterator<_IteratorL>& __x,
        const move_iterator<_IteratorR>& __y)



    { return !(__y < __x); }

  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator>(const move_iterator<_IteratorL>& __x,
       const move_iterator<_IteratorR>& __y)



    { return __y < __x; }

  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline bool
    operator>=(const move_iterator<_IteratorL>& __x,
        const move_iterator<_IteratorR>& __y)



    { return !(__x < __y); }




  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator==(const move_iterator<_Iterator>& __x,
        const move_iterator<_Iterator>& __y)
    { return __x.base() == __y.base(); }
# 1738 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator!=(const move_iterator<_Iterator>& __x,
        const move_iterator<_Iterator>& __y)
    { return !(__x == __y); }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator<(const move_iterator<_Iterator>& __x,
       const move_iterator<_Iterator>& __y)
    { return __x.base() < __y.base(); }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator<=(const move_iterator<_Iterator>& __x,
        const move_iterator<_Iterator>& __y)
    { return !(__y < __x); }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator>(const move_iterator<_Iterator>& __x,
       const move_iterator<_Iterator>& __y)
    { return __y < __x; }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline bool
    operator>=(const move_iterator<_Iterator>& __x,
        const move_iterator<_Iterator>& __y)
    { return !(__x < __y); }



  template<typename _IteratorL, typename _IteratorR>
    [[__nodiscard__]]
    inline auto
    operator-(const move_iterator<_IteratorL>& __x,
       const move_iterator<_IteratorR>& __y)
    -> decltype(__x.base() - __y.base())
    { return __x.base() - __y.base(); }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline move_iterator<_Iterator>
    operator+(typename move_iterator<_Iterator>::difference_type __n,
       const move_iterator<_Iterator>& __x)
    { return __x + __n; }

  template<typename _Iterator>
    [[__nodiscard__]]
    inline move_iterator<_Iterator>
    make_move_iterator(_Iterator __i)
    { return move_iterator<_Iterator>(std::move(__i)); }

  template<typename _Iterator, typename _ReturnType
    = __conditional_t<__move_if_noexcept_cond
      <typename iterator_traits<_Iterator>::value_type>::value,
  _Iterator, move_iterator<_Iterator>>>
    inline _ReturnType
    __make_move_if_noexcept_iterator(_Iterator __i)
    { return _ReturnType(__i); }



  template<typename _Tp, typename _ReturnType
    = __conditional_t<__move_if_noexcept_cond<_Tp>::value,
        const _Tp*, move_iterator<_Tp*>>>
    inline _ReturnType
    __make_move_if_noexcept_iterator(_Tp* __i)
    { return _ReturnType(__i); }
# 2552 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
  template<typename _Iterator>

    auto
    __niter_base(move_iterator<_Iterator> __it)
    -> decltype(make_move_iterator(__niter_base(__it.base())))
    { return make_move_iterator(__niter_base(__it.base())); }

  template<typename _Iterator>
    struct __is_move_iterator<move_iterator<_Iterator> >
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<typename _Iterator>

    auto
    __miter_base(move_iterator<_Iterator> __it)
    -> decltype(__miter_base(__it.base()))
    { return __miter_base(__it.base()); }
# 2602 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_iterator.h" 3
}
# 68 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/debug/debug.h" 1 3
# 48 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/debug/debug.h" 3
namespace std
{
  namespace __debug { }
}




namespace __gnu_debug
{
  using namespace std::__debug;

  template<typename _Ite, typename _Seq, typename _Cat>
    struct _Safe_iterator;
}
# 70 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/predefined_ops.h" 1 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/predefined_ops.h" 3
namespace __gnu_cxx
{
namespace __ops
{
  struct _Iter_less_iter
  {
    template<typename _Iterator1, typename _Iterator2>

      bool
      operator()(_Iterator1 __it1, _Iterator2 __it2) const
      { return *__it1 < *__it2; }
  };


  inline _Iter_less_iter
  __iter_less_iter()
  { return _Iter_less_iter(); }

  struct _Iter_less_val
  {

    constexpr _Iter_less_val() = default;





    explicit
    _Iter_less_val(_Iter_less_iter) { }

    template<typename _Iterator, typename _Value>

      bool
      operator()(_Iterator __it, _Value& __val) const
      { return *__it < __val; }
  };


  inline _Iter_less_val
  __iter_less_val()
  { return _Iter_less_val(); }


  inline _Iter_less_val
  __iter_comp_val(_Iter_less_iter)
  { return _Iter_less_val(); }

  struct _Val_less_iter
  {

    constexpr _Val_less_iter() = default;





    explicit
    _Val_less_iter(_Iter_less_iter) { }

    template<typename _Value, typename _Iterator>

      bool
      operator()(_Value& __val, _Iterator __it) const
      { return __val < *__it; }
  };


  inline _Val_less_iter
  __val_less_iter()
  { return _Val_less_iter(); }


  inline _Val_less_iter
  __val_comp_iter(_Iter_less_iter)
  { return _Val_less_iter(); }

  struct _Iter_equal_to_iter
  {
    template<typename _Iterator1, typename _Iterator2>

      bool
      operator()(_Iterator1 __it1, _Iterator2 __it2) const
      { return *__it1 == *__it2; }
  };


  inline _Iter_equal_to_iter
  __iter_equal_to_iter()
  { return _Iter_equal_to_iter(); }

  struct _Iter_equal_to_val
  {
    template<typename _Iterator, typename _Value>

      bool
      operator()(_Iterator __it, _Value& __val) const
      { return *__it == __val; }
  };


  inline _Iter_equal_to_val
  __iter_equal_to_val()
  { return _Iter_equal_to_val(); }


  inline _Iter_equal_to_val
  __iter_comp_val(_Iter_equal_to_iter)
  { return _Iter_equal_to_val(); }

  template<typename _Compare>
    struct _Iter_comp_iter
    {
      _Compare _M_comp;

      explicit
      _Iter_comp_iter(_Compare __comp)
 : _M_comp(std::move(__comp))
      { }

      template<typename _Iterator1, typename _Iterator2>

        bool
        operator()(_Iterator1 __it1, _Iterator2 __it2)
        { return bool(_M_comp(*__it1, *__it2)); }
    };

  template<typename _Compare>

    inline _Iter_comp_iter<_Compare>
    __iter_comp_iter(_Compare __comp)
    { return _Iter_comp_iter<_Compare>(std::move(__comp)); }

  template<typename _Compare>
    struct _Iter_comp_val
    {
      _Compare _M_comp;


      explicit
      _Iter_comp_val(_Compare __comp)
 : _M_comp(std::move(__comp))
      { }


      explicit
      _Iter_comp_val(const _Iter_comp_iter<_Compare>& __comp)
 : _M_comp(__comp._M_comp)
      { }



      explicit
      _Iter_comp_val(_Iter_comp_iter<_Compare>&& __comp)
 : _M_comp(std::move(__comp._M_comp))
      { }


      template<typename _Iterator, typename _Value>

 bool
 operator()(_Iterator __it, _Value& __val)
 { return bool(_M_comp(*__it, __val)); }
    };

  template<typename _Compare>

    inline _Iter_comp_val<_Compare>
    __iter_comp_val(_Compare __comp)
    { return _Iter_comp_val<_Compare>(std::move(__comp)); }

  template<typename _Compare>

    inline _Iter_comp_val<_Compare>
    __iter_comp_val(_Iter_comp_iter<_Compare> __comp)
    { return _Iter_comp_val<_Compare>(std::move(__comp)); }

  template<typename _Compare>
    struct _Val_comp_iter
    {
      _Compare _M_comp;


      explicit
      _Val_comp_iter(_Compare __comp)
 : _M_comp(std::move(__comp))
      { }


      explicit
      _Val_comp_iter(const _Iter_comp_iter<_Compare>& __comp)
 : _M_comp(__comp._M_comp)
      { }



      explicit
      _Val_comp_iter(_Iter_comp_iter<_Compare>&& __comp)
 : _M_comp(std::move(__comp._M_comp))
      { }


      template<typename _Value, typename _Iterator>

 bool
 operator()(_Value& __val, _Iterator __it)
 { return bool(_M_comp(__val, *__it)); }
    };

  template<typename _Compare>

    inline _Val_comp_iter<_Compare>
    __val_comp_iter(_Compare __comp)
    { return _Val_comp_iter<_Compare>(std::move(__comp)); }

  template<typename _Compare>

    inline _Val_comp_iter<_Compare>
    __val_comp_iter(_Iter_comp_iter<_Compare> __comp)
    { return _Val_comp_iter<_Compare>(std::move(__comp)); }

  template<typename _Value>
    struct _Iter_equals_val
    {
      _Value& _M_value;


      explicit
      _Iter_equals_val(_Value& __value)
 : _M_value(__value)
      { }

      template<typename _Iterator>

 bool
 operator()(_Iterator __it)
 { return *__it == _M_value; }
    };

  template<typename _Value>

    inline _Iter_equals_val<_Value>
    __iter_equals_val(_Value& __val)
    { return _Iter_equals_val<_Value>(__val); }

  template<typename _Iterator1>
    struct _Iter_equals_iter
    {
      _Iterator1 _M_it1;


      explicit
      _Iter_equals_iter(_Iterator1 __it1)
 : _M_it1(__it1)
      { }

      template<typename _Iterator2>

 bool
 operator()(_Iterator2 __it2)
 { return *__it2 == *_M_it1; }
    };

  template<typename _Iterator>

    inline _Iter_equals_iter<_Iterator>
    __iter_comp_iter(_Iter_equal_to_iter, _Iterator __it)
    { return _Iter_equals_iter<_Iterator>(__it); }

  template<typename _Predicate>
    struct _Iter_pred
    {
      _Predicate _M_pred;


      explicit
      _Iter_pred(_Predicate __pred)
 : _M_pred(std::move(__pred))
      { }

      template<typename _Iterator>

 bool
 operator()(_Iterator __it)
 { return bool(_M_pred(*__it)); }
    };

  template<typename _Predicate>

    inline _Iter_pred<_Predicate>
    __pred_iter(_Predicate __pred)
    { return _Iter_pred<_Predicate>(std::move(__pred)); }

  template<typename _Compare, typename _Value>
    struct _Iter_comp_to_val
    {
      _Compare _M_comp;
      _Value& _M_value;


      _Iter_comp_to_val(_Compare __comp, _Value& __value)
 : _M_comp(std::move(__comp)), _M_value(__value)
      { }

      template<typename _Iterator>

 bool
 operator()(_Iterator __it)
 { return bool(_M_comp(*__it, _M_value)); }
    };

  template<typename _Compare, typename _Value>
    _Iter_comp_to_val<_Compare, _Value>

    __iter_comp_val(_Compare __comp, _Value &__val)
    {
      return _Iter_comp_to_val<_Compare, _Value>(std::move(__comp), __val);
    }

  template<typename _Compare, typename _Iterator1>
    struct _Iter_comp_to_iter
    {
      _Compare _M_comp;
      _Iterator1 _M_it1;


      _Iter_comp_to_iter(_Compare __comp, _Iterator1 __it1)
 : _M_comp(std::move(__comp)), _M_it1(__it1)
      { }

      template<typename _Iterator2>

 bool
 operator()(_Iterator2 __it2)
 { return bool(_M_comp(*__it2, *_M_it1)); }
    };

  template<typename _Compare, typename _Iterator>

    inline _Iter_comp_to_iter<_Compare, _Iterator>
    __iter_comp_iter(_Iter_comp_iter<_Compare> __comp, _Iterator __it)
    {
      return _Iter_comp_to_iter<_Compare, _Iterator>(
   std::move(__comp._M_comp), __it);
    }

  template<typename _Predicate>
    struct _Iter_negate
    {
      _Predicate _M_pred;


      explicit
      _Iter_negate(_Predicate __pred)
 : _M_pred(std::move(__pred))
      { }

      template<typename _Iterator>

 bool
 operator()(_Iterator __it)
 { return !bool(_M_pred(*__it)); }
    };

  template<typename _Predicate>

    inline _Iter_negate<_Predicate>
    __negate(_Iter_pred<_Predicate> __pred)
    { return _Iter_negate<_Predicate>(std::move(__pred._M_pred)); }

}
}
# 72 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 2 3







namespace std __attribute__ ((__visibility__ ("default")))
{






  template<typename _Tp, typename _Up>

    inline int
    __memcmp(const _Tp* __first1, const _Up* __first2, size_t __num)
    {

      static_assert(sizeof(_Tp) == sizeof(_Up), "can be compared with memcmp");
# 105 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
 return __builtin_memcmp(__first1, __first2, sizeof(_Tp) * __num);
    }
# 149 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2>

    inline void
    iter_swap(_ForwardIterator1 __a, _ForwardIterator2 __b)
    {
# 182 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
      swap(*__a, *__b);

    }
# 198 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2>

    _ForwardIterator2
    swap_ranges(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  _ForwardIterator2 __first2)
    {





                                                       ;

      for (; __first1 != __last1; ++__first1, (void)++__first2)
 std::iter_swap(__first1, __first2);
      return __first2;
    }
# 227 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _Tp>

    inline const _Tp&
    min(const _Tp& __a, const _Tp& __b)
    {



      if (__b < __a)
 return __b;
      return __a;
    }
# 251 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _Tp>

    inline const _Tp&
    max(const _Tp& __a, const _Tp& __b)
    {



      if (__a < __b)
 return __b;
      return __a;
    }
# 275 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _Tp, typename _Compare>

    inline const _Tp&
    min(const _Tp& __a, const _Tp& __b, _Compare __comp)
    {

      if (__comp(__b, __a))
 return __b;
      return __a;
    }
# 297 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _Tp, typename _Compare>

    inline const _Tp&
    max(const _Tp& __a, const _Tp& __b, _Compare __comp)
    {

      if (__comp(__a, __b))
 return __b;
      return __a;
    }



  template<typename _Iterator>

    inline _Iterator
    __niter_base(_Iterator __it)
    noexcept(std::is_nothrow_copy_constructible<_Iterator>::value)
    { return __it; }

  template<typename _Ite, typename _Seq>
    _Ite
    __niter_base(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq,
   std::random_access_iterator_tag>&);




  template<typename _From, typename _To>

    inline _From
    __niter_wrap(_From __from, _To __res)
    { return __from + (__res - std::__niter_base(__from)); }


  template<typename _Iterator>

    inline _Iterator
    __niter_wrap(const _Iterator&, _Iterator __res)
    { return __res; }







  template<bool _IsMove, bool _IsSimple, typename _Category>
    struct __copy_move
    {
      template<typename _II, typename _OI>

 static _OI
 __copy_m(_II __first, _II __last, _OI __result)
 {
   for (; __first != __last; ++__result, (void)++__first)
     *__result = *__first;
   return __result;
 }
    };


  template<typename _Category>
    struct __copy_move<true, false, _Category>
    {
      template<typename _II, typename _OI>

 static _OI
 __copy_m(_II __first, _II __last, _OI __result)
 {
   for (; __first != __last; ++__result, (void)++__first)
     *__result = std::move(*__first);
   return __result;
 }
    };


  template<>
    struct __copy_move<false, false, random_access_iterator_tag>
    {
      template<typename _II, typename _OI>

 static _OI
 __copy_m(_II __first, _II __last, _OI __result)
 {
   typedef typename iterator_traits<_II>::difference_type _Distance;
   for(_Distance __n = __last - __first; __n > 0; --__n)
     {
       *__result = *__first;
       ++__first;
       ++__result;
     }
   return __result;
 }
    };


  template<>
    struct __copy_move<true, false, random_access_iterator_tag>
    {
      template<typename _II, typename _OI>

 static _OI
 __copy_m(_II __first, _II __last, _OI __result)
 {
   typedef typename iterator_traits<_II>::difference_type _Distance;
   for(_Distance __n = __last - __first; __n > 0; --__n)
     {
       *__result = std::move(*__first);
       ++__first;
       ++__result;
     }
   return __result;
 }
    };


  template<bool _IsMove>
    struct __copy_move<_IsMove, true, random_access_iterator_tag>
    {
      template<typename _Tp>

 static _Tp*
 __copy_m(const _Tp* __first, const _Tp* __last, _Tp* __result)
 {

   using __assignable = __conditional_t<_IsMove,
            is_move_assignable<_Tp>,
            is_copy_assignable<_Tp>>;

   static_assert( __assignable::value, "type must be assignable" );

   const ptrdiff_t _Num = __last - __first;
   if (_Num)
     __builtin_memmove(__result, __first, sizeof(_Tp) * _Num);
   return __result + _Num;
 }
    };



  template<typename _Tp, typename _Ref, typename _Ptr>
    struct _Deque_iterator;

  struct _Bit_iterator;





  template<typename _CharT>
    struct char_traits;

  template<typename _CharT, typename _Traits>
    class istreambuf_iterator;

  template<typename _CharT, typename _Traits>
    class ostreambuf_iterator;

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
      ostreambuf_iterator<_CharT, char_traits<_CharT> > >::__type
    __copy_move_a2(_CharT*, _CharT*,
     ostreambuf_iterator<_CharT, char_traits<_CharT> >);

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
      ostreambuf_iterator<_CharT, char_traits<_CharT> > >::__type
    __copy_move_a2(const _CharT*, const _CharT*,
     ostreambuf_iterator<_CharT, char_traits<_CharT> >);

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        _CharT*>::__type
    __copy_move_a2(istreambuf_iterator<_CharT, char_traits<_CharT> >,
     istreambuf_iterator<_CharT, char_traits<_CharT> >, _CharT*);

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<
      __is_char<_CharT>::__value,
      std::_Deque_iterator<_CharT, _CharT&, _CharT*> >::__type
    __copy_move_a2(
 istreambuf_iterator<_CharT, char_traits<_CharT> >,
 istreambuf_iterator<_CharT, char_traits<_CharT> >,
 std::_Deque_iterator<_CharT, _CharT&, _CharT*>);

  template<bool _IsMove, typename _II, typename _OI>

    inline _OI
    __copy_move_a2(_II __first, _II __last, _OI __result)
    {
      typedef typename iterator_traits<_II>::iterator_category _Category;





      return std::__copy_move<_IsMove, __memcpyable<_OI, _II>::__value,
         _Category>::__copy_m(__first, __last, __result);
    }

  template<bool _IsMove,
    typename _Tp, typename _Ref, typename _Ptr, typename _OI>
    _OI
    __copy_move_a1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
     std::_Deque_iterator<_Tp, _Ref, _Ptr>,
     _OI);

  template<bool _IsMove,
    typename _ITp, typename _IRef, typename _IPtr, typename _OTp>
    std::_Deque_iterator<_OTp, _OTp&, _OTp*>
    __copy_move_a1(std::_Deque_iterator<_ITp, _IRef, _IPtr>,
     std::_Deque_iterator<_ITp, _IRef, _IPtr>,
     std::_Deque_iterator<_OTp, _OTp&, _OTp*>);

  template<bool _IsMove, typename _II, typename _Tp>
    typename __gnu_cxx::__enable_if<
      __is_random_access_iter<_II>::__value,
      std::_Deque_iterator<_Tp, _Tp&, _Tp*> >::__type
    __copy_move_a1(_II, _II, std::_Deque_iterator<_Tp, _Tp&, _Tp*>);

  template<bool _IsMove, typename _II, typename _OI>

    inline _OI
    __copy_move_a1(_II __first, _II __last, _OI __result)
    { return std::__copy_move_a2<_IsMove>(__first, __last, __result); }

  template<bool _IsMove, typename _II, typename _OI>

    inline _OI
    __copy_move_a(_II __first, _II __last, _OI __result)
    {
      return std::__niter_wrap(__result,
  std::__copy_move_a1<_IsMove>(std::__niter_base(__first),
          std::__niter_base(__last),
          std::__niter_base(__result)));
    }

  template<bool _IsMove,
    typename _Ite, typename _Seq, typename _Cat, typename _OI>
    _OI
    __copy_move_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
    const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
    _OI);

  template<bool _IsMove,
    typename _II, typename _Ite, typename _Seq, typename _Cat>
    __gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
    __copy_move_a(_II, _II,
    const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&);

  template<bool _IsMove,
    typename _IIte, typename _ISeq, typename _ICat,
    typename _OIte, typename _OSeq, typename _OCat>
    ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>
    __copy_move_a(const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
    const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
    const ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>&);

  template<typename _InputIterator, typename _Size, typename _OutputIterator>

    _OutputIterator
    __copy_n_a(_InputIterator __first, _Size __n, _OutputIterator __result,
        bool)
    {
      if (__n > 0)
 {
   while (true)
     {
       *__result = *__first;
       ++__result;
       if (--__n > 0)
  ++__first;
       else
  break;
     }
 }
      return __result;
    }

  template<typename _CharT, typename _Size>
    typename __gnu_cxx::__enable_if<
      __is_char<_CharT>::__value, _CharT*>::__type
    __copy_n_a(istreambuf_iterator<_CharT, char_traits<_CharT> >,
        _Size, _CharT*, bool);

  template<typename _CharT, typename _Size>
    typename __gnu_cxx::__enable_if<
      __is_char<_CharT>::__value,
      std::_Deque_iterator<_CharT, _CharT&, _CharT*> >::__type
    __copy_n_a(istreambuf_iterator<_CharT, char_traits<_CharT> >, _Size,
        std::_Deque_iterator<_CharT, _CharT&, _CharT*>,
        bool);
# 608 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _II, typename _OI>

    inline _OI
    copy(_II __first, _II __last, _OI __result)
    {




                                                                       ;

      return std::__copy_move_a<__is_move_iterator<_II>::__value>
      (std::__miter_base(__first), std::__miter_base(__last), __result);
    }
# 641 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _II, typename _OI>

    inline _OI
    move(_II __first, _II __last, _OI __result)
    {




                                                                       ;

      return std::__copy_move_a<true>(std::__miter_base(__first),
          std::__miter_base(__last), __result);
    }






  template<bool _IsMove, bool _IsSimple, typename _Category>
    struct __copy_move_backward
    {
      template<typename _BI1, typename _BI2>

 static _BI2
 __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
 {
   while (__first != __last)
     *--__result = *--__last;
   return __result;
 }
    };


  template<typename _Category>
    struct __copy_move_backward<true, false, _Category>
    {
      template<typename _BI1, typename _BI2>

 static _BI2
 __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
 {
   while (__first != __last)
     *--__result = std::move(*--__last);
   return __result;
 }
    };


  template<>
    struct __copy_move_backward<false, false, random_access_iterator_tag>
    {
      template<typename _BI1, typename _BI2>

 static _BI2
 __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
 {
   typename iterator_traits<_BI1>::difference_type
     __n = __last - __first;
   for (; __n > 0; --__n)
     *--__result = *--__last;
   return __result;
 }
    };


  template<>
    struct __copy_move_backward<true, false, random_access_iterator_tag>
    {
      template<typename _BI1, typename _BI2>

 static _BI2
 __copy_move_b(_BI1 __first, _BI1 __last, _BI2 __result)
 {
   typename iterator_traits<_BI1>::difference_type
     __n = __last - __first;
   for (; __n > 0; --__n)
     *--__result = std::move(*--__last);
   return __result;
 }
    };


  template<bool _IsMove>
    struct __copy_move_backward<_IsMove, true, random_access_iterator_tag>
    {
      template<typename _Tp>

 static _Tp*
 __copy_move_b(const _Tp* __first, const _Tp* __last, _Tp* __result)
 {

   using __assignable = __conditional_t<_IsMove,
            is_move_assignable<_Tp>,
            is_copy_assignable<_Tp>>;

   static_assert( __assignable::value, "type must be assignable" );

   const ptrdiff_t _Num = __last - __first;
   if (_Num)
     __builtin_memmove(__result - _Num, __first, sizeof(_Tp) * _Num);
   return __result - _Num;
 }
    };

  template<bool _IsMove, typename _BI1, typename _BI2>

    inline _BI2
    __copy_move_backward_a2(_BI1 __first, _BI1 __last, _BI2 __result)
    {
      typedef typename iterator_traits<_BI1>::iterator_category _Category;





      return std::__copy_move_backward<_IsMove,
           __memcpyable<_BI2, _BI1>::__value,
           _Category>::__copy_move_b(__first,
         __last,
         __result);
    }

  template<bool _IsMove, typename _BI1, typename _BI2>

    inline _BI2
    __copy_move_backward_a1(_BI1 __first, _BI1 __last, _BI2 __result)
    { return std::__copy_move_backward_a2<_IsMove>(__first, __last, __result); }

  template<bool _IsMove,
    typename _Tp, typename _Ref, typename _Ptr, typename _OI>
    _OI
    __copy_move_backward_a1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
       std::_Deque_iterator<_Tp, _Ref, _Ptr>,
       _OI);

  template<bool _IsMove,
    typename _ITp, typename _IRef, typename _IPtr, typename _OTp>
    std::_Deque_iterator<_OTp, _OTp&, _OTp*>
    __copy_move_backward_a1(
   std::_Deque_iterator<_ITp, _IRef, _IPtr>,
   std::_Deque_iterator<_ITp, _IRef, _IPtr>,
   std::_Deque_iterator<_OTp, _OTp&, _OTp*>);

  template<bool _IsMove, typename _II, typename _Tp>
    typename __gnu_cxx::__enable_if<
      __is_random_access_iter<_II>::__value,
      std::_Deque_iterator<_Tp, _Tp&, _Tp*> >::__type
    __copy_move_backward_a1(_II, _II,
       std::_Deque_iterator<_Tp, _Tp&, _Tp*>);

  template<bool _IsMove, typename _II, typename _OI>

    inline _OI
    __copy_move_backward_a(_II __first, _II __last, _OI __result)
    {
      return std::__niter_wrap(__result,
  std::__copy_move_backward_a1<_IsMove>
    (std::__niter_base(__first), std::__niter_base(__last),
     std::__niter_base(__result)));
    }

  template<bool _IsMove,
    typename _Ite, typename _Seq, typename _Cat, typename _OI>
    _OI
    __copy_move_backward_a(
  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
  _OI);

  template<bool _IsMove,
    typename _II, typename _Ite, typename _Seq, typename _Cat>
    __gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
    __copy_move_backward_a(_II, _II,
  const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&);

  template<bool _IsMove,
    typename _IIte, typename _ISeq, typename _ICat,
    typename _OIte, typename _OSeq, typename _OCat>
    ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>
    __copy_move_backward_a(
  const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
  const ::__gnu_debug::_Safe_iterator<_IIte, _ISeq, _ICat>&,
  const ::__gnu_debug::_Safe_iterator<_OIte, _OSeq, _OCat>&);
# 845 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _BI1, typename _BI2>

    inline _BI2
    copy_backward(_BI1 __first, _BI1 __last, _BI2 __result)
    {





                                                                       ;

      return std::__copy_move_backward_a<__is_move_iterator<_BI1>::__value>
      (std::__miter_base(__first), std::__miter_base(__last), __result);
    }
# 880 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _BI1, typename _BI2>

    inline _BI2
    move_backward(_BI1 __first, _BI1 __last, _BI2 __result)
    {





                                                                       ;

      return std::__copy_move_backward_a<true>(std::__miter_base(__first),
            std::__miter_base(__last),
            __result);
    }






  template<typename _ForwardIterator, typename _Tp>

    inline typename
    __gnu_cxx::__enable_if<!__is_scalar<_Tp>::__value, void>::__type
    __fill_a1(_ForwardIterator __first, _ForwardIterator __last,
       const _Tp& __value)
    {
      for (; __first != __last; ++__first)
 *__first = __value;
    }

  template<typename _ForwardIterator, typename _Tp>

    inline typename
    __gnu_cxx::__enable_if<__is_scalar<_Tp>::__value, void>::__type
    __fill_a1(_ForwardIterator __first, _ForwardIterator __last,
       const _Tp& __value)
    {
      const _Tp __tmp = __value;
      for (; __first != __last; ++__first)
 *__first = __tmp;
    }


  template<typename _Tp>

    inline typename
    __gnu_cxx::__enable_if<__is_byte<_Tp>::__value, void>::__type
    __fill_a1(_Tp* __first, _Tp* __last, const _Tp& __c)
    {
      const _Tp __tmp = __c;
# 941 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
      if (const size_t __len = __last - __first)
 __builtin_memset(__first, static_cast<unsigned char>(__tmp), __len);
    }

  template<typename _Ite, typename _Cont, typename _Tp>

    inline void
    __fill_a1(::__gnu_cxx::__normal_iterator<_Ite, _Cont> __first,
       ::__gnu_cxx::__normal_iterator<_Ite, _Cont> __last,
       const _Tp& __value)
    { std::__fill_a1(__first.base(), __last.base(), __value); }

  template<typename _Tp, typename _VTp>
    void
    __fill_a1(const std::_Deque_iterator<_Tp, _Tp&, _Tp*>&,
       const std::_Deque_iterator<_Tp, _Tp&, _Tp*>&,
       const _VTp&);


  void
  __fill_a1(std::_Bit_iterator, std::_Bit_iterator,
     const bool&);

  template<typename _FIte, typename _Tp>

    inline void
    __fill_a(_FIte __first, _FIte __last, const _Tp& __value)
    { std::__fill_a1(__first, __last, __value); }

  template<typename _Ite, typename _Seq, typename _Cat, typename _Tp>
    void
    __fill_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
      const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>&,
      const _Tp&);
# 988 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _ForwardIterator, typename _Tp>

    inline void
    fill(_ForwardIterator __first, _ForwardIterator __last, const _Tp& __value)
    {



                                                     ;

      std::__fill_a(__first, __last, __value);
    }


  inline constexpr int
  __size_to_integer(int __n) { return __n; }
  inline constexpr unsigned
  __size_to_integer(unsigned __n) { return __n; }
  inline constexpr long
  __size_to_integer(long __n) { return __n; }
  inline constexpr unsigned long
  __size_to_integer(unsigned long __n) { return __n; }
  inline constexpr long long
  __size_to_integer(long long __n) { return __n; }
  inline constexpr unsigned long long
  __size_to_integer(unsigned long long __n) { return __n; }
# 1040 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  inline constexpr long long
  __size_to_integer(float __n) { return (long long)__n; }
  inline constexpr long long
  __size_to_integer(double __n) { return (long long)__n; }
  inline constexpr long long
  __size_to_integer(long double __n) { return (long long)__n; }





  template<typename _OutputIterator, typename _Size, typename _Tp>

    inline typename
    __gnu_cxx::__enable_if<!__is_scalar<_Tp>::__value, _OutputIterator>::__type
    __fill_n_a1(_OutputIterator __first, _Size __n, const _Tp& __value)
    {
      for (; __n > 0; --__n, (void) ++__first)
 *__first = __value;
      return __first;
    }

  template<typename _OutputIterator, typename _Size, typename _Tp>

    inline typename
    __gnu_cxx::__enable_if<__is_scalar<_Tp>::__value, _OutputIterator>::__type
    __fill_n_a1(_OutputIterator __first, _Size __n, const _Tp& __value)
    {
      const _Tp __tmp = __value;
      for (; __n > 0; --__n, (void) ++__first)
 *__first = __tmp;
      return __first;
    }

  template<typename _Ite, typename _Seq, typename _Cat, typename _Size,
    typename _Tp>
    ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>
    __fill_n_a(const ::__gnu_debug::_Safe_iterator<_Ite, _Seq, _Cat>& __first,
        _Size __n, const _Tp& __value,
        std::input_iterator_tag);

  template<typename _OutputIterator, typename _Size, typename _Tp>

    inline _OutputIterator
    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
        std::output_iterator_tag)
    {

      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");

      return __fill_n_a1(__first, __n, __value);
    }

  template<typename _OutputIterator, typename _Size, typename _Tp>

    inline _OutputIterator
    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
        std::input_iterator_tag)
    {

      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");

      return __fill_n_a1(__first, __n, __value);
    }

  template<typename _OutputIterator, typename _Size, typename _Tp>

    inline _OutputIterator
    __fill_n_a(_OutputIterator __first, _Size __n, const _Tp& __value,
        std::random_access_iterator_tag)
    {

      static_assert(is_integral<_Size>{}, "fill_n must pass integral size");

      if (__n <= 0)
 return __first;

                                                    ;

      std::__fill_a(__first, __first + __n, __value);
      return __first + __n;
    }
# 1140 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _OI, typename _Size, typename _Tp>

    inline _OI
    fill_n(_OI __first, _Size __n, const _Tp& __value)
    {



      return std::__fill_n_a(__first, std::__size_to_integer(__n), __value,
          std::__iterator_category(__first));
    }

  template<bool _BoolType>
    struct __equal
    {
      template<typename _II1, typename _II2>

 static bool
 equal(_II1 __first1, _II1 __last1, _II2 __first2)
 {
   for (; __first1 != __last1; ++__first1, (void) ++__first2)
     if (!(*__first1 == *__first2))
       return false;
   return true;
 }
    };

  template<>
    struct __equal<true>
    {
      template<typename _Tp>

 static bool
 equal(const _Tp* __first1, const _Tp* __last1, const _Tp* __first2)
 {
   if (const size_t __len = (__last1 - __first1))
     return !std::__memcmp(__first1, __first2, __len);
   return true;
 }
    };

  template<typename _Tp, typename _Ref, typename _Ptr, typename _II>
    typename __gnu_cxx::__enable_if<
      __is_random_access_iter<_II>::__value, bool>::__type
    __equal_aux1(std::_Deque_iterator<_Tp, _Ref, _Ptr>,
   std::_Deque_iterator<_Tp, _Ref, _Ptr>,
   _II);

  template<typename _Tp1, typename _Ref1, typename _Ptr1,
    typename _Tp2, typename _Ref2, typename _Ptr2>
    bool
    __equal_aux1(std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
   std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
   std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);

  template<typename _II, typename _Tp, typename _Ref, typename _Ptr>
    typename __gnu_cxx::__enable_if<
      __is_random_access_iter<_II>::__value, bool>::__type
    __equal_aux1(_II, _II,
  std::_Deque_iterator<_Tp, _Ref, _Ptr>);

  template<typename _II1, typename _II2>

    inline bool
    __equal_aux1(_II1 __first1, _II1 __last1, _II2 __first2)
    {
      typedef typename iterator_traits<_II1>::value_type _ValueType1;
      const bool __simple = ((__is_integer<_ValueType1>::__value
         || __is_pointer<_ValueType1>::__value)
        && __memcmpable<_II1, _II2>::__value);
      return std::__equal<__simple>::equal(__first1, __last1, __first2);
    }

  template<typename _II1, typename _II2>

    inline bool
    __equal_aux(_II1 __first1, _II1 __last1, _II2 __first2)
    {
      return std::__equal_aux1(std::__niter_base(__first1),
          std::__niter_base(__last1),
          std::__niter_base(__first2));
    }

  template<typename _II1, typename _Seq1, typename _Cat1, typename _II2>
    bool
    __equal_aux(const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
  _II2);

  template<typename _II1, typename _II2, typename _Seq2, typename _Cat2>
    bool
    __equal_aux(_II1, _II1,
  const ::__gnu_debug::_Safe_iterator<_II2, _Seq2, _Cat2>&);

  template<typename _II1, typename _Seq1, typename _Cat1,
    typename _II2, typename _Seq2, typename _Cat2>
    bool
    __equal_aux(const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_II1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_II2, _Seq2, _Cat2>&);

  template<typename, typename>
    struct __lc_rai
    {
      template<typename _II1, typename _II2>

 static _II1
 __newlast1(_II1, _II1 __last1, _II2, _II2)
 { return __last1; }

      template<typename _II>

 static bool
 __cnd2(_II __first, _II __last)
 { return __first != __last; }
    };

  template<>
    struct __lc_rai<random_access_iterator_tag, random_access_iterator_tag>
    {
      template<typename _RAI1, typename _RAI2>

 static _RAI1
 __newlast1(_RAI1 __first1, _RAI1 __last1,
     _RAI2 __first2, _RAI2 __last2)
 {
   const typename iterator_traits<_RAI1>::difference_type
     __diff1 = __last1 - __first1;
   const typename iterator_traits<_RAI2>::difference_type
     __diff2 = __last2 - __first2;
   return __diff2 < __diff1 ? __first1 + __diff2 : __last1;
 }

      template<typename _RAI>
 static bool
 __cnd2(_RAI, _RAI)
 { return true; }
    };

  template<typename _II1, typename _II2, typename _Compare>

    bool
    __lexicographical_compare_impl(_II1 __first1, _II1 __last1,
       _II2 __first2, _II2 __last2,
       _Compare __comp)
    {
      typedef typename iterator_traits<_II1>::iterator_category _Category1;
      typedef typename iterator_traits<_II2>::iterator_category _Category2;
      typedef std::__lc_rai<_Category1, _Category2> __rai_type;

      __last1 = __rai_type::__newlast1(__first1, __last1, __first2, __last2);
      for (; __first1 != __last1 && __rai_type::__cnd2(__first2, __last2);
    ++__first1, (void)++__first2)
 {
   if (__comp(__first1, __first2))
     return true;
   if (__comp(__first2, __first1))
     return false;
 }
      return __first1 == __last1 && __first2 != __last2;
    }

  template<bool _BoolType>
    struct __lexicographical_compare
    {
      template<typename _II1, typename _II2>

 static bool
 __lc(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
 {
   using __gnu_cxx::__ops::__iter_less_iter;
   return std::__lexicographical_compare_impl(__first1, __last1,
           __first2, __last2,
           __iter_less_iter());
 }

      template<typename _II1, typename _II2>

 static int
 __3way(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
 {
   while (__first1 != __last1)
     {
       if (__first2 == __last2)
  return +1;
       if (*__first1 < *__first2)
  return -1;
       if (*__first2 < *__first1)
  return +1;
       ++__first1;
       ++__first2;
     }
   return int(__first2 == __last2) - 1;
 }
    };

  template<>
    struct __lexicographical_compare<true>
    {
      template<typename _Tp, typename _Up>

 static bool
 __lc(const _Tp* __first1, const _Tp* __last1,
      const _Up* __first2, const _Up* __last2)
 { return __3way(__first1, __last1, __first2, __last2) < 0; }

      template<typename _Tp, typename _Up>

 static ptrdiff_t
 __3way(const _Tp* __first1, const _Tp* __last1,
        const _Up* __first2, const _Up* __last2)
 {
   const size_t __len1 = __last1 - __first1;
   const size_t __len2 = __last2 - __first2;
   if (const size_t __len = std::min(__len1, __len2))
     if (int __result = std::__memcmp(__first1, __first2, __len))
       return __result;
   return ptrdiff_t(__len1 - __len2);
 }
    };

  template<typename _II1, typename _II2>

    inline bool
    __lexicographical_compare_aux1(_II1 __first1, _II1 __last1,
       _II2 __first2, _II2 __last2)
    {
      typedef typename iterator_traits<_II1>::value_type _ValueType1;
      typedef typename iterator_traits<_II2>::value_type _ValueType2;
      const bool __simple =
 (__is_memcmp_ordered_with<_ValueType1, _ValueType2>::__value
  && __is_pointer<_II1>::__value
  && __is_pointer<_II2>::__value







  );

      return std::__lexicographical_compare<__simple>::__lc(__first1, __last1,
           __first2, __last2);
    }

  template<typename _Tp1, typename _Ref1, typename _Ptr1,
    typename _Tp2>
    bool
    __lexicographical_compare_aux1(
 std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
 std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
 _Tp2*, _Tp2*);

  template<typename _Tp1,
    typename _Tp2, typename _Ref2, typename _Ptr2>
    bool
    __lexicographical_compare_aux1(_Tp1*, _Tp1*,
 std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>,
 std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);

  template<typename _Tp1, typename _Ref1, typename _Ptr1,
    typename _Tp2, typename _Ref2, typename _Ptr2>
    bool
    __lexicographical_compare_aux1(
 std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
 std::_Deque_iterator<_Tp1, _Ref1, _Ptr1>,
 std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>,
 std::_Deque_iterator<_Tp2, _Ref2, _Ptr2>);

  template<typename _II1, typename _II2>

    inline bool
    __lexicographical_compare_aux(_II1 __first1, _II1 __last1,
      _II2 __first2, _II2 __last2)
    {
      return std::__lexicographical_compare_aux1(std::__niter_base(__first1),
       std::__niter_base(__last1),
       std::__niter_base(__first2),
       std::__niter_base(__last2));
    }

  template<typename _Iter1, typename _Seq1, typename _Cat1,
    typename _II2>
    bool
    __lexicographical_compare_aux(
  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
  _II2, _II2);

  template<typename _II1,
    typename _Iter2, typename _Seq2, typename _Cat2>
    bool
    __lexicographical_compare_aux(
  _II1, _II1,
  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&,
  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&);

  template<typename _Iter1, typename _Seq1, typename _Cat1,
    typename _Iter2, typename _Seq2, typename _Cat2>
    bool
    __lexicographical_compare_aux(
  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_Iter1, _Seq1, _Cat1>&,
  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&,
  const ::__gnu_debug::_Safe_iterator<_Iter2, _Seq2, _Cat2>&);

  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    _ForwardIterator
    __lower_bound(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __val, _Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::difference_type
 _DistanceType;

      _DistanceType __len = std::distance(__first, __last);

      while (__len > 0)
 {
   _DistanceType __half = __len >> 1;
   _ForwardIterator __middle = __first;
   std::advance(__middle, __half);
   if (__comp(__middle, __val))
     {
       __first = __middle;
       ++__first;
       __len = __len - __half - 1;
     }
   else
     __len = __half;
 }
      return __first;
    }
# 1486 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _ForwardIterator, typename _Tp>

    inline _ForwardIterator
    lower_bound(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val)
    {




                                                                  ;

      return std::__lower_bound(__first, __last, __val,
    __gnu_cxx::__ops::__iter_less_val());
    }



  inline constexpr int
  __lg(int __n)
  { return (int)sizeof(int) * 8 - 1 - __builtin_clz(__n); }

  inline constexpr unsigned
  __lg(unsigned __n)
  { return (int)sizeof(int) * 8 - 1 - __builtin_clz(__n); }

  inline constexpr long
  __lg(long __n)
  { return (int)sizeof(long) * 8 - 1 - __builtin_clzl(__n); }

  inline constexpr unsigned long
  __lg(unsigned long __n)
  { return (int)sizeof(long) * 8 - 1 - __builtin_clzl(__n); }

  inline constexpr long long
  __lg(long long __n)
  { return (int)sizeof(long long) * 8 - 1 - __builtin_clzll(__n); }

  inline constexpr unsigned long long
  __lg(unsigned long long __n)
  { return (int)sizeof(long long) * 8 - 1 - __builtin_clzll(__n); }
# 1542 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _II1, typename _II2>

    inline bool
    equal(_II1 __first1, _II1 __last1, _II2 __first2)
    {






                                                                         ;

      return std::__equal_aux(__first1, __last1, __first2);
    }
# 1573 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _IIter1, typename _IIter2, typename _BinaryPredicate>

    inline bool
    equal(_IIter1 __first1, _IIter1 __last1,
   _IIter2 __first2, _BinaryPredicate __binary_pred)
    {



                                                       ;

      for (; __first1 != __last1; ++__first1, (void)++__first2)
 if (!bool(__binary_pred(*__first1, *__first2)))
   return false;
      return true;
    }



  template<typename _II1, typename _II2>

    inline bool
    __equal4(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2)
    {
      using _RATag = random_access_iterator_tag;
      using _Cat1 = typename iterator_traits<_II1>::iterator_category;
      using _Cat2 = typename iterator_traits<_II2>::iterator_category;
      using _RAIters = __and_<is_same<_Cat1, _RATag>, is_same<_Cat2, _RATag>>;
      if (_RAIters())
 {
   auto __d1 = std::distance(__first1, __last1);
   auto __d2 = std::distance(__first2, __last2);
   if (__d1 != __d2)
     return false;
   return std::equal(__first1, __last1, __first2);
 }

      for (; __first1 != __last1 && __first2 != __last2;
   ++__first1, (void)++__first2)
 if (!(*__first1 == *__first2))
   return false;
      return __first1 == __last1 && __first2 == __last2;
    }


  template<typename _II1, typename _II2, typename _BinaryPredicate>

    inline bool
    __equal4(_II1 __first1, _II1 __last1, _II2 __first2, _II2 __last2,
      _BinaryPredicate __binary_pred)
    {
      using _RATag = random_access_iterator_tag;
      using _Cat1 = typename iterator_traits<_II1>::iterator_category;
      using _Cat2 = typename iterator_traits<_II2>::iterator_category;
      using _RAIters = __and_<is_same<_Cat1, _RATag>, is_same<_Cat2, _RATag>>;
      if (_RAIters())
 {
   auto __d1 = std::distance(__first1, __last1);
   auto __d2 = std::distance(__first2, __last2);
   if (__d1 != __d2)
     return false;
   return std::equal(__first1, __last1, __first2,
           __binary_pred);
 }

      for (; __first1 != __last1 && __first2 != __last2;
   ++__first1, (void)++__first2)
 if (!bool(__binary_pred(*__first1, *__first2)))
   return false;
      return __first1 == __last1 && __first2 == __last2;
    }
# 1728 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _II1, typename _II2>

    inline bool
    lexicographical_compare(_II1 __first1, _II1 __last1,
       _II2 __first2, _II2 __last2)
    {
# 1743 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
                                                       ;
                                                       ;

      return std::__lexicographical_compare_aux(__first1, __last1,
      __first2, __last2);
    }
# 1763 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _II1, typename _II2, typename _Compare>

    inline bool
    lexicographical_compare(_II1 __first1, _II1 __last1,
       _II2 __first2, _II2 __last2, _Compare __comp)
    {



                                                       ;
                                                       ;

      return std::__lexicographical_compare_impl
 (__first1, __last1, __first2, __last2,
  __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 1875 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _BinaryPredicate>

    pair<_InputIterator1, _InputIterator2>
    __mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
        _InputIterator2 __first2, _BinaryPredicate __binary_pred)
    {
      while (__first1 != __last1 && __binary_pred(__first1, __first2))
 {
   ++__first1;
   ++__first2;
 }
      return pair<_InputIterator1, _InputIterator2>(__first1, __first2);
    }
# 1903 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _InputIterator1, typename _InputIterator2>

    inline pair<_InputIterator1, _InputIterator2>
    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
      _InputIterator2 __first2)
    {






                                                       ;

      return std::__mismatch(__first1, __last1, __first2,
        __gnu_cxx::__ops::__iter_equal_to_iter());
    }
# 1937 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _BinaryPredicate>

    inline pair<_InputIterator1, _InputIterator2>
    mismatch(_InputIterator1 __first1, _InputIterator1 __last1,
      _InputIterator2 __first2, _BinaryPredicate __binary_pred)
    {



                                                       ;

      return std::__mismatch(__first1, __last1, __first2,
 __gnu_cxx::__ops::__iter_comp_iter(__binary_pred));
    }
# 2044 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline _InputIterator
    __find_if(_InputIterator __first, _InputIterator __last,
       _Predicate __pred, input_iterator_tag)
    {
      while (__first != __last && !__pred(__first))
 ++__first;
      return __first;
    }


  template<typename _RandomAccessIterator, typename _Predicate>

    _RandomAccessIterator
    __find_if(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Predicate __pred, random_access_iterator_tag)
    {
      typename iterator_traits<_RandomAccessIterator>::difference_type
 __trip_count = (__last - __first) >> 2;

      for (; __trip_count > 0; --__trip_count)
 {
   if (__pred(__first))
     return __first;
   ++__first;

   if (__pred(__first))
     return __first;
   ++__first;

   if (__pred(__first))
     return __first;
   ++__first;

   if (__pred(__first))
     return __first;
   ++__first;
 }

      switch (__last - __first)
 {
 case 3:
   if (__pred(__first))
     return __first;
   ++__first;

 case 2:
   if (__pred(__first))
     return __first;
   ++__first;

 case 1:
   if (__pred(__first))
     return __first;
   ++__first;

 case 0:
 default:
   return __last;
 }
    }

  template<typename _Iterator, typename _Predicate>

    inline _Iterator
    __find_if(_Iterator __first, _Iterator __last, _Predicate __pred)
    {
      return __find_if(__first, __last, __pred,
         std::__iterator_category(__first));
    }

  template<typename _InputIterator, typename _Predicate>

    typename iterator_traits<_InputIterator>::difference_type
    __count_if(_InputIterator __first, _InputIterator __last, _Predicate __pred)
    {
      typename iterator_traits<_InputIterator>::difference_type __n = 0;
      for (; __first != __last; ++__first)
 if (__pred(__first))
   ++__n;
      return __n;
    }

  template<typename _ForwardIterator, typename _Predicate>

    _ForwardIterator
    __remove_if(_ForwardIterator __first, _ForwardIterator __last,
  _Predicate __pred)
    {
      __first = std::__find_if(__first, __last, __pred);
      if (__first == __last)
 return __first;
      _ForwardIterator __result = __first;
      ++__first;
      for (; __first != __last; ++__first)
 if (!__pred(__first))
   {
     *__result = std::move(*__first);
     ++__result;
   }
      return __result;
    }


  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    bool
    __is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
       _ForwardIterator2 __first2, _BinaryPredicate __pred)
    {


      for (; __first1 != __last1; ++__first1, (void)++__first2)
 if (!__pred(__first1, __first2))
   break;

      if (__first1 == __last1)
 return true;



      _ForwardIterator2 __last2 = __first2;
      std::advance(__last2, std::distance(__first1, __last1));
      for (_ForwardIterator1 __scan = __first1; __scan != __last1; ++__scan)
 {
   if (__scan != std::__find_if(__first1, __scan,
     __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan)))
     continue;

   auto __matches
     = std::__count_if(__first2, __last2,
   __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan));
   if (0 == __matches ||
       std::__count_if(__scan, __last1,
   __gnu_cxx::__ops::__iter_comp_iter(__pred, __scan))
       != __matches)
     return false;
 }
      return true;
    }
# 2199 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algobase.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2>

    inline bool
    is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
     _ForwardIterator2 __first2)
    {






                                                       ;

      return std::__is_permutation(__first1, __last1, __first2,
       __gnu_cxx::__ops::__iter_equal_to_iter());
    }



}
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/algorithm" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 3





# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/initializer_list" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/initializer_list" 3





#pragma GCC visibility push(default)



namespace std
{

  template<class _E>
    class initializer_list
    {
    public:
      typedef _E value_type;
      typedef const _E& reference;
      typedef const _E& const_reference;
      typedef size_t size_type;
      typedef const _E* iterator;
      typedef const _E* const_iterator;

    private:
      iterator _M_array;
      size_type _M_len;


      constexpr initializer_list(const_iterator __a, size_type __l)
      : _M_array(__a), _M_len(__l) { }

    public:
      constexpr initializer_list() noexcept
      : _M_array(0), _M_len(0) { }


      constexpr size_type
      size() const noexcept { return _M_len; }


      constexpr const_iterator
      begin() const noexcept { return _M_array; }


      constexpr const_iterator
      end() const noexcept { return begin() + size(); }
    };







  template<class _Tp>
    constexpr const _Tp*
    begin(initializer_list<_Tp> __ils) noexcept
    { return __ils.begin(); }







  template<class _Tp>
    constexpr const _Tp*
    end(initializer_list<_Tp> __ils) noexcept
    { return __ils.end(); }
}

#pragma GCC visibility pop
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 2 3


namespace std __attribute__ ((__visibility__ ("default")))
{
# 199 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 3
  template<typename _IIter, typename _Predicate>

    bool
    all_of(_IIter, _IIter, _Predicate);

  template<typename _IIter, typename _Predicate>

    bool
    any_of(_IIter, _IIter, _Predicate);


  template<typename _FIter, typename _Tp>

    bool
    binary_search(_FIter, _FIter, const _Tp&);

  template<typename _FIter, typename _Tp, typename _Compare>

    bool
    binary_search(_FIter, _FIter, const _Tp&, _Compare);
# 232 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 3
  template<typename _IIter, typename _OIter>

    _OIter
    copy(_IIter, _IIter, _OIter);

  template<typename _BIter1, typename _BIter2>

    _BIter2
    copy_backward(_BIter1, _BIter1, _BIter2);


  template<typename _IIter, typename _OIter, typename _Predicate>

    _OIter
    copy_if(_IIter, _IIter, _OIter, _Predicate);

  template<typename _IIter, typename _Size, typename _OIter>

    _OIter
    copy_n(_IIter, _Size, _OIter);





  template<typename _FIter, typename _Tp>

    pair<_FIter, _FIter>
    equal_range(_FIter, _FIter, const _Tp&);

  template<typename _FIter, typename _Tp, typename _Compare>

    pair<_FIter, _FIter>
    equal_range(_FIter, _FIter, const _Tp&, _Compare);

  template<typename _FIter, typename _Tp>

    void
    fill(_FIter, _FIter, const _Tp&);

  template<typename _OIter, typename _Size, typename _Tp>

    _OIter
    fill_n(_OIter, _Size, const _Tp&);



  template<typename _FIter1, typename _FIter2>

    _FIter1
    find_end(_FIter1, _FIter1, _FIter2, _FIter2);

  template<typename _FIter1, typename _FIter2, typename _BinaryPredicate>

    _FIter1
    find_end(_FIter1, _FIter1, _FIter2, _FIter2, _BinaryPredicate);





  template<typename _IIter, typename _Predicate>

    _IIter
    find_if_not(_IIter, _IIter, _Predicate);






  template<typename _IIter1, typename _IIter2>

    bool
    includes(_IIter1, _IIter1, _IIter2, _IIter2);

  template<typename _IIter1, typename _IIter2, typename _Compare>

    bool
    includes(_IIter1, _IIter1, _IIter2, _IIter2, _Compare);

  template<typename _BIter>
    void
    inplace_merge(_BIter, _BIter, _BIter);

  template<typename _BIter, typename _Compare>
    void
    inplace_merge(_BIter, _BIter, _BIter, _Compare);


  template<typename _RAIter>

    bool
    is_heap(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    bool
    is_heap(_RAIter, _RAIter, _Compare);

  template<typename _RAIter>

    _RAIter
    is_heap_until(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    _RAIter
    is_heap_until(_RAIter, _RAIter, _Compare);

  template<typename _IIter, typename _Predicate>

    bool
    is_partitioned(_IIter, _IIter, _Predicate);

  template<typename _FIter1, typename _FIter2>

    bool
    is_permutation(_FIter1, _FIter1, _FIter2);

  template<typename _FIter1, typename _FIter2,
    typename _BinaryPredicate>

    bool
    is_permutation(_FIter1, _FIter1, _FIter2, _BinaryPredicate);

  template<typename _FIter>

    bool
    is_sorted(_FIter, _FIter);

  template<typename _FIter, typename _Compare>

    bool
    is_sorted(_FIter, _FIter, _Compare);

  template<typename _FIter>

    _FIter
    is_sorted_until(_FIter, _FIter);

  template<typename _FIter, typename _Compare>

    _FIter
    is_sorted_until(_FIter, _FIter, _Compare);


  template<typename _FIter1, typename _FIter2>

    void
    iter_swap(_FIter1, _FIter2);

  template<typename _FIter, typename _Tp>

    _FIter
    lower_bound(_FIter, _FIter, const _Tp&);

  template<typename _FIter, typename _Tp, typename _Compare>

    _FIter
    lower_bound(_FIter, _FIter, const _Tp&, _Compare);

  template<typename _RAIter>

    void
    make_heap(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    make_heap(_RAIter, _RAIter, _Compare);

  template<typename _Tp>

    const _Tp&
    max(const _Tp&, const _Tp&);

  template<typename _Tp, typename _Compare>

    const _Tp&
    max(const _Tp&, const _Tp&, _Compare);




  template<typename _Tp>

    const _Tp&
    min(const _Tp&, const _Tp&);

  template<typename _Tp, typename _Compare>

    const _Tp&
    min(const _Tp&, const _Tp&, _Compare);




  template<typename _Tp>

    pair<const _Tp&, const _Tp&>
    minmax(const _Tp&, const _Tp&);

  template<typename _Tp, typename _Compare>

    pair<const _Tp&, const _Tp&>
    minmax(const _Tp&, const _Tp&, _Compare);

  template<typename _FIter>

    pair<_FIter, _FIter>
    minmax_element(_FIter, _FIter);

  template<typename _FIter, typename _Compare>

    pair<_FIter, _FIter>
    minmax_element(_FIter, _FIter, _Compare);

  template<typename _Tp>

    _Tp
    min(initializer_list<_Tp>);

  template<typename _Tp, typename _Compare>

    _Tp
    min(initializer_list<_Tp>, _Compare);

  template<typename _Tp>

    _Tp
    max(initializer_list<_Tp>);

  template<typename _Tp, typename _Compare>

    _Tp
    max(initializer_list<_Tp>, _Compare);

  template<typename _Tp>

    pair<_Tp, _Tp>
    minmax(initializer_list<_Tp>);

  template<typename _Tp, typename _Compare>

    pair<_Tp, _Tp>
    minmax(initializer_list<_Tp>, _Compare);




  template<typename _BIter>

    bool
    next_permutation(_BIter, _BIter);

  template<typename _BIter, typename _Compare>

    bool
    next_permutation(_BIter, _BIter, _Compare);


  template<typename _IIter, typename _Predicate>

    bool
    none_of(_IIter, _IIter, _Predicate);





  template<typename _IIter, typename _RAIter>

    _RAIter
    partial_sort_copy(_IIter, _IIter, _RAIter, _RAIter);

  template<typename _IIter, typename _RAIter, typename _Compare>

    _RAIter
    partial_sort_copy(_IIter, _IIter, _RAIter, _RAIter, _Compare);




  template<typename _IIter, typename _OIter1,
    typename _OIter2, typename _Predicate>

    pair<_OIter1, _OIter2>
    partition_copy(_IIter, _IIter, _OIter1, _OIter2, _Predicate);

  template<typename _FIter, typename _Predicate>

    _FIter
    partition_point(_FIter, _FIter, _Predicate);


  template<typename _RAIter>

    void
    pop_heap(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    pop_heap(_RAIter, _RAIter, _Compare);

  template<typename _BIter>

    bool
    prev_permutation(_BIter, _BIter);

  template<typename _BIter, typename _Compare>

    bool
    prev_permutation(_BIter, _BIter, _Compare);

  template<typename _RAIter>

    void
    push_heap(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    push_heap(_RAIter, _RAIter, _Compare);



  template<typename _FIter, typename _Tp>

    _FIter
    remove(_FIter, _FIter, const _Tp&);

  template<typename _FIter, typename _Predicate>

    _FIter
    remove_if(_FIter, _FIter, _Predicate);

  template<typename _IIter, typename _OIter, typename _Tp>

    _OIter
    remove_copy(_IIter, _IIter, _OIter, const _Tp&);

  template<typename _IIter, typename _OIter, typename _Predicate>

    _OIter
    remove_copy_if(_IIter, _IIter, _OIter, _Predicate);



  template<typename _IIter, typename _OIter, typename _Tp>

    _OIter
    replace_copy(_IIter, _IIter, _OIter, const _Tp&, const _Tp&);

  template<typename _Iter, typename _OIter, typename _Predicate, typename _Tp>

    _OIter
    replace_copy_if(_Iter, _Iter, _OIter, _Predicate, const _Tp&);



  template<typename _BIter>

    void
    reverse(_BIter, _BIter);

  template<typename _BIter, typename _OIter>

    _OIter
    reverse_copy(_BIter, _BIter, _OIter);

  inline namespace _V2
  {
    template<typename _FIter>

      _FIter
      rotate(_FIter, _FIter, _FIter);
  }

  template<typename _FIter, typename _OIter>

    _OIter
    rotate_copy(_FIter, _FIter, _FIter, _OIter);
# 625 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 3
  template<typename _RAIter, typename _UGenerator>
    void
    shuffle(_RAIter, _RAIter, _UGenerator&&);


  template<typename _RAIter>

    void
    sort_heap(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    sort_heap(_RAIter, _RAIter, _Compare);

  template<typename _BIter, typename _Predicate>
    _BIter
    stable_partition(_BIter, _BIter, _Predicate);
# 658 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/algorithmfwd.h" 3
  template<typename _FIter1, typename _FIter2>

    _FIter2
    swap_ranges(_FIter1, _FIter1, _FIter2);



  template<typename _FIter>

    _FIter
    unique(_FIter, _FIter);

  template<typename _FIter, typename _BinaryPredicate>

    _FIter
    unique(_FIter, _FIter, _BinaryPredicate);



  template<typename _FIter, typename _Tp>

    _FIter
    upper_bound(_FIter, _FIter, const _Tp&);

  template<typename _FIter, typename _Tp, typename _Compare>

    _FIter
    upper_bound(_FIter, _FIter, const _Tp&, _Compare);



  template<typename _FIter>

    _FIter
    adjacent_find(_FIter, _FIter);

  template<typename _FIter, typename _BinaryPredicate>

    _FIter
    adjacent_find(_FIter, _FIter, _BinaryPredicate);

  template<typename _IIter, typename _Tp>

    typename iterator_traits<_IIter>::difference_type
    count(_IIter, _IIter, const _Tp&);

  template<typename _IIter, typename _Predicate>

    typename iterator_traits<_IIter>::difference_type
    count_if(_IIter, _IIter, _Predicate);

  template<typename _IIter1, typename _IIter2>

    bool
    equal(_IIter1, _IIter1, _IIter2);

  template<typename _IIter1, typename _IIter2, typename _BinaryPredicate>

    bool
    equal(_IIter1, _IIter1, _IIter2, _BinaryPredicate);

  template<typename _IIter, typename _Tp>

    _IIter
    find(_IIter, _IIter, const _Tp&);

  template<typename _FIter1, typename _FIter2>

    _FIter1
    find_first_of(_FIter1, _FIter1, _FIter2, _FIter2);

  template<typename _FIter1, typename _FIter2, typename _BinaryPredicate>

    _FIter1
    find_first_of(_FIter1, _FIter1, _FIter2, _FIter2, _BinaryPredicate);

  template<typename _IIter, typename _Predicate>

    _IIter
    find_if(_IIter, _IIter, _Predicate);

  template<typename _IIter, typename _Funct>

    _Funct
    for_each(_IIter, _IIter, _Funct);

  template<typename _FIter, typename _Generator>

    void
    generate(_FIter, _FIter, _Generator);

  template<typename _OIter, typename _Size, typename _Generator>

    _OIter
    generate_n(_OIter, _Size, _Generator);

  template<typename _IIter1, typename _IIter2>

    bool
    lexicographical_compare(_IIter1, _IIter1, _IIter2, _IIter2);

  template<typename _IIter1, typename _IIter2, typename _Compare>

    bool
    lexicographical_compare(_IIter1, _IIter1, _IIter2, _IIter2, _Compare);

  template<typename _FIter>

    _FIter
    max_element(_FIter, _FIter);

  template<typename _FIter, typename _Compare>

    _FIter
    max_element(_FIter, _FIter, _Compare);

  template<typename _IIter1, typename _IIter2, typename _OIter>

    _OIter
    merge(_IIter1, _IIter1, _IIter2, _IIter2, _OIter);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _Compare>

    _OIter
    merge(_IIter1, _IIter1, _IIter2, _IIter2, _OIter, _Compare);

  template<typename _FIter>

    _FIter
    min_element(_FIter, _FIter);

  template<typename _FIter, typename _Compare>

    _FIter
    min_element(_FIter, _FIter, _Compare);

  template<typename _IIter1, typename _IIter2>

    pair<_IIter1, _IIter2>
    mismatch(_IIter1, _IIter1, _IIter2);

  template<typename _IIter1, typename _IIter2, typename _BinaryPredicate>

    pair<_IIter1, _IIter2>
    mismatch(_IIter1, _IIter1, _IIter2, _BinaryPredicate);

  template<typename _RAIter>

    void
    nth_element(_RAIter, _RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    nth_element(_RAIter, _RAIter, _RAIter, _Compare);

  template<typename _RAIter>

    void
    partial_sort(_RAIter, _RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    partial_sort(_RAIter, _RAIter, _RAIter, _Compare);

  template<typename _BIter, typename _Predicate>

    _BIter
    partition(_BIter, _BIter, _Predicate);

  template<typename _RAIter>
    void
    random_shuffle(_RAIter, _RAIter);

  template<typename _RAIter, typename _Generator>
    void
    random_shuffle(_RAIter, _RAIter,

     _Generator&&);




  template<typename _FIter, typename _Tp>

    void
    replace(_FIter, _FIter, const _Tp&, const _Tp&);

  template<typename _FIter, typename _Predicate, typename _Tp>

    void
    replace_if(_FIter, _FIter, _Predicate, const _Tp&);

  template<typename _FIter1, typename _FIter2>

    _FIter1
    search(_FIter1, _FIter1, _FIter2, _FIter2);

  template<typename _FIter1, typename _FIter2, typename _BinaryPredicate>

    _FIter1
    search(_FIter1, _FIter1, _FIter2, _FIter2, _BinaryPredicate);

  template<typename _FIter, typename _Size, typename _Tp>

    _FIter
    search_n(_FIter, _FIter, _Size, const _Tp&);

  template<typename _FIter, typename _Size, typename _Tp,
    typename _BinaryPredicate>

    _FIter
    search_n(_FIter, _FIter, _Size, const _Tp&, _BinaryPredicate);

  template<typename _IIter1, typename _IIter2, typename _OIter>

    _OIter
    set_difference(_IIter1, _IIter1, _IIter2, _IIter2, _OIter);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _Compare>

    _OIter
    set_difference(_IIter1, _IIter1, _IIter2, _IIter2, _OIter, _Compare);

  template<typename _IIter1, typename _IIter2, typename _OIter>

    _OIter
    set_intersection(_IIter1, _IIter1, _IIter2, _IIter2, _OIter);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _Compare>

    _OIter
    set_intersection(_IIter1, _IIter1, _IIter2, _IIter2, _OIter, _Compare);

  template<typename _IIter1, typename _IIter2, typename _OIter>

    _OIter
    set_symmetric_difference(_IIter1, _IIter1, _IIter2, _IIter2, _OIter);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _Compare>

    _OIter
    set_symmetric_difference(_IIter1, _IIter1, _IIter2, _IIter2,
        _OIter, _Compare);

  template<typename _IIter1, typename _IIter2, typename _OIter>

    _OIter
    set_union(_IIter1, _IIter1, _IIter2, _IIter2, _OIter);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _Compare>

    _OIter
    set_union(_IIter1, _IIter1, _IIter2, _IIter2, _OIter, _Compare);

  template<typename _RAIter>

    void
    sort(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>

    void
    sort(_RAIter, _RAIter, _Compare);

  template<typename _RAIter>
    void
    stable_sort(_RAIter, _RAIter);

  template<typename _RAIter, typename _Compare>
    void
    stable_sort(_RAIter, _RAIter, _Compare);

  template<typename _IIter, typename _OIter, typename _UnaryOperation>

    _OIter
    transform(_IIter, _IIter, _OIter, _UnaryOperation);

  template<typename _IIter1, typename _IIter2, typename _OIter,
    typename _BinaryOperation>

    _OIter
    transform(_IIter1, _IIter1, _IIter2, _OIter, _BinaryOperation);

  template<typename _IIter, typename _OIter>

    _OIter
    unique_copy(_IIter, _IIter, _OIter);

  template<typename _IIter, typename _OIter, typename _BinaryPredicate>

    _OIter
    unique_copy(_IIter, _IIter, _OIter, _BinaryPredicate);



}
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 1 3
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{







  template<typename _RandomAccessIterator, typename _Distance,
    typename _Compare>

    _Distance
    __is_heap_until(_RandomAccessIterator __first, _Distance __n,
      _Compare& __comp)
    {
      _Distance __parent = 0;
      for (_Distance __child = 1; __child < __n; ++__child)
 {
   if (__comp(__first + __parent, __first + __child))
     return __child;
   if ((__child & 1) == 0)
     ++__parent;
 }
      return __n;
    }



  template<typename _RandomAccessIterator, typename _Distance>

    inline bool
    __is_heap(_RandomAccessIterator __first, _Distance __n)
    {
      __gnu_cxx::__ops::_Iter_less_iter __comp;
      return std::__is_heap_until(__first, __n, __comp) == __n;
    }

  template<typename _RandomAccessIterator, typename _Compare,
    typename _Distance>

    inline bool
    __is_heap(_RandomAccessIterator __first, _Compare __comp, _Distance __n)
    {
      typedef __decltype(__comp) _Cmp;
      __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
      return std::__is_heap_until(__first, __n, __cmp) == __n;
    }

  template<typename _RandomAccessIterator>

    inline bool
    __is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    { return std::__is_heap(__first, std::distance(__first, __last)); }

  template<typename _RandomAccessIterator, typename _Compare>

    inline bool
    __is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Compare __comp)
    {
      return std::__is_heap(__first, std::move(__comp),
       std::distance(__first, __last));
    }




  template<typename _RandomAccessIterator, typename _Distance, typename _Tp,
    typename _Compare>

    void
    __push_heap(_RandomAccessIterator __first,
  _Distance __holeIndex, _Distance __topIndex, _Tp __value,
  _Compare& __comp)
    {
      _Distance __parent = (__holeIndex - 1) / 2;
      while (__holeIndex > __topIndex && __comp(__first + __parent, __value))
 {
   *(__first + __holeIndex) = std::move(*(__first + __parent));
   __holeIndex = __parent;
   __parent = (__holeIndex - 1) / 2;
 }
      *(__first + __holeIndex) = std::move(__value);
    }
# 159 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline void
    push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
   _ValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
   _DistanceType;





                                                     ;
                                                     ;
                                                  ;

      __gnu_cxx::__ops::_Iter_less_val __comp;
      _ValueType __value = std::move(*(__last - 1));
      std::__push_heap(__first, _DistanceType((__last - __first) - 1),
         _DistanceType(0), std::move(__value), __comp);
    }
# 195 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
   _ValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
   _DistanceType;




                                                     ;
                                                                  ;
                                                               ;

      __decltype(__gnu_cxx::__ops::__iter_comp_val(std::move(__comp)))
 __cmp(std::move(__comp));
      _ValueType __value = std::move(*(__last - 1));
      std::__push_heap(__first, _DistanceType((__last - __first) - 1),
         _DistanceType(0), std::move(__value), __cmp);
    }

  template<typename _RandomAccessIterator, typename _Distance,
    typename _Tp, typename _Compare>

    void
    __adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
    _Distance __len, _Tp __value, _Compare __comp)
    {
      const _Distance __topIndex = __holeIndex;
      _Distance __secondChild = __holeIndex;
      while (__secondChild < (__len - 1) / 2)
 {
   __secondChild = 2 * (__secondChild + 1);
   if (__comp(__first + __secondChild,
       __first + (__secondChild - 1)))
     __secondChild--;
   *(__first + __holeIndex) = std::move(*(__first + __secondChild));
   __holeIndex = __secondChild;
 }
      if ((__len & 1) == 0 && __secondChild == (__len - 2) / 2)
 {
   __secondChild = 2 * (__secondChild + 1);
   *(__first + __holeIndex) = std::move(*(__first + (__secondChild - 1)));

   __holeIndex = __secondChild - 1;
 }
      __decltype(__gnu_cxx::__ops::__iter_comp_val(std::move(__comp)))
 __cmp(std::move(__comp));
      std::__push_heap(__first, __holeIndex, __topIndex,
         std::move(__value), __cmp);
    }

  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    __pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
        _RandomAccessIterator __result, _Compare& __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
 _ValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
 _DistanceType;

      _ValueType __value = std::move(*__result);
      *__result = std::move(*__first);
      std::__adjust_heap(__first, _DistanceType(0),
    _DistanceType(__last - __first),
    std::move(__value), __comp);
    }
# 280 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline void
    pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                         ;
                                                     ;
                                                     ;
                                              ;

      if (__last - __first > 1)
 {
   --__last;
   __gnu_cxx::__ops::_Iter_less_iter __comp;
   std::__pop_heap(__first, __last, __last, __comp);
 }
    }
# 314 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    pop_heap(_RandomAccessIterator __first,
      _RandomAccessIterator __last, _Compare __comp)
    {



                                                     ;
                                                                  ;
                                                         ;
                                                           ;

      if (__last - __first > 1)
 {
   typedef __decltype(__comp) _Cmp;
   __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
   --__last;
   std::__pop_heap(__first, __last, __last, __cmp);
 }
    }

  template<typename _RandomAccessIterator, typename _Compare>

    void
    __make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
  _Compare& __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
   _ValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
   _DistanceType;

      if (__last - __first < 2)
 return;

      const _DistanceType __len = __last - __first;
      _DistanceType __parent = (__len - 2) / 2;
      while (true)
 {
   _ValueType __value = std::move(*(__first + __parent));
   std::__adjust_heap(__first, __parent, __len, std::move(__value),
        __comp);
   if (__parent == 0)
     return;
   __parent--;
 }
    }
# 372 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline void
    make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                     ;
                                                     ;

      __gnu_cxx::__ops::_Iter_less_iter __comp;
      std::__make_heap(__first, __last, __comp);
    }
# 399 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Compare __comp)
    {



                                                     ;
                                                                  ;

      typedef __decltype(__comp) _Cmp;
      __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
      std::__make_heap(__first, __last, __cmp);
    }

  template<typename _RandomAccessIterator, typename _Compare>

    void
    __sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
  _Compare& __comp)
    {
      while (__last - __first > 1)
 {
   --__last;
   std::__pop_heap(__first, __last, __last, __comp);
 }
    }
# 437 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline void
    sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                     ;
                                                     ;
                                              ;

      __gnu_cxx::__ops::_Iter_less_iter __comp;
      std::__sort_heap(__first, __last, __comp);
    }
# 465 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
       _Compare __comp)
    {



                                                     ;
                                                                  ;
                                                           ;

      typedef __decltype(__comp) _Cmp;
      __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
      std::__sort_heap(__first, __last, __cmp);
    }
# 494 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline _RandomAccessIterator
    is_heap_until(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                     ;
                                                     ;

      __gnu_cxx::__ops::_Iter_less_iter __comp;
      return __first +
 std::__is_heap_until(__first, std::distance(__first, __last), __comp);
    }
# 523 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline _RandomAccessIterator
    is_heap_until(_RandomAccessIterator __first, _RandomAccessIterator __last,
    _Compare __comp)
    {



                                                     ;
                                                                  ;

      typedef __decltype(__comp) _Cmp;
      __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
      return __first
 + std::__is_heap_until(__first, std::distance(__first, __last), __cmp);
    }
# 548 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator>

    inline bool
    is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
    { return std::is_heap_until(__first, __last) == __last; }
# 562 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_heap.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline bool
    is_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
     _Compare __comp)
    {



                                                     ;
                                                                  ;

      const auto __dist = std::distance(__first, __last);
      typedef __decltype(__comp) _Cmp;
      __gnu_cxx::__ops::_Iter_comp_iter<_Cmp> __cmp(std::move(__comp));
      return std::__is_heap_until(__first, __dist, __cmp) == __dist;
    }



}
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 1 3
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/new" 1 3
# 27 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/new" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 1 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception.h" 1 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception.h" 3

#pragma GCC visibility push(default)



extern "C++" {

namespace std
{
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception.h" 3
  class exception
  {
  public:
    exception() noexcept { }
    virtual ~exception() noexcept;

    exception(const exception&) = default;
    exception& operator=(const exception&) = default;
    exception(exception&&) = default;
    exception& operator=(exception&&) = default;




    virtual const char*
    what() const noexcept;
  };



}

}

#pragma GCC visibility pop
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 2 3

#pragma GCC visibility push(default)

extern "C++" {

namespace std
{






  class bad_alloc : public exception
  {
  public:
    bad_alloc() throw() { }


    bad_alloc(const bad_alloc&) = default;
    bad_alloc& operator=(const bad_alloc&) = default;




    virtual ~bad_alloc() throw();


    virtual const char* what() const throw();
  };


  class bad_array_new_length : public bad_alloc
  {
  public:
    bad_array_new_length() throw() { }



    virtual ~bad_array_new_length() throw();


    virtual const char* what() const throw();
  };






  struct nothrow_t
  {

    explicit nothrow_t() = default;

  };

  extern const nothrow_t nothrow;



  typedef void (*new_handler)();



  new_handler set_new_handler(new_handler) throw();



  new_handler get_new_handler() noexcept;

}
# 126 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 3
                   void* operator new(std::size_t)
  __attribute__((__externally_visible__));
                   void* operator new[](std::size_t)
  __attribute__((__externally_visible__));
void operator delete(void*) noexcept
  __attribute__((__externally_visible__));
void operator delete[](void*) noexcept
  __attribute__((__externally_visible__));






                   void* operator new(std::size_t, const std::nothrow_t&) noexcept
  __attribute__((__externally_visible__, __alloc_size__ (1), __malloc__));
                   void* operator new[](std::size_t, const std::nothrow_t&) noexcept
  __attribute__((__externally_visible__, __alloc_size__ (1), __malloc__));
void operator delete(void*, const std::nothrow_t&) noexcept
  __attribute__((__externally_visible__));
void operator delete[](void*, const std::nothrow_t&) noexcept
  __attribute__((__externally_visible__));
# 174 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 3
                   inline void* operator new(std::size_t, void* __p) noexcept
{ return __p; }
                   inline void* operator new[](std::size_t, void* __p) noexcept
{ return __p; }


inline void operator delete (void*, void*) noexcept { }
inline void operator delete[](void*, void*) noexcept { }

}
# 236 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/new" 3
#pragma GCC visibility pop
# 28 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/new" 2 3
# 44 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/new" 3
__attribute__((device)) inline void *operator new(long unsigned int size) {
  if (size == 0) {
    size = 1;
  }
  return ::malloc(size);
}
__attribute__((device)) inline void *operator new(long unsigned int size,
                                     const std::nothrow_t &) noexcept {
  return ::operator new(size);
}

__attribute__((device)) inline void *operator new[](long unsigned int size) {
  return ::operator new(size);
}
__attribute__((device)) inline void *operator new[](long unsigned int size,
                                       const std::nothrow_t &) {
  return ::operator new(size);
}

__attribute__((device)) inline void operator delete(void* ptr) noexcept {
  if (ptr) {
    ::free(ptr);
  }
}
__attribute__((device)) inline void operator delete(void *ptr,
                                       const std::nothrow_t &) noexcept {
  ::operator delete(ptr);
}

__attribute__((device)) inline void operator delete[](void* ptr) noexcept {
  ::operator delete(ptr);
}
__attribute__((device)) inline void operator delete[](void *ptr,
                                         const std::nothrow_t &) noexcept {
  ::operator delete(ptr);
}
# 94 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/new" 3
__attribute__((device)) inline void *operator new(long unsigned int, void *__ptr) noexcept {
  return __ptr;
}
__attribute__((device)) inline void *operator new[](long unsigned int, void *__ptr) noexcept {
  return __ptr;
}
__attribute__((device)) inline void operator delete(void *, void *) noexcept {}
__attribute__((device)) inline void operator delete[](void *, void *) noexcept {}
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 2 3
# 73 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 106 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
  template<typename _Tp, typename... _Args>

    inline void
    _Construct(_Tp* __p, _Args&&... __args)
    {
# 119 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
      ::new((void*)__p) _Tp(std::forward<_Args>(__args)...);
    }
# 132 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
  template<typename _T1>
    inline void
    _Construct_novalue(_T1* __p)
    { ::new((void*)__p) _T1; }

  template<typename _ForwardIterator>
                         void
    _Destroy(_ForwardIterator __first, _ForwardIterator __last);




  template<typename _Tp>
                         inline void
    _Destroy(_Tp* __pointer)
    {



      __pointer->~_Tp();

    }

  template<bool>
    struct _Destroy_aux
    {
      template<typename _ForwardIterator>
 static void
 __destroy(_ForwardIterator __first, _ForwardIterator __last)
 {
   for (; __first != __last; ++__first)
     std::_Destroy(std::__addressof(*__first));
 }
    };

  template<>
    struct _Destroy_aux<true>
    {
      template<typename _ForwardIterator>
        static void
        __destroy(_ForwardIterator, _ForwardIterator) { }
    };






  template<typename _ForwardIterator>
                         inline void
    _Destroy(_ForwardIterator __first, _ForwardIterator __last)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
                       _Value_type;


      static_assert(is_destructible<_Value_type>::value,
      "value type is destructible");





      std::_Destroy_aux<__has_trivial_destructor(_Value_type)>::
 __destroy(__first, __last);
    }

  template<bool>
    struct _Destroy_n_aux
    {
      template<typename _ForwardIterator, typename _Size>
 static _ForwardIterator
 __destroy_n(_ForwardIterator __first, _Size __count)
 {
   for (; __count > 0; (void)++__first, --__count)
     std::_Destroy(std::__addressof(*__first));
   return __first;
 }
    };

  template<>
    struct _Destroy_n_aux<true>
    {
      template<typename _ForwardIterator, typename _Size>
        static _ForwardIterator
        __destroy_n(_ForwardIterator __first, _Size __count)
 {
   std::advance(__first, __count);
   return __first;
 }
    };






  template<typename _ForwardIterator, typename _Size>
                         inline _ForwardIterator
    _Destroy_n(_ForwardIterator __first, _Size __count)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
                       _Value_type;


      static_assert(is_destructible<_Value_type>::value,
      "value type is destructible");





      return std::_Destroy_n_aux<__has_trivial_destructor(_Value_type)>::
 __destroy_n(__first, __count);
    }
# 265 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_construct.h" 3
}
# 61 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  namespace __detail
  {
    template<typename _Tp>
      inline void
      __return_temporary_buffer(_Tp* __p,
    size_t __len __attribute__((__unused__)))
      {



 ::operator delete(__p);

      }
  }
# 98 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 3
  template<typename _Tp>

    pair<_Tp*, ptrdiff_t>
    get_temporary_buffer(ptrdiff_t __len) noexcept
    {
      const ptrdiff_t __max =
 __gnu_cxx::__numeric_traits<ptrdiff_t>::__max / sizeof(_Tp);
      if (__len > __max)
 __len = __max;

      while (__len > 0)
 {
   _Tp* __tmp = static_cast<_Tp*>(::operator new(__len * sizeof(_Tp),
       std::nothrow));
   if (__tmp != 0)
     return std::pair<_Tp*, ptrdiff_t>(__tmp, __len);
   __len = __len == 1 ? 0 : ((__len + 1) / 2);
 }
      return std::pair<_Tp*, ptrdiff_t>(static_cast<_Tp*>(0), 0);
    }
# 126 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 3
  template<typename _Tp>
    inline void
    return_temporary_buffer(_Tp* __p)
    { ::operator delete(__p); }






  template<typename _ForwardIterator, typename _Tp>
    class _Temporary_buffer
    {



    public:
      typedef _Tp value_type;
      typedef value_type* pointer;
      typedef pointer iterator;
      typedef ptrdiff_t size_type;

    protected:
      size_type _M_original_len;
      size_type _M_len;
      pointer _M_buffer;

    public:

      size_type
      size() const
      { return _M_len; }


      size_type
      requested_size() const
      { return _M_original_len; }


      iterator
      begin()
      { return _M_buffer; }


      iterator
      end()
      { return _M_buffer + _M_len; }





      _Temporary_buffer(_ForwardIterator __seed, size_type __original_len);

      ~_Temporary_buffer()
      {
 std::_Destroy(_M_buffer, _M_buffer + _M_len);
 std::__detail::__return_temporary_buffer(_M_buffer, _M_len);
      }

    private:

      _Temporary_buffer(const _Temporary_buffer&);

      void
      operator=(const _Temporary_buffer&);
    };


  template<bool>
    struct __uninitialized_construct_buf_dispatch
    {
      template<typename _Pointer, typename _ForwardIterator>
        static void
        __ucr(_Pointer __first, _Pointer __last,
       _ForwardIterator __seed)
        {
   if (__first == __last)
     return;

   _Pointer __cur = __first;
   try
     {
       std::_Construct(std::__addressof(*__first),
         std::move(*__seed));
       _Pointer __prev = __cur;
       ++__cur;
       for(; __cur != __last; ++__cur, ++__prev)
  std::_Construct(std::__addressof(*__cur),
    std::move(*__prev));
       *__seed = std::move(*__prev);
     }
   catch(...)
     {
       std::_Destroy(__first, __cur);
       throw;
     }
 }
    };

  template<>
    struct __uninitialized_construct_buf_dispatch<true>
    {
      template<typename _Pointer, typename _ForwardIterator>
        static void
        __ucr(_Pointer, _Pointer, _ForwardIterator) { }
    };
# 244 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_tempbuf.h" 3
  template<typename _Pointer, typename _ForwardIterator>
    inline void
    __uninitialized_construct_buf(_Pointer __first, _Pointer __last,
      _ForwardIterator __seed)
    {
      typedef typename std::iterator_traits<_Pointer>::value_type
 _ValueType;

      std::__uninitialized_construct_buf_dispatch<
        __has_trivial_constructor(_ValueType)>::
   __ucr(__first, __last, __seed);
    }

  template<typename _ForwardIterator, typename _Tp>
    _Temporary_buffer<_ForwardIterator, _Tp>::
    _Temporary_buffer(_ForwardIterator __seed, size_type __original_len)
    : _M_original_len(__original_len), _M_len(0), _M_buffer(0)
    {
      std::pair<pointer, size_type> __p(
  std::get_temporary_buffer<value_type>(_M_original_len));

      if (__p.first)
 {
   try
     {
       std::__uninitialized_construct_buf(__p.first, __p.first + __p.second,
       __seed);
       _M_buffer = __p.first;
       _M_len = __p.second;
     }
   catch(...)
     {
       std::__detail::__return_temporary_buffer(__p.first, __p.second);
       throw;
     }
 }
    }


}
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 2 3



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/uniform_int_dist.h" 1 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/uniform_int_dist.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 58 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/uniform_int_dist.h" 3
  namespace __detail
  {



    template<typename _Tp>
      constexpr bool
      _Power_of_2(_Tp __x)
      {
 return ((__x - 1) & __x) == 0;
      }
  }






  template<typename _IntType = int>
    class uniform_int_distribution
    {
      static_assert(std::is_integral<_IntType>::value,
      "template argument must be an integral type");

    public:

      typedef _IntType result_type;

      struct param_type
      {
 typedef uniform_int_distribution<_IntType> distribution_type;

 param_type() : param_type(0) { }

 explicit
 param_type(_IntType __a,
     _IntType __b = __gnu_cxx::__int_traits<_IntType>::__max)
 : _M_a(__a), _M_b(__b)
 {
   do { if (std::__is_constant_evaluated() && !bool(_M_a <= _M_b)) __builtin_unreachable(); } while (false);
 }

 result_type
 a() const
 { return _M_a; }

 result_type
 b() const
 { return _M_b; }

 friend bool
 operator==(const param_type& __p1, const param_type& __p2)
 { return __p1._M_a == __p2._M_a && __p1._M_b == __p2._M_b; }

 friend bool
 operator!=(const param_type& __p1, const param_type& __p2)
 { return !(__p1 == __p2); }

      private:
 _IntType _M_a;
 _IntType _M_b;
      };

    public:



      uniform_int_distribution() : uniform_int_distribution(0) { }




      explicit
      uniform_int_distribution(_IntType __a,
          _IntType __b
     = __gnu_cxx::__int_traits<_IntType>::__max)
      : _M_param(__a, __b)
      { }

      explicit
      uniform_int_distribution(const param_type& __p)
      : _M_param(__p)
      { }






      void
      reset() { }

      result_type
      a() const
      { return _M_param.a(); }

      result_type
      b() const
      { return _M_param.b(); }




      param_type
      param() const
      { return _M_param; }





      void
      param(const param_type& __param)
      { _M_param = __param; }




      result_type
      min() const
      { return this->a(); }




      result_type
      max() const
      { return this->b(); }




      template<typename _UniformRandomBitGenerator>
 result_type
 operator()(_UniformRandomBitGenerator& __urng)
        { return this->operator()(__urng, _M_param); }

      template<typename _UniformRandomBitGenerator>
 result_type
 operator()(_UniformRandomBitGenerator& __urng,
     const param_type& __p);

      template<typename _ForwardIterator,
        typename _UniformRandomBitGenerator>
 void
 __generate(_ForwardIterator __f, _ForwardIterator __t,
     _UniformRandomBitGenerator& __urng)
 { this->__generate(__f, __t, __urng, _M_param); }

      template<typename _ForwardIterator,
        typename _UniformRandomBitGenerator>
 void
 __generate(_ForwardIterator __f, _ForwardIterator __t,
     _UniformRandomBitGenerator& __urng,
     const param_type& __p)
 { this->__generate_impl(__f, __t, __urng, __p); }

      template<typename _UniformRandomBitGenerator>
 void
 __generate(result_type* __f, result_type* __t,
     _UniformRandomBitGenerator& __urng,
     const param_type& __p)
 { this->__generate_impl(__f, __t, __urng, __p); }





      friend bool
      operator==(const uniform_int_distribution& __d1,
   const uniform_int_distribution& __d2)
      { return __d1._M_param == __d2._M_param; }

    private:
      template<typename _ForwardIterator,
        typename _UniformRandomBitGenerator>
 void
 __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
   _UniformRandomBitGenerator& __urng,
   const param_type& __p);

      param_type _M_param;




      template<typename _Wp, typename _Urbg, typename _Up>
 static _Up
 _S_nd(_Urbg& __g, _Up __range)
 {
   using _Up_traits = __gnu_cxx::__int_traits<_Up>;
   using _Wp_traits = __gnu_cxx::__int_traits<_Wp>;
   static_assert(!_Up_traits::__is_signed, "U must be unsigned");
   static_assert(!_Wp_traits::__is_signed, "W must be unsigned");
   static_assert(_Wp_traits::__digits == (2 * _Up_traits::__digits),
   "W must be twice as wide as U");




   _Wp __product = _Wp(__g()) * _Wp(__range);
   _Up __low = _Up(__product);
   if (__low < __range)
     {
       _Up __threshold = -__range % __range;
       while (__low < __threshold)
  {
    __product = _Wp(__g()) * _Wp(__range);
    __low = _Up(__product);
  }
     }
   return __product >> _Up_traits::__digits;
 }
    };

  template<typename _IntType>
    template<typename _UniformRandomBitGenerator>
      typename uniform_int_distribution<_IntType>::result_type
      uniform_int_distribution<_IntType>::
      operator()(_UniformRandomBitGenerator& __urng,
   const param_type& __param)
      {
 typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
 typedef typename make_unsigned<result_type>::type __utype;
 typedef typename common_type<_Gresult_type, __utype>::type __uctype;

 constexpr __uctype __urngmin = _UniformRandomBitGenerator::min();
 constexpr __uctype __urngmax = _UniformRandomBitGenerator::max();
 static_assert( __urngmin < __urngmax,
     "Uniform random bit generator must define min() < max()");
 constexpr __uctype __urngrange = __urngmax - __urngmin;

 const __uctype __urange
   = __uctype(__param.b()) - __uctype(__param.a());

 __uctype __ret;
 if (__urngrange > __urange)
   {


     const __uctype __uerange = __urange + 1;



     if (__urngrange == 18446744073709551615UL)
       {


  long unsigned int __u64erange = __uerange;
  __ret = __extension__ _S_nd<unsigned __int128>(__urng,
              __u64erange);
       }
     else

     if (__urngrange == 4294967295U)
       {


  unsigned int __u32erange = __uerange;
  __ret = _S_nd<long unsigned int>(__urng, __u32erange);
       }
     else

       {

  const __uctype __scaling = __urngrange / __uerange;
  const __uctype __past = __uerange * __scaling;
  do
    __ret = __uctype(__urng()) - __urngmin;
  while (__ret >= __past);
  __ret /= __scaling;
       }
   }
 else if (__urngrange < __urange)
   {
# 348 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/uniform_int_dist.h" 3
     __uctype __tmp;
     do
       {
  const __uctype __uerngrange = __urngrange + 1;
  __tmp = (__uerngrange * operator()
    (__urng, param_type(0, __urange / __uerngrange)));
  __ret = __tmp + (__uctype(__urng()) - __urngmin);
       }
     while (__ret > __urange || __ret < __tmp);
   }
 else
   __ret = __uctype(__urng()) - __urngmin;

 return __ret + __param.a();
      }


  template<typename _IntType>
    template<typename _ForwardIterator,
      typename _UniformRandomBitGenerator>
      void
      uniform_int_distribution<_IntType>::
      __generate_impl(_ForwardIterator __f, _ForwardIterator __t,
        _UniformRandomBitGenerator& __urng,
        const param_type& __param)
      {

 typedef typename _UniformRandomBitGenerator::result_type _Gresult_type;
 typedef typename make_unsigned<result_type>::type __utype;
 typedef typename common_type<_Gresult_type, __utype>::type __uctype;

 static_assert( __urng.min() < __urng.max(),
     "Uniform random bit generator must define min() < max()");

 constexpr __uctype __urngmin = __urng.min();
 constexpr __uctype __urngmax = __urng.max();
 constexpr __uctype __urngrange = __urngmax - __urngmin;
 const __uctype __urange
   = __uctype(__param.b()) - __uctype(__param.a());

 __uctype __ret;

 if (__urngrange > __urange)
   {
     if (__detail::_Power_of_2(__urngrange + 1)
  && __detail::_Power_of_2(__urange + 1))
       {
  while (__f != __t)
    {
      __ret = __uctype(__urng()) - __urngmin;
      *__f++ = (__ret & __urange) + __param.a();
    }
       }
     else
       {

  const __uctype __uerange = __urange + 1;
  const __uctype __scaling = __urngrange / __uerange;
  const __uctype __past = __uerange * __scaling;
  while (__f != __t)
    {
      do
        __ret = __uctype(__urng()) - __urngmin;
      while (__ret >= __past);
      *__f++ = __ret / __scaling + __param.a();
    }
       }
   }
 else if (__urngrange < __urange)
   {
# 433 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/uniform_int_dist.h" 3
     __uctype __tmp;
     while (__f != __t)
       {
  do
    {
      constexpr __uctype __uerngrange = __urngrange + 1;
      __tmp = (__uerngrange * operator()
        (__urng, param_type(0, __urange / __uerngrange)));
      __ret = __tmp + (__uctype(__urng()) - __urngmin);
    }
  while (__ret > __urange || __ret < __tmp);
  *__f++ = __ret;
       }
   }
 else
   while (__f != __t)
     *__f++ = __uctype(__urng()) - __urngmin + __param.a();
      }




}
# 66 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 2 3



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
# 70 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 2 3




namespace std __attribute__ ((__visibility__ ("default")))
{



  template<typename _Iterator, typename _Compare>

    void
    __move_median_to_first(_Iterator __result,_Iterator __a, _Iterator __b,
      _Iterator __c, _Compare __comp)
    {
      if (__comp(__a, __b))
 {
   if (__comp(__b, __c))
     std::iter_swap(__result, __b);
   else if (__comp(__a, __c))
     std::iter_swap(__result, __c);
   else
     std::iter_swap(__result, __a);
 }
      else if (__comp(__a, __c))
 std::iter_swap(__result, __a);
      else if (__comp(__b, __c))
 std::iter_swap(__result, __c);
      else
 std::iter_swap(__result, __b);
    }


  template<typename _InputIterator, typename _Predicate>

    inline _InputIterator
    __find_if_not(_InputIterator __first, _InputIterator __last,
    _Predicate __pred)
    {
      return std::__find_if(__first, __last,
       __gnu_cxx::__ops::__negate(__pred),
       std::__iterator_category(__first));
    }




  template<typename _InputIterator, typename _Predicate, typename _Distance>

    _InputIterator
    __find_if_not_n(_InputIterator __first, _Distance& __len, _Predicate __pred)
    {
      for (; __len; --__len, (void) ++__first)
 if (!__pred(__first))
   break;
      return __first;
    }
# 141 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    _ForwardIterator1
    __search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
      _ForwardIterator2 __first2, _ForwardIterator2 __last2,
      _BinaryPredicate __predicate)
    {

      if (__first1 == __last1 || __first2 == __last2)
 return __first1;


      _ForwardIterator2 __p1(__first2);
      if (++__p1 == __last2)
 return std::__find_if(__first1, __last1,
  __gnu_cxx::__ops::__iter_comp_iter(__predicate, __first2));


      _ForwardIterator1 __current = __first1;

      for (;;)
 {
   __first1 =
     std::__find_if(__first1, __last1,
  __gnu_cxx::__ops::__iter_comp_iter(__predicate, __first2));

   if (__first1 == __last1)
     return __last1;

   _ForwardIterator2 __p = __p1;
   __current = __first1;
   if (++__current == __last1)
     return __last1;

   while (__predicate(__current, __p))
     {
       if (++__p == __last2)
  return __first1;
       if (++__current == __last1)
  return __last1;
     }
   ++__first1;
 }
      return __first1;
    }






  template<typename _ForwardIterator, typename _Integer,
    typename _UnaryPredicate>

    _ForwardIterator
    __search_n_aux(_ForwardIterator __first, _ForwardIterator __last,
     _Integer __count, _UnaryPredicate __unary_pred,
     std::forward_iterator_tag)
    {
      __first = std::__find_if(__first, __last, __unary_pred);
      while (__first != __last)
 {
   typename iterator_traits<_ForwardIterator>::difference_type
     __n = __count;
   _ForwardIterator __i = __first;
   ++__i;
   while (__i != __last && __n != 1 && __unary_pred(__i))
     {
       ++__i;
       --__n;
     }
   if (__n == 1)
     return __first;
   if (__i == __last)
     return __last;
   __first = std::__find_if(++__i, __last, __unary_pred);
 }
      return __last;
    }





  template<typename _RandomAccessIter, typename _Integer,
    typename _UnaryPredicate>

    _RandomAccessIter
    __search_n_aux(_RandomAccessIter __first, _RandomAccessIter __last,
     _Integer __count, _UnaryPredicate __unary_pred,
     std::random_access_iterator_tag)
    {
      typedef typename std::iterator_traits<_RandomAccessIter>::difference_type
 _DistanceType;

      _DistanceType __tailSize = __last - __first;
      _DistanceType __remainder = __count;

      while (__remainder <= __tailSize)
 {
   __first += __remainder;
   __tailSize -= __remainder;


   _RandomAccessIter __backTrack = __first;
   while (__unary_pred(--__backTrack))
     {
       if (--__remainder == 0)
  return (__first - __count);
     }
   __remainder = __count + 1 - (__first - __backTrack);
 }
      return __last;
    }

  template<typename _ForwardIterator, typename _Integer,
    typename _UnaryPredicate>

    _ForwardIterator
    __search_n(_ForwardIterator __first, _ForwardIterator __last,
        _Integer __count,
        _UnaryPredicate __unary_pred)
    {
      if (__count <= 0)
 return __first;

      if (__count == 1)
 return std::__find_if(__first, __last, __unary_pred);

      return std::__search_n_aux(__first, __last, __count, __unary_pred,
     std::__iterator_category(__first));
    }


  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    _ForwardIterator1
    __find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
        _ForwardIterator2 __first2, _ForwardIterator2 __last2,
        forward_iterator_tag, forward_iterator_tag,
        _BinaryPredicate __comp)
    {
      if (__first2 == __last2)
 return __last1;

      _ForwardIterator1 __result = __last1;
      while (1)
 {
   _ForwardIterator1 __new_result
     = std::__search(__first1, __last1, __first2, __last2, __comp);
   if (__new_result == __last1)
     return __result;
   else
     {
       __result = __new_result;
       __first1 = __new_result;
       ++__first1;
     }
 }
    }


  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
    typename _BinaryPredicate>

    _BidirectionalIterator1
    __find_end(_BidirectionalIterator1 __first1,
        _BidirectionalIterator1 __last1,
        _BidirectionalIterator2 __first2,
        _BidirectionalIterator2 __last2,
        bidirectional_iterator_tag, bidirectional_iterator_tag,
        _BinaryPredicate __comp)
    {






      typedef reverse_iterator<_BidirectionalIterator1> _RevIterator1;
      typedef reverse_iterator<_BidirectionalIterator2> _RevIterator2;

      _RevIterator1 __rlast1(__first1);
      _RevIterator2 __rlast2(__first2);
      _RevIterator1 __rresult = std::__search(_RevIterator1(__last1), __rlast1,
           _RevIterator2(__last2), __rlast2,
           __comp);

      if (__rresult == __rlast1)
 return __last1;
      else
 {
   _BidirectionalIterator1 __result = __rresult.base();
   std::advance(__result, -std::distance(__first2, __last2));
   return __result;
 }
    }
# 367 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2>

    inline _ForwardIterator1
    find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
      _ForwardIterator2 __first2, _ForwardIterator2 __last2)
    {






                                                       ;
                                                       ;

      return std::__find_end(__first1, __last1, __first2, __last2,
        std::__iterator_category(__first1),
        std::__iterator_category(__first2),
        __gnu_cxx::__ops::__iter_equal_to_iter());
    }
# 416 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    inline _ForwardIterator1
    find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
      _ForwardIterator2 __first2, _ForwardIterator2 __last2,
      _BinaryPredicate __comp)
    {






                                                       ;
                                                       ;

      return std::__find_end(__first1, __last1, __first2, __last2,
        std::__iterator_category(__first1),
        std::__iterator_category(__first2),
        __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 452 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline bool
    all_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
    { return __last == std::find_if_not(__first, __last, __pred); }
# 470 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline bool
    none_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
    { return __last == std::find_if(__first, __last, __pred); }
# 489 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline bool
    any_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
    { return !std::none_of(__first, __last, __pred); }
# 505 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline _InputIterator
    find_if_not(_InputIterator __first, _InputIterator __last,
  _Predicate __pred)
    {




                                                     ;
      return std::__find_if_not(__first, __last,
    __gnu_cxx::__ops::__pred_iter(__pred));
    }
# 530 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline bool
    is_partitioned(_InputIterator __first, _InputIterator __last,
     _Predicate __pred)
    {
      __first = std::find_if_not(__first, __last, __pred);
      if (__first == __last)
 return true;
      ++__first;
      return std::none_of(__first, __last, __pred);
    }
# 552 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Predicate>

    _ForwardIterator
    partition_point(_ForwardIterator __first, _ForwardIterator __last,
      _Predicate __pred)
    {






                                                     ;

      typedef typename iterator_traits<_ForwardIterator>::difference_type
 _DistanceType;

      _DistanceType __len = std::distance(__first, __last);

      while (__len > 0)
 {
   _DistanceType __half = __len >> 1;
   _ForwardIterator __middle = __first;
   std::advance(__middle, __half);
   if (__pred(*__middle))
     {
       __first = __middle;
       ++__first;
       __len = __len - __half - 1;
     }
   else
     __len = __half;
 }
      return __first;
    }


  template<typename _InputIterator, typename _OutputIterator,
    typename _Predicate>

    _OutputIterator
    __remove_copy_if(_InputIterator __first, _InputIterator __last,
       _OutputIterator __result, _Predicate __pred)
    {
      for (; __first != __last; ++__first)
 if (!__pred(__first))
   {
     *__result = *__first;
     ++__result;
   }
      return __result;
    }
# 619 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator, typename _Tp>

    inline _OutputIterator
    remove_copy(_InputIterator __first, _InputIterator __last,
  _OutputIterator __result, const _Tp& __value)
    {






                                                     ;

      return std::__remove_copy_if(__first, __last, __result,
 __gnu_cxx::__ops::__iter_equals_val(__value));
    }
# 652 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator,
    typename _Predicate>

    inline _OutputIterator
    remove_copy_if(_InputIterator __first, _InputIterator __last,
     _OutputIterator __result, _Predicate __pred)
    {






                                                     ;

      return std::__remove_copy_if(__first, __last, __result,
       __gnu_cxx::__ops::__pred_iter(__pred));
    }
# 687 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator,
    typename _Predicate>

    _OutputIterator
    copy_if(_InputIterator __first, _InputIterator __last,
     _OutputIterator __result, _Predicate __pred)
    {






                                                     ;

      for (; __first != __last; ++__first)
 if (__pred(*__first))
   {
     *__result = *__first;
     ++__result;
   }
      return __result;
    }

  template<typename _InputIterator, typename _Size, typename _OutputIterator>

    _OutputIterator
    __copy_n(_InputIterator __first, _Size __n,
      _OutputIterator __result, input_iterator_tag)
    {
      return std::__niter_wrap(__result,
          __copy_n_a(__first, __n,
       std::__niter_base(__result), true));
    }

  template<typename _RandomAccessIterator, typename _Size,
    typename _OutputIterator>

    inline _OutputIterator
    __copy_n(_RandomAccessIterator __first, _Size __n,
      _OutputIterator __result, random_access_iterator_tag)
    { return std::copy(__first, __first + __n, __result); }
# 743 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Size, typename _OutputIterator>

    inline _OutputIterator
    copy_n(_InputIterator __first, _Size __n, _OutputIterator __result)
    {





      const auto __n2 = std::__size_to_integer(__n);
      if (__n2 <= 0)
 return __result;

                                                     ;
                                                      ;

      return std::__copy_n(__first, __n2, __result,
      std::__iterator_category(__first));
    }
# 779 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator1,
    typename _OutputIterator2, typename _Predicate>

    pair<_OutputIterator1, _OutputIterator2>
    partition_copy(_InputIterator __first, _InputIterator __last,
     _OutputIterator1 __out_true, _OutputIterator2 __out_false,
     _Predicate __pred)
    {
# 795 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                     ;

      for (; __first != __last; ++__first)
 if (__pred(*__first))
   {
     *__out_true = *__first;
     ++__out_true;
   }
 else
   {
     *__out_false = *__first;
     ++__out_false;
   }

      return pair<_OutputIterator1, _OutputIterator2>(__out_true, __out_false);
    }
# 830 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp>

    inline _ForwardIterator
    remove(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __value)
    {





                                                     ;

      return std::__remove_if(__first, __last,
  __gnu_cxx::__ops::__iter_equals_val(__value));
    }
# 864 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Predicate>

    inline _ForwardIterator
    remove_if(_ForwardIterator __first, _ForwardIterator __last,
       _Predicate __pred)
    {





                                                     ;

      return std::__remove_if(__first, __last,
         __gnu_cxx::__ops::__pred_iter(__pred));
    }

  template<typename _ForwardIterator, typename _BinaryPredicate>

    _ForwardIterator
    __adjacent_find(_ForwardIterator __first, _ForwardIterator __last,
      _BinaryPredicate __binary_pred)
    {
      if (__first == __last)
 return __last;
      _ForwardIterator __next = __first;
      while (++__next != __last)
 {
   if (__binary_pred(__first, __next))
     return __first;
   __first = __next;
 }
      return __last;
    }

  template<typename _ForwardIterator, typename _BinaryPredicate>

    _ForwardIterator
    __unique(_ForwardIterator __first, _ForwardIterator __last,
      _BinaryPredicate __binary_pred)
    {

      __first = std::__adjacent_find(__first, __last, __binary_pred);
      if (__first == __last)
 return __last;


      _ForwardIterator __dest = __first;
      ++__first;
      while (++__first != __last)
 if (!__binary_pred(__dest, __first))
   *++__dest = std::move(*__first);
      return ++__dest;
    }
# 933 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline _ForwardIterator
    unique(_ForwardIterator __first, _ForwardIterator __last)
    {





                                                     ;

      return std::__unique(__first, __last,
      __gnu_cxx::__ops::__iter_equal_to_iter());
    }
# 964 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _BinaryPredicate>

    inline _ForwardIterator
    unique(_ForwardIterator __first, _ForwardIterator __last,
    _BinaryPredicate __binary_pred)
    {






                                                     ;

      return std::__unique(__first, __last,
      __gnu_cxx::__ops::__iter_comp_iter(__binary_pred));
    }







  template<typename _ForwardIterator, typename _OutputIterator,
    typename _BinaryPredicate>

    _OutputIterator
    __unique_copy(_ForwardIterator __first, _ForwardIterator __last,
    _OutputIterator __result, _BinaryPredicate __binary_pred,
    forward_iterator_tag, output_iterator_tag)
    {





      _ForwardIterator __next = __first;
      *__result = *__first;
      while (++__next != __last)
 if (!__binary_pred(__first, __next))
   {
     __first = __next;
     *++__result = *__first;
   }
      return ++__result;
    }







  template<typename _InputIterator, typename _OutputIterator,
    typename _BinaryPredicate>

    _OutputIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
    _OutputIterator __result, _BinaryPredicate __binary_pred,
    input_iterator_tag, output_iterator_tag)
    {





      typename iterator_traits<_InputIterator>::value_type __value = *__first;
      __decltype(__gnu_cxx::__ops::__iter_comp_val(__binary_pred))
 __rebound_pred
 = __gnu_cxx::__ops::__iter_comp_val(__binary_pred);
      *__result = __value;
      while (++__first != __last)
 if (!__rebound_pred(__first, __value))
   {
     __value = *__first;
     *++__result = __value;
   }
      return ++__result;
    }







  template<typename _InputIterator, typename _ForwardIterator,
    typename _BinaryPredicate>

    _ForwardIterator
    __unique_copy(_InputIterator __first, _InputIterator __last,
    _ForwardIterator __result, _BinaryPredicate __binary_pred,
    input_iterator_tag, forward_iterator_tag)
    {




      *__result = *__first;
      while (++__first != __last)
 if (!__binary_pred(__result, __first))
   *++__result = *__first;
      return ++__result;
    }






  template<typename _BidirectionalIterator>

    void
    __reverse(_BidirectionalIterator __first, _BidirectionalIterator __last,
       bidirectional_iterator_tag)
    {
      while (true)
 if (__first == __last || __first == --__last)
   return;
 else
   {
     std::iter_swap(__first, __last);
     ++__first;
   }
    }






  template<typename _RandomAccessIterator>

    void
    __reverse(_RandomAccessIterator __first, _RandomAccessIterator __last,
       random_access_iterator_tag)
    {
      if (__first == __last)
 return;
      --__last;
      while (__first < __last)
 {
   std::iter_swap(__first, __last);
   ++__first;
   --__last;
 }
    }
# 1125 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator>

    inline void
    reverse(_BidirectionalIterator __first, _BidirectionalIterator __last)
    {



                                                     ;
      std::__reverse(__first, __last, std::__iterator_category(__first));
    }
# 1153 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator, typename _OutputIterator>

    _OutputIterator
    reverse_copy(_BidirectionalIterator __first, _BidirectionalIterator __last,
   _OutputIterator __result)
    {





                                                     ;

      while (__first != __last)
 {
   --__last;
   *__result = *__last;
   ++__result;
 }
      return __result;
    }





  template<typename _EuclideanRingElement>

    _EuclideanRingElement
    __gcd(_EuclideanRingElement __m, _EuclideanRingElement __n)
    {
      while (__n != 0)
 {
   _EuclideanRingElement __t = __m % __n;
   __m = __n;
   __n = __t;
 }
      return __m;
    }

  inline namespace _V2
  {


  template<typename _ForwardIterator>

    _ForwardIterator
    __rotate(_ForwardIterator __first,
      _ForwardIterator __middle,
      _ForwardIterator __last,
      forward_iterator_tag)
    {
      if (__first == __middle)
 return __last;
      else if (__last == __middle)
 return __first;

      _ForwardIterator __first2 = __middle;
      do
 {
   std::iter_swap(__first, __first2);
   ++__first;
   ++__first2;
   if (__first == __middle)
     __middle = __first2;
 }
      while (__first2 != __last);

      _ForwardIterator __ret = __first;

      __first2 = __middle;

      while (__first2 != __last)
 {
   std::iter_swap(__first, __first2);
   ++__first;
   ++__first2;
   if (__first == __middle)
     __middle = __first2;
   else if (__first2 == __last)
     __first2 = __middle;
 }
      return __ret;
    }


  template<typename _BidirectionalIterator>

    _BidirectionalIterator
    __rotate(_BidirectionalIterator __first,
      _BidirectionalIterator __middle,
      _BidirectionalIterator __last,
       bidirectional_iterator_tag)
    {




      if (__first == __middle)
 return __last;
      else if (__last == __middle)
 return __first;

      std::__reverse(__first, __middle, bidirectional_iterator_tag());
      std::__reverse(__middle, __last, bidirectional_iterator_tag());

      while (__first != __middle && __middle != __last)
 {
   std::iter_swap(__first, --__last);
   ++__first;
 }

      if (__first == __middle)
 {
   std::__reverse(__middle, __last, bidirectional_iterator_tag());
   return __last;
 }
      else
 {
   std::__reverse(__first, __middle, bidirectional_iterator_tag());
   return __first;
 }
    }


  template<typename _RandomAccessIterator>

    _RandomAccessIterator
    __rotate(_RandomAccessIterator __first,
      _RandomAccessIterator __middle,
      _RandomAccessIterator __last,
      random_access_iterator_tag)
    {




      if (__first == __middle)
 return __last;
      else if (__last == __middle)
 return __first;

      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
 _Distance;
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
 _ValueType;

      _Distance __n = __last - __first;
      _Distance __k = __middle - __first;

      if (__k == __n - __k)
 {
   std::swap_ranges(__first, __middle, __middle);
   return __middle;
 }

      _RandomAccessIterator __p = __first;
      _RandomAccessIterator __ret = __first + (__last - __middle);

      for (;;)
 {
   if (__k < __n - __k)
     {
       if (__is_pod(_ValueType) && __k == 1)
  {
    _ValueType __t = std::move(*__p);
    std::move(__p + 1, __p + __n, __p);
    *(__p + __n - 1) = std::move(__t);
    return __ret;
  }
       _RandomAccessIterator __q = __p + __k;
       for (_Distance __i = 0; __i < __n - __k; ++ __i)
  {
    std::iter_swap(__p, __q);
    ++__p;
    ++__q;
  }
       __n %= __k;
       if (__n == 0)
  return __ret;
       std::swap(__n, __k);
       __k = __n - __k;
     }
   else
     {
       __k = __n - __k;
       if (__is_pod(_ValueType) && __k == 1)
  {
    _ValueType __t = std::move(*(__p + __n - 1));
    std::move_backward(__p, __p + __n - 1, __p + __n);
    *__p = std::move(__t);
    return __ret;
  }
       _RandomAccessIterator __q = __p + __n;
       __p = __q - __k;
       for (_Distance __i = 0; __i < __n - __k; ++ __i)
  {
    --__p;
    --__q;
    std::iter_swap(__p, __q);
  }
       __n %= __k;
       if (__n == 0)
  return __ret;
       std::swap(__n, __k);
     }
 }
    }
# 1385 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline _ForwardIterator
    rotate(_ForwardIterator __first, _ForwardIterator __middle,
    _ForwardIterator __last)
    {



                                                       ;
                                                      ;

      return std::__rotate(__first, __middle, __last,
      std::__iterator_category(__first));
    }

  }
# 1423 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _OutputIterator>

    inline _OutputIterator
    rotate_copy(_ForwardIterator __first, _ForwardIterator __middle,
  _ForwardIterator __last, _OutputIterator __result)
    {




                                                       ;
                                                      ;

      return std::copy(__first, __middle,
         std::copy(__middle, __last, __result));
    }


  template<typename _ForwardIterator, typename _Predicate>

    _ForwardIterator
    __partition(_ForwardIterator __first, _ForwardIterator __last,
  _Predicate __pred, forward_iterator_tag)
    {
      if (__first == __last)
 return __first;

      while (__pred(*__first))
 if (++__first == __last)
   return __first;

      _ForwardIterator __next = __first;

      while (++__next != __last)
 if (__pred(*__next))
   {
     std::iter_swap(__first, __next);
     ++__first;
   }

      return __first;
    }


  template<typename _BidirectionalIterator, typename _Predicate>

    _BidirectionalIterator
    __partition(_BidirectionalIterator __first, _BidirectionalIterator __last,
  _Predicate __pred, bidirectional_iterator_tag)
    {
      while (true)
 {
   while (true)
     if (__first == __last)
       return __first;
     else if (__pred(*__first))
       ++__first;
     else
       break;
   --__last;
   while (true)
     if (__first == __last)
       return __first;
     else if (!bool(__pred(*__last)))
       --__last;
     else
       break;
   std::iter_swap(__first, __last);
   ++__first;
 }
    }
# 1503 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Pointer, typename _Predicate,
    typename _Distance>
    _ForwardIterator
    __stable_partition_adaptive(_ForwardIterator __first,
    _ForwardIterator __last,
    _Predicate __pred, _Distance __len,
    _Pointer __buffer,
    _Distance __buffer_size)
    {
      if (__len == 1)
 return __first;

      if (__len <= __buffer_size)
 {
   _ForwardIterator __result1 = __first;
   _Pointer __result2 = __buffer;




   *__result2 = std::move(*__first);
   ++__result2;
   ++__first;
   for (; __first != __last; ++__first)
     if (__pred(__first))
       {
  *__result1 = std::move(*__first);
  ++__result1;
       }
     else
       {
  *__result2 = std::move(*__first);
  ++__result2;
       }

   std::move(__buffer, __result2, __result1);
   return __result1;
 }

      _ForwardIterator __middle = __first;
      std::advance(__middle, __len / 2);
      _ForwardIterator __left_split =
 std::__stable_partition_adaptive(__first, __middle, __pred,
      __len / 2, __buffer,
      __buffer_size);



      _Distance __right_len = __len - __len / 2;
      _ForwardIterator __right_split =
 std::__find_if_not_n(__middle, __right_len, __pred);

      if (__right_len)
 __right_split =
   std::__stable_partition_adaptive(__right_split, __last, __pred,
        __right_len,
        __buffer, __buffer_size);

      return std::rotate(__left_split, __middle, __right_split);
    }

  template<typename _ForwardIterator, typename _Predicate>
    _ForwardIterator
    __stable_partition(_ForwardIterator __first, _ForwardIterator __last,
         _Predicate __pred)
    {
      __first = std::__find_if_not(__first, __last, __pred);

      if (__first == __last)
 return __first;

      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;
      typedef typename iterator_traits<_ForwardIterator>::difference_type
 _DistanceType;

      _Temporary_buffer<_ForwardIterator, _ValueType>
 __buf(__first, std::distance(__first, __last));
      return
 std::__stable_partition_adaptive(__first, __last, __pred,
      _DistanceType(__buf.requested_size()),
      __buf.begin(),
      _DistanceType(__buf.size()));
    }
# 1605 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Predicate>
    inline _ForwardIterator
    stable_partition(_ForwardIterator __first, _ForwardIterator __last,
       _Predicate __pred)
    {





                                                     ;

      return std::__stable_partition(__first, __last,
         __gnu_cxx::__ops::__pred_iter(__pred));
    }


  template<typename _RandomAccessIterator, typename _Compare>

    void
    __heap_select(_RandomAccessIterator __first,
    _RandomAccessIterator __middle,
    _RandomAccessIterator __last, _Compare __comp)
    {
      std::__make_heap(__first, __middle, __comp);
      for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
 if (__comp(__i, __first))
   std::__pop_heap(__first, __middle, __i, __comp);
    }



  template<typename _InputIterator, typename _RandomAccessIterator,
    typename _Compare>

    _RandomAccessIterator
    __partial_sort_copy(_InputIterator __first, _InputIterator __last,
   _RandomAccessIterator __result_first,
   _RandomAccessIterator __result_last,
   _Compare __comp)
    {
      typedef typename iterator_traits<_InputIterator>::value_type
 _InputValueType;
      typedef iterator_traits<_RandomAccessIterator> _RItTraits;
      typedef typename _RItTraits::difference_type _DistanceType;

      if (__result_first == __result_last)
 return __result_last;
      _RandomAccessIterator __result_real_last = __result_first;
      while (__first != __last && __result_real_last != __result_last)
 {
   *__result_real_last = *__first;
   ++__result_real_last;
   ++__first;
 }

      std::__make_heap(__result_first, __result_real_last, __comp);
      while (__first != __last)
 {
   if (__comp(__first, __result_first))
     std::__adjust_heap(__result_first, _DistanceType(0),
          _DistanceType(__result_real_last
          - __result_first),
          _InputValueType(*__first), __comp);
   ++__first;
 }
      std::__sort_heap(__result_first, __result_real_last, __comp);
      return __result_real_last;
    }
# 1693 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _RandomAccessIterator>

    inline _RandomAccessIterator
    partial_sort_copy(_InputIterator __first, _InputIterator __last,
        _RandomAccessIterator __result_first,
        _RandomAccessIterator __result_last)
    {
# 1714 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                     ;
                                                     ;
                                                                   ;

      return std::__partial_sort_copy(__first, __last,
          __result_first, __result_last,
          __gnu_cxx::__ops::__iter_less_iter());
    }
# 1743 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _RandomAccessIterator,
    typename _Compare>

    inline _RandomAccessIterator
    partial_sort_copy(_InputIterator __first, _InputIterator __last,
        _RandomAccessIterator __result_first,
        _RandomAccessIterator __result_last,
        _Compare __comp)
    {
# 1769 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                     ;
                                                                  ;
                                                                   ;

      return std::__partial_sort_copy(__first, __last,
          __result_first, __result_last,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }


  template<typename _RandomAccessIterator, typename _Compare>

    void
    __unguarded_linear_insert(_RandomAccessIterator __last,
         _Compare __comp)
    {
      typename iterator_traits<_RandomAccessIterator>::value_type
 __val = std::move(*__last);
      _RandomAccessIterator __next = __last;
      --__next;
      while (__comp(__val, __next))
 {
   *__last = std::move(*__next);
   __last = __next;
   --__next;
 }
      *__last = std::move(__val);
    }


  template<typename _RandomAccessIterator, typename _Compare>

    void
    __insertion_sort(_RandomAccessIterator __first,
       _RandomAccessIterator __last, _Compare __comp)
    {
      if (__first == __last) return;

      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
 {
   if (__comp(__i, __first))
     {
       typename iterator_traits<_RandomAccessIterator>::value_type
  __val = std::move(*__i);
       std::move_backward(__first, __i, __i + 1);
       *__first = std::move(__val);
     }
   else
     std::__unguarded_linear_insert(__i,
    __gnu_cxx::__ops::__val_comp_iter(__comp));
 }
    }


  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    __unguarded_insertion_sort(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp)
    {
      for (_RandomAccessIterator __i = __first; __i != __last; ++__i)
 std::__unguarded_linear_insert(__i,
    __gnu_cxx::__ops::__val_comp_iter(__comp));
    }





  enum { _S_threshold = 16 };


  template<typename _RandomAccessIterator, typename _Compare>

    void
    __final_insertion_sort(_RandomAccessIterator __first,
      _RandomAccessIterator __last, _Compare __comp)
    {
      if (__last - __first > int(_S_threshold))
 {
   std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
   std::__unguarded_insertion_sort(__first + int(_S_threshold), __last,
       __comp);
 }
      else
 std::__insertion_sort(__first, __last, __comp);
    }


  template<typename _RandomAccessIterator, typename _Compare>

    _RandomAccessIterator
    __unguarded_partition(_RandomAccessIterator __first,
     _RandomAccessIterator __last,
     _RandomAccessIterator __pivot, _Compare __comp)
    {
      while (true)
 {
   while (__comp(__first, __pivot))
     ++__first;
   --__last;
   while (__comp(__pivot, __last))
     --__last;
   if (!(__first < __last))
     return __first;
   std::iter_swap(__first, __last);
   ++__first;
 }
    }


  template<typename _RandomAccessIterator, typename _Compare>

    inline _RandomAccessIterator
    __unguarded_partition_pivot(_RandomAccessIterator __first,
    _RandomAccessIterator __last, _Compare __comp)
    {
      _RandomAccessIterator __mid = __first + (__last - __first) / 2;
      std::__move_median_to_first(__first, __first + 1, __mid, __last - 1,
      __comp);
      return std::__unguarded_partition(__first + 1, __last, __first, __comp);
    }

  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    __partial_sort(_RandomAccessIterator __first,
     _RandomAccessIterator __middle,
     _RandomAccessIterator __last,
     _Compare __comp)
    {
      std::__heap_select(__first, __middle, __last, __comp);
      std::__sort_heap(__first, __middle, __comp);
    }


  template<typename _RandomAccessIterator, typename _Size, typename _Compare>

    void
    __introsort_loop(_RandomAccessIterator __first,
       _RandomAccessIterator __last,
       _Size __depth_limit, _Compare __comp)
    {
      while (__last - __first > int(_S_threshold))
 {
   if (__depth_limit == 0)
     {
       std::__partial_sort(__first, __last, __last, __comp);
       return;
     }
   --__depth_limit;
   _RandomAccessIterator __cut =
     std::__unguarded_partition_pivot(__first, __last, __comp);
   std::__introsort_loop(__cut, __last, __depth_limit, __comp);
   __last = __cut;
 }
    }



  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    __sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
    _Compare __comp)
    {
      if (__first != __last)
 {
   std::__introsort_loop(__first, __last,
    std::__lg(__last - __first) * 2,
    __comp);
   std::__final_insertion_sort(__first, __last, __comp);
 }
    }

  template<typename _RandomAccessIterator, typename _Size, typename _Compare>

    void
    __introselect(_RandomAccessIterator __first, _RandomAccessIterator __nth,
    _RandomAccessIterator __last, _Size __depth_limit,
    _Compare __comp)
    {
      while (__last - __first > 3)
 {
   if (__depth_limit == 0)
     {
       std::__heap_select(__first, __nth + 1, __last, __comp);

       std::iter_swap(__first, __nth);
       return;
     }
   --__depth_limit;
   _RandomAccessIterator __cut =
     std::__unguarded_partition_pivot(__first, __last, __comp);
   if (__cut <= __nth)
     __first = __cut;
   else
     __last = __cut;
 }
      std::__insertion_sort(__first, __last, __comp);
    }
# 1991 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    inline _ForwardIterator
    lower_bound(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val, _Compare __comp)
    {





                    ;

      return std::__lower_bound(__first, __last, __val,
    __gnu_cxx::__ops::__iter_comp_val(__comp));
    }

  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    _ForwardIterator
    __upper_bound(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __val, _Compare __comp)
    {
      typedef typename iterator_traits<_ForwardIterator>::difference_type
 _DistanceType;

      _DistanceType __len = std::distance(__first, __last);

      while (__len > 0)
 {
   _DistanceType __half = __len >> 1;
   _ForwardIterator __middle = __first;
   std::advance(__middle, __half);
   if (__comp(__val, __middle))
     __len = __half;
   else
     {
       __first = __middle;
       ++__first;
       __len = __len - __half - 1;
     }
 }
      return __first;
    }
# 2047 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp>

    inline _ForwardIterator
    upper_bound(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val)
    {




                                                                  ;

      return std::__upper_bound(__first, __last, __val,
    __gnu_cxx::__ops::__val_less_iter());
    }
# 2078 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    inline _ForwardIterator
    upper_bound(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val, _Compare __comp)
    {





                    ;

      return std::__upper_bound(__first, __last, __val,
    __gnu_cxx::__ops::__val_comp_iter(__comp));
    }

  template<typename _ForwardIterator, typename _Tp,
    typename _CompareItTp, typename _CompareTpIt>

    pair<_ForwardIterator, _ForwardIterator>
    __equal_range(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __val,
    _CompareItTp __comp_it_val, _CompareTpIt __comp_val_it)
    {
      typedef typename iterator_traits<_ForwardIterator>::difference_type
 _DistanceType;

      _DistanceType __len = std::distance(__first, __last);

      while (__len > 0)
 {
   _DistanceType __half = __len >> 1;
   _ForwardIterator __middle = __first;
   std::advance(__middle, __half);
   if (__comp_it_val(__middle, __val))
     {
       __first = __middle;
       ++__first;
       __len = __len - __half - 1;
     }
   else if (__comp_val_it(__val, __middle))
     __len = __half;
   else
     {
       _ForwardIterator __left
  = std::__lower_bound(__first, __middle, __val, __comp_it_val);
       std::advance(__first, __len);
       _ForwardIterator __right
  = std::__upper_bound(++__middle, __first, __val, __comp_val_it);
       return pair<_ForwardIterator, _ForwardIterator>(__left, __right);
     }
 }
      return pair<_ForwardIterator, _ForwardIterator>(__first, __first);
    }
# 2151 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp>

    inline pair<_ForwardIterator, _ForwardIterator>
    equal_range(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val)
    {






                                                                  ;
                                                                  ;

      return std::__equal_range(__first, __last, __val,
    __gnu_cxx::__ops::__iter_less_val(),
    __gnu_cxx::__ops::__val_less_iter());
    }
# 2188 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    inline pair<_ForwardIterator, _ForwardIterator>
    equal_range(_ForwardIterator __first, _ForwardIterator __last,
  const _Tp& __val, _Compare __comp)
    {







                    ;

                    ;

      return std::__equal_range(__first, __last, __val,
    __gnu_cxx::__ops::__iter_comp_val(__comp),
    __gnu_cxx::__ops::__val_comp_iter(__comp));
    }
# 2222 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp>

    bool
    binary_search(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __val)
    {




                                                                  ;
                                                                  ;

      _ForwardIterator __i
 = std::__lower_bound(__first, __last, __val,
        __gnu_cxx::__ops::__iter_less_val());
      return __i != __last && !(__val < *__i);
    }
# 2256 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp, typename _Compare>

    bool
    binary_search(_ForwardIterator __first, _ForwardIterator __last,
    const _Tp& __val, _Compare __comp)
    {





                    ;

                    ;

      _ForwardIterator __i
 = std::__lower_bound(__first, __last, __val,
        __gnu_cxx::__ops::__iter_comp_val(__comp));
      return __i != __last && !bool(__comp(__val, *__i));
    }




  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>
    void
    __move_merge_adaptive(_InputIterator1 __first1, _InputIterator1 __last1,
     _InputIterator2 __first2, _InputIterator2 __last2,
     _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 {
   if (__comp(__first2, __first1))
     {
       *__result = std::move(*__first2);
       ++__first2;
     }
   else
     {
       *__result = std::move(*__first1);
       ++__first1;
     }
   ++__result;
 }
      if (__first1 != __last1)
 std::move(__first1, __last1, __result);
    }


  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
    typename _BidirectionalIterator3, typename _Compare>
    void
    __move_merge_adaptive_backward(_BidirectionalIterator1 __first1,
       _BidirectionalIterator1 __last1,
       _BidirectionalIterator2 __first2,
       _BidirectionalIterator2 __last2,
       _BidirectionalIterator3 __result,
       _Compare __comp)
    {
      if (__first1 == __last1)
 {
   std::move_backward(__first2, __last2, __result);
   return;
 }
      else if (__first2 == __last2)
 return;

      --__last1;
      --__last2;
      while (true)
 {
   if (__comp(__last2, __last1))
     {
       *--__result = std::move(*__last1);
       if (__first1 == __last1)
  {
    std::move_backward(__first2, ++__last2, __result);
    return;
  }
       --__last1;
     }
   else
     {
       *--__result = std::move(*__last2);
       if (__first2 == __last2)
  return;
       --__last2;
     }
 }
    }


  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
    typename _Distance>
    _BidirectionalIterator1
    __rotate_adaptive(_BidirectionalIterator1 __first,
        _BidirectionalIterator1 __middle,
        _BidirectionalIterator1 __last,
        _Distance __len1, _Distance __len2,
        _BidirectionalIterator2 __buffer,
        _Distance __buffer_size)
    {
      _BidirectionalIterator2 __buffer_end;
      if (__len1 > __len2 && __len2 <= __buffer_size)
 {
   if (__len2)
     {
       __buffer_end = std::move(__middle, __last, __buffer);
       std::move_backward(__first, __middle, __last);
       return std::move(__buffer, __buffer_end, __first);
     }
   else
     return __first;
 }
      else if (__len1 <= __buffer_size)
 {
   if (__len1)
     {
       __buffer_end = std::move(__first, __middle, __buffer);
       std::move(__middle, __last, __first);
       return std::move_backward(__buffer, __buffer_end, __last);
     }
   else
     return __last;
 }
      else
 return std::rotate(__first, __middle, __last);
    }


  template<typename _BidirectionalIterator, typename _Distance,
    typename _Pointer, typename _Compare>
    void
    __merge_adaptive(_BidirectionalIterator __first,
       _BidirectionalIterator __middle,
       _BidirectionalIterator __last,
       _Distance __len1, _Distance __len2,
       _Pointer __buffer, _Distance __buffer_size,
       _Compare __comp)
    {
      if (__len1 <= __len2 && __len1 <= __buffer_size)
 {
   _Pointer __buffer_end = std::move(__first, __middle, __buffer);
   std::__move_merge_adaptive(__buffer, __buffer_end, __middle, __last,
         __first, __comp);
 }
      else if (__len2 <= __buffer_size)
 {
   _Pointer __buffer_end = std::move(__middle, __last, __buffer);
   std::__move_merge_adaptive_backward(__first, __middle, __buffer,
           __buffer_end, __last, __comp);
 }
      else
 {
   _BidirectionalIterator __first_cut = __first;
   _BidirectionalIterator __second_cut = __middle;
   _Distance __len11 = 0;
   _Distance __len22 = 0;
   if (__len1 > __len2)
     {
       __len11 = __len1 / 2;
       std::advance(__first_cut, __len11);
       __second_cut
  = std::__lower_bound(__middle, __last, *__first_cut,
         __gnu_cxx::__ops::__iter_comp_val(__comp));
       __len22 = std::distance(__middle, __second_cut);
     }
   else
     {
       __len22 = __len2 / 2;
       std::advance(__second_cut, __len22);
       __first_cut
  = std::__upper_bound(__first, __middle, *__second_cut,
         __gnu_cxx::__ops::__val_comp_iter(__comp));
       __len11 = std::distance(__first, __first_cut);
     }

   _BidirectionalIterator __new_middle
     = std::__rotate_adaptive(__first_cut, __middle, __second_cut,
         __len1 - __len11, __len22, __buffer,
         __buffer_size);
   std::__merge_adaptive(__first, __first_cut, __new_middle, __len11,
    __len22, __buffer, __buffer_size, __comp);
   std::__merge_adaptive(__new_middle, __second_cut, __last,
    __len1 - __len11,
    __len2 - __len22, __buffer,
    __buffer_size, __comp);
 }
    }


  template<typename _BidirectionalIterator, typename _Distance,
    typename _Compare>
    void
    __merge_without_buffer(_BidirectionalIterator __first,
      _BidirectionalIterator __middle,
      _BidirectionalIterator __last,
      _Distance __len1, _Distance __len2,
      _Compare __comp)
    {
      if (__len1 == 0 || __len2 == 0)
 return;

      if (__len1 + __len2 == 2)
 {
   if (__comp(__middle, __first))
     std::iter_swap(__first, __middle);
   return;
 }

      _BidirectionalIterator __first_cut = __first;
      _BidirectionalIterator __second_cut = __middle;
      _Distance __len11 = 0;
      _Distance __len22 = 0;
      if (__len1 > __len2)
 {
   __len11 = __len1 / 2;
   std::advance(__first_cut, __len11);
   __second_cut
     = std::__lower_bound(__middle, __last, *__first_cut,
     __gnu_cxx::__ops::__iter_comp_val(__comp));
   __len22 = std::distance(__middle, __second_cut);
 }
      else
 {
   __len22 = __len2 / 2;
   std::advance(__second_cut, __len22);
   __first_cut
     = std::__upper_bound(__first, __middle, *__second_cut,
     __gnu_cxx::__ops::__val_comp_iter(__comp));
   __len11 = std::distance(__first, __first_cut);
 }

      _BidirectionalIterator __new_middle
 = std::rotate(__first_cut, __middle, __second_cut);
      std::__merge_without_buffer(__first, __first_cut, __new_middle,
      __len11, __len22, __comp);
      std::__merge_without_buffer(__new_middle, __second_cut, __last,
      __len1 - __len11, __len2 - __len22, __comp);
    }

  template<typename _BidirectionalIterator, typename _Compare>
    void
    __inplace_merge(_BidirectionalIterator __first,
      _BidirectionalIterator __middle,
      _BidirectionalIterator __last,
      _Compare __comp)
    {
      typedef typename iterator_traits<_BidirectionalIterator>::value_type
   _ValueType;
      typedef typename iterator_traits<_BidirectionalIterator>::difference_type
   _DistanceType;
      typedef _Temporary_buffer<_BidirectionalIterator, _ValueType> _TmpBuf;

      if (__first == __middle || __middle == __last)
 return;

      const _DistanceType __len1 = std::distance(__first, __middle);
      const _DistanceType __len2 = std::distance(__middle, __last);



      _TmpBuf __buf(__first, std::min(__len1, __len2));

      if (__buf.begin() == 0)
 std::__merge_without_buffer
   (__first, __middle, __last, __len1, __len2, __comp);
      else
 std::__merge_adaptive
   (__first, __middle, __last, __len1, __len2, __buf.begin(),
    _DistanceType(__buf.size()), __comp);
    }
# 2548 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator>
    inline void
    inplace_merge(_BidirectionalIterator __first,
    _BidirectionalIterator __middle,
    _BidirectionalIterator __last)
    {





                                                  ;
                                                 ;
                                                     ;

      std::__inplace_merge(__first, __middle, __last,
      __gnu_cxx::__ops::__iter_less_iter());
    }
# 2589 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator, typename _Compare>
    inline void
    inplace_merge(_BidirectionalIterator __first,
    _BidirectionalIterator __middle,
    _BidirectionalIterator __last,
    _Compare __comp)
    {






                                                               ;
                                                              ;
                                                                  ;

      std::__inplace_merge(__first, __middle, __last,
      __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }



  template<typename _InputIterator, typename _OutputIterator,
    typename _Compare>
    _OutputIterator
    __move_merge(_InputIterator __first1, _InputIterator __last1,
   _InputIterator __first2, _InputIterator __last2,
   _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 {
   if (__comp(__first2, __first1))
     {
       *__result = std::move(*__first2);
       ++__first2;
     }
   else
     {
       *__result = std::move(*__first1);
       ++__first1;
     }
   ++__result;
 }
      return std::move(__first2, __last2, std::move(__first1, __last1, __result));


    }

  template<typename _RandomAccessIterator1, typename _RandomAccessIterator2,
    typename _Distance, typename _Compare>
    void
    __merge_sort_loop(_RandomAccessIterator1 __first,
        _RandomAccessIterator1 __last,
        _RandomAccessIterator2 __result, _Distance __step_size,
        _Compare __comp)
    {
      const _Distance __two_step = 2 * __step_size;

      while (__last - __first >= __two_step)
 {
   __result = std::__move_merge(__first, __first + __step_size,
           __first + __step_size,
           __first + __two_step,
           __result, __comp);
   __first += __two_step;
 }
      __step_size = std::min(_Distance(__last - __first), __step_size);

      std::__move_merge(__first, __first + __step_size,
   __first + __step_size, __last, __result, __comp);
    }

  template<typename _RandomAccessIterator, typename _Distance,
    typename _Compare>

    void
    __chunk_insertion_sort(_RandomAccessIterator __first,
      _RandomAccessIterator __last,
      _Distance __chunk_size, _Compare __comp)
    {
      while (__last - __first >= __chunk_size)
 {
   std::__insertion_sort(__first, __first + __chunk_size, __comp);
   __first += __chunk_size;
 }
      std::__insertion_sort(__first, __last, __comp);
    }

  enum { _S_chunk_size = 7 };

  template<typename _RandomAccessIterator, typename _Pointer, typename _Compare>
    void
    __merge_sort_with_buffer(_RandomAccessIterator __first,
        _RandomAccessIterator __last,
        _Pointer __buffer, _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
 _Distance;

      const _Distance __len = __last - __first;
      const _Pointer __buffer_last = __buffer + __len;

      _Distance __step_size = _S_chunk_size;
      std::__chunk_insertion_sort(__first, __last, __step_size, __comp);

      while (__step_size < __len)
 {
   std::__merge_sort_loop(__first, __last, __buffer,
     __step_size, __comp);
   __step_size *= 2;
   std::__merge_sort_loop(__buffer, __buffer_last, __first,
     __step_size, __comp);
   __step_size *= 2;
 }
    }

  template<typename _RandomAccessIterator, typename _Pointer,
    typename _Distance, typename _Compare>
    void
    __stable_sort_adaptive(_RandomAccessIterator __first,
      _RandomAccessIterator __last,
      _Pointer __buffer, _Distance __buffer_size,
      _Compare __comp)
    {
      const _Distance __len = (__last - __first + 1) / 2;
      const _RandomAccessIterator __middle = __first + __len;
      if (__len > __buffer_size)
 {
   std::__stable_sort_adaptive(__first, __middle, __buffer,
          __buffer_size, __comp);
   std::__stable_sort_adaptive(__middle, __last, __buffer,
          __buffer_size, __comp);
 }
      else
 {
   std::__merge_sort_with_buffer(__first, __middle, __buffer, __comp);
   std::__merge_sort_with_buffer(__middle, __last, __buffer, __comp);
 }

      std::__merge_adaptive(__first, __middle, __last,
       _Distance(__middle - __first),
       _Distance(__last - __middle),
       __buffer, __buffer_size,
       __comp);
    }


  template<typename _RandomAccessIterator, typename _Compare>
    void
    __inplace_stable_sort(_RandomAccessIterator __first,
     _RandomAccessIterator __last, _Compare __comp)
    {
      if (__last - __first < 15)
 {
   std::__insertion_sort(__first, __last, __comp);
   return;
 }
      _RandomAccessIterator __middle = __first + (__last - __first) / 2;
      std::__inplace_stable_sort(__first, __middle, __comp);
      std::__inplace_stable_sort(__middle, __last, __comp);
      std::__merge_without_buffer(__first, __middle, __last,
      __middle - __first,
      __last - __middle,
      __comp);
    }
# 2763 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _Compare>

    bool
    __includes(_InputIterator1 __first1, _InputIterator1 __last1,
        _InputIterator2 __first2, _InputIterator2 __last2,
        _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 {
   if (__comp(__first2, __first1))
     return false;
   if (!__comp(__first1, __first2))
     ++__first2;
   ++__first1;
 }

      return __first2 == __last2;
    }
# 2801 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2>

    inline bool
    includes(_InputIterator1 __first1, _InputIterator1 __last1,
      _InputIterator2 __first2, _InputIterator2 __last2)
    {
# 2816 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__includes(__first1, __last1, __first2, __last2,
        __gnu_cxx::__ops::__iter_less_iter());
    }
# 2846 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _Compare>

    inline bool
    includes(_InputIterator1 __first1, _InputIterator1 __last1,
      _InputIterator2 __first2, _InputIterator2 __last2,
      _Compare __comp)
    {
# 2863 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__includes(__first1, __last1, __first2, __last2,
        __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 2882 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator, typename _Compare>

    bool
    __next_permutation(_BidirectionalIterator __first,
         _BidirectionalIterator __last, _Compare __comp)
    {
      if (__first == __last)
 return false;
      _BidirectionalIterator __i = __first;
      ++__i;
      if (__i == __last)
 return false;
      __i = __last;
      --__i;

      for(;;)
 {
   _BidirectionalIterator __ii = __i;
   --__i;
   if (__comp(__i, __ii))
     {
       _BidirectionalIterator __j = __last;
       while (!__comp(__i, --__j))
  {}
       std::iter_swap(__i, __j);
       std::__reverse(__ii, __last,
        std::__iterator_category(__first));
       return true;
     }
   if (__i == __first)
     {
       std::__reverse(__first, __last,
        std::__iterator_category(__first));
       return false;
     }
 }
    }
# 2932 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator>

    inline bool
    next_permutation(_BidirectionalIterator __first,
       _BidirectionalIterator __last)
    {





                                                     ;
                                                     ;

      return std::__next_permutation
 (__first, __last, __gnu_cxx::__ops::__iter_less_iter());
    }
# 2965 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator, typename _Compare>

    inline bool
    next_permutation(_BidirectionalIterator __first,
       _BidirectionalIterator __last, _Compare __comp)
    {






                                                     ;
                                                                  ;

      return std::__next_permutation
 (__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _BidirectionalIterator, typename _Compare>

    bool
    __prev_permutation(_BidirectionalIterator __first,
         _BidirectionalIterator __last, _Compare __comp)
    {
      if (__first == __last)
 return false;
      _BidirectionalIterator __i = __first;
      ++__i;
      if (__i == __last)
 return false;
      __i = __last;
      --__i;

      for(;;)
 {
   _BidirectionalIterator __ii = __i;
   --__i;
   if (__comp(__ii, __i))
     {
       _BidirectionalIterator __j = __last;
       while (!__comp(--__j, __i))
  {}
       std::iter_swap(__i, __j);
       std::__reverse(__ii, __last,
        std::__iterator_category(__first));
       return true;
     }
   if (__i == __first)
     {
       std::__reverse(__first, __last,
        std::__iterator_category(__first));
       return false;
     }
 }
    }
# 3035 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator>

    inline bool
    prev_permutation(_BidirectionalIterator __first,
       _BidirectionalIterator __last)
    {





                                                     ;
                                                     ;

      return std::__prev_permutation(__first, __last,
         __gnu_cxx::__ops::__iter_less_iter());
    }
# 3068 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _BidirectionalIterator, typename _Compare>

    inline bool
    prev_permutation(_BidirectionalIterator __first,
       _BidirectionalIterator __last, _Compare __comp)
    {






                                                     ;
                                                                  ;

      return std::__prev_permutation(__first, __last,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }




  template<typename _InputIterator, typename _OutputIterator,
    typename _Predicate, typename _Tp>

    _OutputIterator
    __replace_copy_if(_InputIterator __first, _InputIterator __last,
        _OutputIterator __result,
        _Predicate __pred, const _Tp& __new_value)
    {
      for (; __first != __last; ++__first, (void)++__result)
 if (__pred(__first))
   *__result = __new_value;
 else
   *__result = *__first;
      return __result;
    }
# 3120 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator, typename _Tp>

    inline _OutputIterator
    replace_copy(_InputIterator __first, _InputIterator __last,
   _OutputIterator __result,
   const _Tp& __old_value, const _Tp& __new_value)
    {






                                                     ;

      return std::__replace_copy_if(__first, __last, __result,
   __gnu_cxx::__ops::__iter_equals_val(__old_value),
           __new_value);
    }
# 3155 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator,
    typename _Predicate, typename _Tp>

    inline _OutputIterator
    replace_copy_if(_InputIterator __first, _InputIterator __last,
      _OutputIterator __result,
      _Predicate __pred, const _Tp& __new_value)
    {






                                                     ;

      return std::__replace_copy_if(__first, __last, __result,
    __gnu_cxx::__ops::__pred_iter(__pred),
           __new_value);
    }
# 3184 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline bool
    is_sorted(_ForwardIterator __first, _ForwardIterator __last)
    { return std::is_sorted_until(__first, __last) == __last; }
# 3199 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Compare>

    inline bool
    is_sorted(_ForwardIterator __first, _ForwardIterator __last,
       _Compare __comp)
    { return std::is_sorted_until(__first, __last, __comp) == __last; }

  template<typename _ForwardIterator, typename _Compare>

    _ForwardIterator
    __is_sorted_until(_ForwardIterator __first, _ForwardIterator __last,
        _Compare __comp)
    {
      if (__first == __last)
 return __last;

      _ForwardIterator __next = __first;
      for (++__next; __next != __last; __first = __next, (void)++__next)
 if (__comp(__next, __first))
   return __next;
      return __next;
    }
# 3230 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline _ForwardIterator
    is_sorted_until(_ForwardIterator __first, _ForwardIterator __last)
    {




                                                     ;
                                                     ;

      return std::__is_sorted_until(__first, __last,
        __gnu_cxx::__ops::__iter_less_iter());
    }
# 3255 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Compare>

    inline _ForwardIterator
    is_sorted_until(_ForwardIterator __first, _ForwardIterator __last,
      _Compare __comp)
    {





                                                     ;
                                                                  ;

      return std::__is_sorted_until(__first, __last,
        __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 3281 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _Tp>

    inline pair<const _Tp&, const _Tp&>
    minmax(const _Tp& __a, const _Tp& __b)
    {



      return __b < __a ? pair<const _Tp&, const _Tp&>(__b, __a)
         : pair<const _Tp&, const _Tp&>(__a, __b);
    }
# 3302 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _Tp, typename _Compare>

    inline pair<const _Tp&, const _Tp&>
    minmax(const _Tp& __a, const _Tp& __b, _Compare __comp)
    {
      return __comp(__b, __a) ? pair<const _Tp&, const _Tp&>(__b, __a)
         : pair<const _Tp&, const _Tp&>(__a, __b);
    }

  template<typename _ForwardIterator, typename _Compare>

    pair<_ForwardIterator, _ForwardIterator>
    __minmax_element(_ForwardIterator __first, _ForwardIterator __last,
       _Compare __comp)
    {
      _ForwardIterator __next = __first;
      if (__first == __last
   || ++__next == __last)
 return std::make_pair(__first, __first);

      _ForwardIterator __min{}, __max{};
      if (__comp(__next, __first))
 {
   __min = __next;
   __max = __first;
 }
      else
 {
   __min = __first;
   __max = __next;
 }

      __first = __next;
      ++__first;

      while (__first != __last)
 {
   __next = __first;
   if (++__next == __last)
     {
       if (__comp(__first, __min))
  __min = __first;
       else if (!__comp(__first, __max))
  __max = __first;
       break;
     }

   if (__comp(__next, __first))
     {
       if (__comp(__next, __min))
  __min = __next;
       if (!__comp(__first, __max))
  __max = __first;
     }
   else
     {
       if (__comp(__first, __min))
  __min = __first;
       if (!__comp(__next, __max))
  __max = __next;
     }

   __first = __next;
   ++__first;
 }

      return std::make_pair(__min, __max);
    }
# 3382 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline pair<_ForwardIterator, _ForwardIterator>
    minmax_element(_ForwardIterator __first, _ForwardIterator __last)
    {




                                                     ;
                                                     ;

      return std::__minmax_element(__first, __last,
       __gnu_cxx::__ops::__iter_less_iter());
    }
# 3410 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Compare>

    inline pair<_ForwardIterator, _ForwardIterator>
    minmax_element(_ForwardIterator __first, _ForwardIterator __last,
     _Compare __comp)
    {





                                                     ;
                                                                  ;

      return std::__minmax_element(__first, __last,
       __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _Tp>

    inline pair<_Tp, _Tp>
    minmax(initializer_list<_Tp> __l)
    {
                                                            ;
      pair<const _Tp*, const _Tp*> __p =
 std::__minmax_element(__l.begin(), __l.end(),
         __gnu_cxx::__ops::__iter_less_iter());
      return std::make_pair(*__p.first, *__p.second);
    }

  template<typename _Tp, typename _Compare>

    inline pair<_Tp, _Tp>
    minmax(initializer_list<_Tp> __l, _Compare __comp)
    {
                                                                         ;
      pair<const _Tp*, const _Tp*> __p =
 std::__minmax_element(__l.begin(), __l.end(),
         __gnu_cxx::__ops::__iter_comp_iter(__comp));
      return std::make_pair(*__p.first, *__p.second);
    }
# 3466 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    inline bool
    is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
     _ForwardIterator2 __first2, _BinaryPredicate __pred)
    {






                                                       ;

      return std::__is_permutation(__first1, __last1, __first2,
       __gnu_cxx::__ops::__iter_comp_iter(__pred));
    }
# 3671 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _IntType, typename _UniformRandomBitGenerator>
    pair<_IntType, _IntType>
    __gen_two_uniform_ints(_IntType __b0, _IntType __b1,
      _UniformRandomBitGenerator&& __g)
    {
      _IntType __x
 = uniform_int_distribution<_IntType>{0, (__b0 * __b1) - 1}(__g);
      return std::make_pair(__x / __b1, __x % __b1);
    }
# 3693 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator,
    typename _UniformRandomNumberGenerator>
    void
    shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last,
     _UniformRandomNumberGenerator&& __g)
    {



                                                     ;

      if (__first == __last)
 return;

      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
 _DistanceType;

      typedef typename std::make_unsigned<_DistanceType>::type __ud_type;
      typedef typename std::uniform_int_distribution<__ud_type> __distr_type;
      typedef typename __distr_type::param_type __p_type;

      typedef typename remove_reference<_UniformRandomNumberGenerator>::type
 _Gen;
      typedef typename common_type<typename _Gen::result_type, __ud_type>::type
 __uc_type;

      const __uc_type __urngrange = __g.max() - __g.min();
      const __uc_type __urange = __uc_type(__last - __first);

      if (__urngrange / __urange >= __urange)

      {
 _RandomAccessIterator __i = __first + 1;





 if ((__urange % 2) == 0)
 {
   __distr_type __d{0, 1};
   std::iter_swap(__i++, __first + __d(__g));
 }





 while (__i != __last)
 {
   const __uc_type __swap_range = __uc_type(__i - __first) + 1;

   const pair<__uc_type, __uc_type> __pospos =
     __gen_two_uniform_ints(__swap_range, __swap_range + 1, __g);

   std::iter_swap(__i++, __first + __pospos.first);
   std::iter_swap(__i++, __first + __pospos.second);
 }

 return;
      }

      __distr_type __d;

      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
 std::iter_swap(__i, __first + __d(__g, __p_type(0, __i - __first)));
    }
# 3778 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Function>

    _Function
    for_each(_InputIterator __first, _InputIterator __last, _Function __f)
    {


                                                     ;
      for (; __first != __last; ++__first)
 __f(*__first);
      return __f;
    }
# 3840 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Tp>

    inline _InputIterator
    find(_InputIterator __first, _InputIterator __last,
  const _Tp& __val)
    {




                                                     ;
      return std::__find_if(__first, __last,
       __gnu_cxx::__ops::__iter_equals_val(__val));
    }
# 3865 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline _InputIterator
    find_if(_InputIterator __first, _InputIterator __last,
     _Predicate __pred)
    {




                                                     ;

      return std::__find_if(__first, __last,
       __gnu_cxx::__ops::__pred_iter(__pred));
    }
# 3897 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _ForwardIterator>

    _InputIterator
    find_first_of(_InputIterator __first1, _InputIterator __last1,
    _ForwardIterator __first2, _ForwardIterator __last2)
    {






                                                       ;
                                                       ;

      for (; __first1 != __last1; ++__first1)
 for (_ForwardIterator __iter = __first2; __iter != __last2; ++__iter)
   if (*__first1 == *__iter)
     return __first1;
      return __last1;
    }
# 3938 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _ForwardIterator,
    typename _BinaryPredicate>

    _InputIterator
    find_first_of(_InputIterator __first1, _InputIterator __last1,
    _ForwardIterator __first2, _ForwardIterator __last2,
    _BinaryPredicate __comp)
    {






                                                       ;
                                                       ;

      for (; __first1 != __last1; ++__first1)
 for (_ForwardIterator __iter = __first2; __iter != __last2; ++__iter)
   if (__comp(*__first1, *__iter))
     return __first1;
      return __last1;
    }
# 3971 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline _ForwardIterator
    adjacent_find(_ForwardIterator __first, _ForwardIterator __last)
    {




                                                     ;

      return std::__adjacent_find(__first, __last,
      __gnu_cxx::__ops::__iter_equal_to_iter());
    }
# 3997 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _BinaryPredicate>

    inline _ForwardIterator
    adjacent_find(_ForwardIterator __first, _ForwardIterator __last,
    _BinaryPredicate __binary_pred)
    {





                                                     ;

      return std::__adjacent_find(__first, __last,
   __gnu_cxx::__ops::__iter_comp_iter(__binary_pred));
    }
# 4023 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Tp>

    inline typename iterator_traits<_InputIterator>::difference_type
    count(_InputIterator __first, _InputIterator __last, const _Tp& __value)
    {




                                                     ;

      return std::__count_if(__first, __last,
        __gnu_cxx::__ops::__iter_equals_val(__value));
    }
# 4047 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _Predicate>

    inline typename iterator_traits<_InputIterator>::difference_type
    count_if(_InputIterator __first, _InputIterator __last, _Predicate __pred)
    {




                                                     ;

      return std::__count_if(__first, __last,
        __gnu_cxx::__ops::__pred_iter(__pred));
    }
# 4088 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2>

    inline _ForwardIterator1
    search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
    _ForwardIterator2 __first2, _ForwardIterator2 __last2)
    {






                                                       ;
                                                       ;

      return std::__search(__first1, __last1, __first2, __last2,
      __gnu_cxx::__ops::__iter_equal_to_iter());
    }
# 4128 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator1, typename _ForwardIterator2,
    typename _BinaryPredicate>

    inline _ForwardIterator1
    search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
    _ForwardIterator2 __first2, _ForwardIterator2 __last2,
    _BinaryPredicate __predicate)
    {






                                                       ;
                                                       ;

      return std::__search(__first1, __last1, __first2, __last2,
      __gnu_cxx::__ops::__iter_comp_iter(__predicate));
    }
# 4164 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Integer, typename _Tp>

    inline _ForwardIterator
    search_n(_ForwardIterator __first, _ForwardIterator __last,
      _Integer __count, const _Tp& __val)
    {




                                                     ;

      return std::__search_n(__first, __last, __count,
        __gnu_cxx::__ops::__iter_equals_val(__val));
    }
# 4198 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Integer, typename _Tp,
    typename _BinaryPredicate>

    inline _ForwardIterator
    search_n(_ForwardIterator __first, _ForwardIterator __last,
      _Integer __count, const _Tp& __val,
      _BinaryPredicate __binary_pred)
    {




                                                     ;

      return std::__search_n(__first, __last, __count,
  __gnu_cxx::__ops::__iter_comp_val(__binary_pred, __val));
    }
# 4248 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator,
    typename _UnaryOperation>

    _OutputIterator
    transform(_InputIterator __first, _InputIterator __last,
       _OutputIterator __result, _UnaryOperation __unary_op)
    {





                                                     ;

      for (; __first != __last; ++__first, (void)++__result)
 *__result = __unary_op(*__first);
      return __result;
    }
# 4286 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _BinaryOperation>

    _OutputIterator
    transform(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _OutputIterator __result,
       _BinaryOperation __binary_op)
    {






                                                       ;

      for (; __first1 != __last1; ++__first1, (void)++__first2, ++__result)
 *__result = __binary_op(*__first1, *__first2);
      return __result;
    }
# 4320 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Tp>

    void
    replace(_ForwardIterator __first, _ForwardIterator __last,
     const _Tp& __old_value, const _Tp& __new_value)
    {







                                                     ;

      for (; __first != __last; ++__first)
 if (*__first == __old_value)
   *__first = __new_value;
    }
# 4353 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Predicate, typename _Tp>

    void
    replace_if(_ForwardIterator __first, _ForwardIterator __last,
        _Predicate __pred, const _Tp& __new_value)
    {







                                                     ;

      for (; __first != __last; ++__first)
 if (__pred(*__first))
   *__first = __new_value;
    }
# 4386 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Generator>

    void
    generate(_ForwardIterator __first, _ForwardIterator __last,
      _Generator __gen)
    {




                                                     ;

      for (; __first != __last; ++__first)
 *__first = __gen();
    }
# 4420 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _OutputIterator, typename _Size, typename _Generator>

    _OutputIterator
    generate_n(_OutputIterator __first, _Size __n, _Generator __gen)
    {





      typedef __decltype(std::__size_to_integer(__n)) _IntSize;
      for (_IntSize __niter = std::__size_to_integer(__n);
    __niter > 0; --__niter, (void) ++__first)
 *__first = __gen();
      return __first;
    }
# 4458 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator>

    inline _OutputIterator
    unique_copy(_InputIterator __first, _InputIterator __last,
  _OutputIterator __result)
    {






                                                     ;

      if (__first == __last)
 return __result;
      return std::__unique_copy(__first, __last, __result,
    __gnu_cxx::__ops::__iter_equal_to_iter(),
    std::__iterator_category(__first),
    std::__iterator_category(__result));
    }
# 4499 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator, typename _OutputIterator,
    typename _BinaryPredicate>

    inline _OutputIterator
    unique_copy(_InputIterator __first, _InputIterator __last,
  _OutputIterator __result,
  _BinaryPredicate __binary_pred)
    {




                                                     ;

      if (__first == __last)
 return __result;
      return std::__unique_copy(__first, __last, __result,
   __gnu_cxx::__ops::__iter_comp_iter(__binary_pred),
    std::__iterator_category(__first),
    std::__iterator_category(__result));
    }
# 4538 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator>

    inline void
    random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {



                                                     ;

      if (__first != __last)
 for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
   {

     _RandomAccessIterator __j = __first
     + std::rand() % ((__i - __first) + 1);
     if (__i != __j)
       std::iter_swap(__i, __j);
   }
    }
# 4578 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator, typename _RandomNumberGenerator>

    void
    random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last,

     _RandomNumberGenerator&& __rand)



    {



                                                     ;

      if (__first == __last)
 return;
      for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
 {
   _RandomAccessIterator __j = __first + __rand((__i - __first) + 1);
   if (__i != __j)
     std::iter_swap(__i, __j);
 }
    }
# 4619 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Predicate>

    inline _ForwardIterator
    partition(_ForwardIterator __first, _ForwardIterator __last,
       _Predicate __pred)
    {





                                                     ;

      return std::__partition(__first, __last, __pred,
         std::__iterator_category(__first));
    }
# 4653 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator>

    inline void
    partial_sort(_RandomAccessIterator __first,
   _RandomAccessIterator __middle,
   _RandomAccessIterator __last)
    {





                                                       ;
                                                      ;
                                                     ;

      std::__partial_sort(__first, __middle, __last,
     __gnu_cxx::__ops::__iter_less_iter());
    }
# 4692 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    partial_sort(_RandomAccessIterator __first,
   _RandomAccessIterator __middle,
   _RandomAccessIterator __last,
   _Compare __comp)
    {






                                                       ;
                                                      ;
                                                                  ;

      std::__partial_sort(__first, __middle, __last,
     __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 4729 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator>

    inline void
    nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth,
  _RandomAccessIterator __last)
    {





                                                    ;
                                                   ;
                                                     ;

      if (__first == __last || __nth == __last)
 return;

      std::__introselect(__first, __nth, __last,
    std::__lg(__last - __first) * 2,
    __gnu_cxx::__ops::__iter_less_iter());
    }
# 4769 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth,
  _RandomAccessIterator __last, _Compare __comp)
    {






                                                    ;
                                                   ;
                                                                  ;

      if (__first == __last || __nth == __last)
 return;

      std::__introselect(__first, __nth, __last,
    std::__lg(__last - __first) * 2,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 4807 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator>

    inline void
    sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                     ;
                                                     ;

      std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
    }
# 4838 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator, typename _Compare>

    inline void
    sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
  _Compare __comp)
    {






                                                     ;
                                                                  ;

      std::__sort(__first, __last, __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    _OutputIterator
    __merge(_InputIterator1 __first1, _InputIterator1 __last1,
     _InputIterator2 __first2, _InputIterator2 __last2,
     _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 {
   if (__comp(__first2, __first1))
     {
       *__result = *__first2;
       ++__first2;
     }
   else
     {
       *__result = *__first1;
       ++__first1;
     }
   ++__result;
 }
      return std::copy(__first2, __last2,
         std::copy(__first1, __last1, __result));
    }
# 4901 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator>

    inline _OutputIterator
    merge(_InputIterator1 __first1, _InputIterator1 __last1,
   _InputIterator2 __first2, _InputIterator2 __last2,
   _OutputIterator __result)
    {
# 4919 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__merge(__first1, __last1,
         __first2, __last2, __result,
         __gnu_cxx::__ops::__iter_less_iter());
    }
# 4952 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    inline _OutputIterator
    merge(_InputIterator1 __first1, _InputIterator1 __last1,
   _InputIterator2 __first2, _InputIterator2 __last2,
   _OutputIterator __result, _Compare __comp)
    {
# 4970 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__merge(__first1, __last1,
    __first2, __last2, __result,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _RandomAccessIterator, typename _Compare>
    inline void
    __stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
    _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
 _ValueType;
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
 _DistanceType;
      typedef _Temporary_buffer<_RandomAccessIterator, _ValueType> _TmpBuf;

      if (__first == __last)
 return;



      _TmpBuf __buf(__first, (__last - __first + 1) / 2);

      if (__buf.begin() == 0)
 std::__inplace_stable_sort(__first, __last, __comp);
      else
 std::__stable_sort_adaptive(__first, __last, __buf.begin(),
        _DistanceType(__buf.size()), __comp);
    }
# 5022 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator>
    inline void
    stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
    {





                                                     ;
                                                     ;

      std::__stable_sort(__first, __last,
        __gnu_cxx::__ops::__iter_less_iter());
    }
# 5056 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _RandomAccessIterator, typename _Compare>
    inline void
    stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
  _Compare __comp)
    {






                                                     ;
                                                                  ;

      std::__stable_sort(__first, __last,
        __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator,
    typename _Compare>

    _OutputIterator
    __set_union(_InputIterator1 __first1, _InputIterator1 __last1,
  _InputIterator2 __first2, _InputIterator2 __last2,
  _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 {
   if (__comp(__first1, __first2))
     {
       *__result = *__first1;
       ++__first1;
     }
   else if (__comp(__first2, __first1))
     {
       *__result = *__first2;
       ++__first2;
     }
   else
     {
       *__result = *__first1;
       ++__first1;
       ++__first2;
     }
   ++__result;
 }
      return std::copy(__first2, __last2,
         std::copy(__first1, __last1, __result));
    }
# 5126 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator>

    inline _OutputIterator
    set_union(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _InputIterator2 __last2,
       _OutputIterator __result)
    {
# 5147 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__set_union(__first1, __last1,
    __first2, __last2, __result,
    __gnu_cxx::__ops::__iter_less_iter());
    }
# 5177 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    inline _OutputIterator
    set_union(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _InputIterator2 __last2,
       _OutputIterator __result, _Compare __comp)
    {
# 5198 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__set_union(__first1, __last1,
    __first2, __last2, __result,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator,
    typename _Compare>

    _OutputIterator
    __set_intersection(_InputIterator1 __first1, _InputIterator1 __last1,
         _InputIterator2 __first2, _InputIterator2 __last2,
         _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 if (__comp(__first1, __first2))
   ++__first1;
 else if (__comp(__first2, __first1))
   ++__first2;
 else
   {
     *__result = *__first1;
     ++__first1;
     ++__first2;
     ++__result;
   }
      return __result;
    }
# 5250 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator>

    inline _OutputIterator
    set_intersection(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _InputIterator2 __last2,
       _OutputIterator __result)
    {
# 5269 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__set_intersection(__first1, __last1,
         __first2, __last2, __result,
         __gnu_cxx::__ops::__iter_less_iter());
    }
# 5300 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    inline _OutputIterator
    set_intersection(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _InputIterator2 __last2,
       _OutputIterator __result, _Compare __comp)
    {
# 5319 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__set_intersection(__first1, __last1,
    __first2, __last2, __result,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator,
    typename _Compare>

    _OutputIterator
    __set_difference(_InputIterator1 __first1, _InputIterator1 __last1,
       _InputIterator2 __first2, _InputIterator2 __last2,
       _OutputIterator __result, _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 if (__comp(__first1, __first2))
   {
     *__result = *__first1;
     ++__first1;
     ++__result;
   }
 else if (__comp(__first2, __first1))
   ++__first2;
 else
   {
     ++__first1;
     ++__first2;
   }
      return std::copy(__first1, __last1, __result);
    }
# 5375 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator>

    inline _OutputIterator
    set_difference(_InputIterator1 __first1, _InputIterator1 __last1,
     _InputIterator2 __first2, _InputIterator2 __last2,
     _OutputIterator __result)
    {
# 5394 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__set_difference(__first1, __last1,
       __first2, __last2, __result,
       __gnu_cxx::__ops::__iter_less_iter());
    }
# 5427 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    inline _OutputIterator
    set_difference(_InputIterator1 __first1, _InputIterator1 __last1,
     _InputIterator2 __first2, _InputIterator2 __last2,
     _OutputIterator __result, _Compare __comp)
    {
# 5446 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__set_difference(__first1, __last1,
       __first2, __last2, __result,
       __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator,
    typename _Compare>

    _OutputIterator
    __set_symmetric_difference(_InputIterator1 __first1,
          _InputIterator1 __last1,
          _InputIterator2 __first2,
          _InputIterator2 __last2,
          _OutputIterator __result,
          _Compare __comp)
    {
      while (__first1 != __last1 && __first2 != __last2)
 if (__comp(__first1, __first2))
   {
     *__result = *__first1;
     ++__first1;
     ++__result;
   }
 else if (__comp(__first2, __first1))
   {
     *__result = *__first2;
     ++__first2;
     ++__result;
   }
 else
   {
     ++__first1;
     ++__first2;
   }
      return std::copy(__first2, __last2,
         std::copy(__first1, __last1, __result));
    }
# 5508 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator>

    inline _OutputIterator
    set_symmetric_difference(_InputIterator1 __first1, _InputIterator1 __last1,
        _InputIterator2 __first2, _InputIterator2 __last2,
        _OutputIterator __result)
    {
# 5529 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                ;
                                                                ;
                                                        ;
                                                        ;

      return std::__set_symmetric_difference(__first1, __last1,
     __first2, __last2, __result,
     __gnu_cxx::__ops::__iter_less_iter());
    }
# 5560 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _OutputIterator, typename _Compare>

    inline _OutputIterator
    set_symmetric_difference(_InputIterator1 __first1, _InputIterator1 __last1,
        _InputIterator2 __first2, _InputIterator2 __last2,
        _OutputIterator __result,
        _Compare __comp)
    {
# 5582 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
                                                                             ;
                                                                             ;
                                                                     ;
                                                                     ;

      return std::__set_symmetric_difference(__first1, __last1,
    __first2, __last2, __result,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _ForwardIterator, typename _Compare>

    _ForwardIterator
    __min_element(_ForwardIterator __first, _ForwardIterator __last,
    _Compare __comp)
    {
      if (__first == __last)
 return __first;
      _ForwardIterator __result = __first;
      while (++__first != __last)
 if (__comp(__first, __result))
   __result = __first;
      return __result;
    }
# 5614 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    _ForwardIterator
    inline min_element(_ForwardIterator __first, _ForwardIterator __last)
    {




                                                     ;
                                                     ;

      return std::__min_element(__first, __last,
    __gnu_cxx::__ops::__iter_less_iter());
    }
# 5639 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Compare>

    inline _ForwardIterator
    min_element(_ForwardIterator __first, _ForwardIterator __last,
  _Compare __comp)
    {





                                                     ;
                                                                  ;

      return std::__min_element(__first, __last,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _ForwardIterator, typename _Compare>

    _ForwardIterator
    __max_element(_ForwardIterator __first, _ForwardIterator __last,
    _Compare __comp)
    {
      if (__first == __last) return __first;
      _ForwardIterator __result = __first;
      while (++__first != __last)
 if (__comp(__result, __first))
   __result = __first;
      return __result;
    }
# 5678 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator>

    inline _ForwardIterator
    max_element(_ForwardIterator __first, _ForwardIterator __last)
    {




                                                     ;
                                                     ;

      return std::__max_element(__first, __last,
    __gnu_cxx::__ops::__iter_less_iter());
    }
# 5703 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
  template<typename _ForwardIterator, typename _Compare>

    inline _ForwardIterator
    max_element(_ForwardIterator __first, _ForwardIterator __last,
  _Compare __comp)
    {





                                                     ;
                                                                  ;

      return std::__max_element(__first, __last,
    __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }



  template<typename _Tp>

    inline _Tp
    min(initializer_list<_Tp> __l)
    {
                                                            ;
      return *std::__min_element(__l.begin(), __l.end(),
   __gnu_cxx::__ops::__iter_less_iter());
    }

  template<typename _Tp, typename _Compare>

    inline _Tp
    min(initializer_list<_Tp> __l, _Compare __comp)
    {
                                                                         ;
      return *std::__min_element(__l.begin(), __l.end(),
   __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }

  template<typename _Tp>

    inline _Tp
    max(initializer_list<_Tp> __l)
    {
                                                            ;
      return *std::__max_element(__l.begin(), __l.end(),
   __gnu_cxx::__ops::__iter_less_iter());
    }

  template<typename _Tp, typename _Compare>

    inline _Tp
    max(initializer_list<_Tp> __l, _Compare __comp)
    {
                                                                         ;
      return *std::__max_element(__l.begin(), __l.end(),
   __gnu_cxx::__ops::__iter_comp_iter(__comp));
    }
# 5894 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_algo.h" 3
}
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/algorithm" 2 3
# 56 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/algorithm" 2 3








namespace std {
# 77 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/algorithm" 3
template <class __T, class __Cmp>
__attribute__((enable_if(true, "")))
inline __attribute__((host)) __attribute__((device)) const __T &
max(const __T &__a, const __T &__b, __Cmp __cmp) {
  return __cmp(__a, __b) ? __b : __a;
}

template <class __T>
__attribute__((enable_if(true, "")))
inline __attribute__((host)) __attribute__((device)) const __T &
max(const __T &__a, const __T &__b) {
  return __a < __b ? __b : __a;
}

template <class __T, class __Cmp>
__attribute__((enable_if(true, "")))
inline __attribute__((host)) __attribute__((device)) const __T &
min(const __T &__a, const __T &__b, __Cmp __cmp) {
  return __cmp(__b, __a) ? __b : __a;
}

template <class __T>
__attribute__((enable_if(true, "")))
inline __attribute__((host)) __attribute__((device)) const __T &
min(const __T &__a, const __T &__b) {
  return __a < __b ? __a : __b;
}
# 113 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/algorithm" 3
}
# 19 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 2 3

# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/limits.h" 1 3
# 21 "/usr/lib/llvm-15/lib/clang/15.0.6/include/limits.h" 3
# 1 "/usr/include/limits.h" 1 3 4
# 26 "/usr/include/limits.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/limits.h" 2 3 4
# 195 "/usr/include/limits.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/posix1_lim.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/posix1_lim.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 28 "/usr/include/x86_64-linux-gnu/bits/posix1_lim.h" 2 3 4
# 161 "/usr/include/x86_64-linux-gnu/bits/posix1_lim.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/local_lim.h" 1 3 4
# 38 "/usr/include/x86_64-linux-gnu/bits/local_lim.h" 3 4
# 1 "/usr/include/linux/limits.h" 1 3 4
# 39 "/usr/include/x86_64-linux-gnu/bits/local_lim.h" 2 3 4
# 81 "/usr/include/x86_64-linux-gnu/bits/local_lim.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/pthread_stack_min-dynamic.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/pthread_stack_min-dynamic.h" 3 4
extern "C" {
extern long int __sysconf (int __name) noexcept (true);
}
# 82 "/usr/include/x86_64-linux-gnu/bits/local_lim.h" 2 3 4
# 162 "/usr/include/x86_64-linux-gnu/bits/posix1_lim.h" 2 3 4
# 196 "/usr/include/limits.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/posix2_lim.h" 1 3 4
# 200 "/usr/include/limits.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/xopen_lim.h" 1 3 4
# 64 "/usr/include/x86_64-linux-gnu/bits/xopen_lim.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/uio_lim.h" 1 3 4
# 65 "/usr/include/x86_64-linux-gnu/bits/xopen_lim.h" 2 3 4
# 204 "/usr/include/limits.h" 2 3 4
# 22 "/usr/lib/llvm-15/lib/clang/15.0.6/include/limits.h" 2 3
# 21 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 2 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdint.h" 1 3
# 52 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdint.h" 3
# 1 "/usr/include/stdint.h" 1 3 4
# 26 "/usr/include/stdint.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 27 "/usr/include/stdint.h" 2 3 4

# 1 "/usr/include/x86_64-linux-gnu/bits/wchar.h" 1 3 4
# 29 "/usr/include/stdint.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 30 "/usr/include/stdint.h" 2 3 4







# 1 "/usr/include/x86_64-linux-gnu/bits/stdint-uintn.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/bits/stdint-uintn.h" 3 4
typedef __uint8_t uint8_t;
typedef __uint16_t uint16_t;
typedef __uint32_t uint32_t;
typedef __uint64_t uint64_t;
# 38 "/usr/include/stdint.h" 2 3 4





typedef __int_least8_t int_least8_t;
typedef __int_least16_t int_least16_t;
typedef __int_least32_t int_least32_t;
typedef __int_least64_t int_least64_t;


typedef __uint_least8_t uint_least8_t;
typedef __uint_least16_t uint_least16_t;
typedef __uint_least32_t uint_least32_t;
typedef __uint_least64_t uint_least64_t;





typedef signed char int_fast8_t;

typedef long int int_fast16_t;
typedef long int int_fast32_t;
typedef long int int_fast64_t;
# 71 "/usr/include/stdint.h" 3 4
typedef unsigned char uint_fast8_t;

typedef unsigned long int uint_fast16_t;
typedef unsigned long int uint_fast32_t;
typedef unsigned long int uint_fast64_t;
# 87 "/usr/include/stdint.h" 3 4
typedef long int intptr_t;


typedef unsigned long int uintptr_t;
# 101 "/usr/include/stdint.h" 3 4
typedef __intmax_t intmax_t;
typedef __uintmax_t uintmax_t;
# 53 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdint.h" 2 3
# 22 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 2 3
# 72 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
uint64_t __make_mantissa_base8(const char *__tagp) {
  uint64_t __r = 0;
  while (__tagp) {
    char __tmp = *__tagp;

    if (__tmp >= '0' && __tmp <= '7')
      __r = (__r * 8u) + __tmp - '0';
    else
      return 0;

    ++__tagp;
  }

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
uint64_t __make_mantissa_base10(const char *__tagp) {
  uint64_t __r = 0;
  while (__tagp) {
    char __tmp = *__tagp;

    if (__tmp >= '0' && __tmp <= '9')
      __r = (__r * 10u) + __tmp - '0';
    else
      return 0;

    ++__tagp;
  }

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
uint64_t __make_mantissa_base16(const char *__tagp) {
  uint64_t __r = 0;
  while (__tagp) {
    char __tmp = *__tagp;

    if (__tmp >= '0' && __tmp <= '9')
      __r = (__r * 16u) + __tmp - '0';
    else if (__tmp >= 'a' && __tmp <= 'f')
      __r = (__r * 16u) + __tmp - 'a' + 10;
    else if (__tmp >= 'A' && __tmp <= 'F')
      __r = (__r * 16u) + __tmp - 'A' + 10;
    else
      return 0;

    ++__tagp;
  }

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
uint64_t __make_mantissa(const char *__tagp) {
  if (!__tagp)
    return 0u;

  if (*__tagp == '0') {
    ++__tagp;

    if (*__tagp == 'x' || *__tagp == 'X')
      return __make_mantissa_base16(__tagp);
    else
      return __make_mantissa_base8(__tagp);
  }

  return __make_mantissa_base10(__tagp);
}



static __attribute__((device)) inline __attribute__((always_inline))
int abs(int __x) {
  int __sgn = __x >> (sizeof(int) * 8 - 1);
  return (__x ^ __sgn) - __sgn;
}
static __attribute__((device)) inline __attribute__((always_inline))
long labs(long __x) {
  long __sgn = __x >> (sizeof(long) * 8 - 1);
  return (__x ^ __sgn) - __sgn;
}
static __attribute__((device)) inline __attribute__((always_inline))
long long llabs(long long __x) {
  long long __sgn = __x >> (sizeof(long long) * 8 - 1);
  return (__x ^ __sgn) - __sgn;
}


static __attribute__((device)) inline __attribute__((always_inline))
float acosf(float __x) { return __ocml_acos_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float acoshf(float __x) { return __ocml_acosh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float asinf(float __x) { return __ocml_asin_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float asinhf(float __x) { return __ocml_asinh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float atan2f(float __x, float __y) { return __ocml_atan2_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float atanf(float __x) { return __ocml_atan_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float atanhf(float __x) { return __ocml_atanh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float cbrtf(float __x) { return __ocml_cbrt_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float ceilf(float __x) { return __ocml_ceil_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float copysignf(float __x, float __y) { return __ocml_copysign_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float cosf(float __x) { return __ocml_cos_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float coshf(float __x) { return __ocml_cosh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float cospif(float __x) { return __ocml_cospi_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float cyl_bessel_i0f(float __x) { return __ocml_i0_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float cyl_bessel_i1f(float __x) { return __ocml_i1_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float erfcf(float __x) { return __ocml_erfc_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float erfcinvf(float __x) { return __ocml_erfcinv_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float erfcxf(float __x) { return __ocml_erfcx_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float erff(float __x) { return __ocml_erf_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float erfinvf(float __x) { return __ocml_erfinv_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float exp10f(float __x) { return __ocml_exp10_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float exp2f(float __x) { return __ocml_exp2_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float expf(float __x) { return __ocml_exp_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float expm1f(float __x) { return __ocml_expm1_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float fabsf(float __x) { return __ocml_fabs_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float fdimf(float __x, float __y) { return __ocml_fdim_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float fdividef(float __x, float __y) { return __x / __y; }

static __attribute__((device)) inline __attribute__((always_inline))
float floorf(float __x) { return __ocml_floor_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float fmaf(float __x, float __y, float __z) {
  return __ocml_fma_f32(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
float fmaxf(float __x, float __y) { return __ocml_fmax_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float fminf(float __x, float __y) { return __ocml_fmin_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float fmodf(float __x, float __y) { return __ocml_fmod_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float frexpf(float __x, int *__nptr) {
  int __tmp;



  float __r =
      __ocml_frexp_f32(__x, (__attribute__((address_space(5))) int *)&__tmp);
  *__nptr = __tmp;

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
float hypotf(float __x, float __y) { return __ocml_hypot_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
int ilogbf(float __x) { return __ocml_ilogb_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __finitef(float __x) { return __ocml_isfinite_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __isinff(float __x) { return __ocml_isinf_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __isnanf(float __x) { return __ocml_isnan_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float j0f(float __x) { return __ocml_j0_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float j1f(float __x) { return __ocml_j1_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float jnf(int __n, float __x) {



  if (__n == 0)
    return j0f(__x);
  if (__n == 1)
    return j1f(__x);

  float __x0 = j0f(__x);
  float __x1 = j1f(__x);
  for (int __i = 1; __i < __n; ++__i) {
    float __x2 = (2 * __i) / __x * __x1 - __x0;
    __x0 = __x1;
    __x1 = __x2;
  }

  return __x1;
}

static __attribute__((device)) inline __attribute__((always_inline))
float ldexpf(float __x, int __e) { return __ocml_ldexp_f32(__x, __e); }

static __attribute__((device)) inline __attribute__((always_inline))
float lgammaf(float __x) { return __ocml_lgamma_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long long int llrintf(float __x) { return __ocml_rint_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long long int llroundf(float __x) { return __ocml_round_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float log10f(float __x) { return __ocml_log10_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float log1pf(float __x) { return __ocml_log1p_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float log2f(float __x) { return __ocml_log2_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float logbf(float __x) { return __ocml_logb_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float logf(float __x) { return __ocml_log_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long int lrintf(float __x) { return __ocml_rint_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long int lroundf(float __x) { return __ocml_round_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float modff(float __x, float *__iptr) {
  float __tmp;



  float __r =
      __ocml_modf_f32(__x, (__attribute__((address_space(5))) float *)&__tmp);
  *__iptr = __tmp;
  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
float nanf(const char *__tagp) {
  union {
    float val;
    struct ieee_float {
      unsigned int mantissa : 22;
      unsigned int quiet : 1;
      unsigned int exponent : 8;
      unsigned int sign : 1;
    } bits;
  } __tmp;
  static_assert((sizeof(__tmp.val)) == (sizeof(__tmp.bits)), "");

  __tmp.bits.sign = 0u;
  __tmp.bits.exponent = ~0u;
  __tmp.bits.quiet = 1u;
  __tmp.bits.mantissa = __make_mantissa(__tagp);

  return __tmp.val;
}

static __attribute__((device)) inline __attribute__((always_inline))
float nearbyintf(float __x) { return __ocml_nearbyint_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float nextafterf(float __x, float __y) {
  return __ocml_nextafter_f32(__x, __y);
}

static __attribute__((device)) inline __attribute__((always_inline))
float norm3df(float __x, float __y, float __z) {
  return __ocml_len3_f32(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
float norm4df(float __x, float __y, float __z, float __w) {
  return __ocml_len4_f32(__x, __y, __z, __w);
}

static __attribute__((device)) inline __attribute__((always_inline))
float normcdff(float __x) { return __ocml_ncdf_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float normcdfinvf(float __x) { return __ocml_ncdfinv_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float normf(int __dim,
            const float *__a) {
  float __r = 0;
  while (__dim--) {
    __r += __a[0] * __a[0];
    ++__a;
  }

  return __ocml_sqrt_f32(__r);
}

static __attribute__((device)) inline __attribute__((always_inline))
float powf(float __x, float __y) { return __ocml_pow_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float powif(float __x, int __y) { return __ocml_pown_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float rcbrtf(float __x) { return __ocml_rcbrt_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float remainderf(float __x, float __y) {
  return __ocml_remainder_f32(__x, __y);
}

static __attribute__((device)) inline __attribute__((always_inline))
float remquof(float __x, float __y, int *__quo) {
  int __tmp;



  float __r = __ocml_remquo_f32(
      __x, __y, (__attribute__((address_space(5))) int *)&__tmp);
  *__quo = __tmp;

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
float rhypotf(float __x, float __y) { return __ocml_rhypot_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float rintf(float __x) { return __ocml_rint_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float rnorm3df(float __x, float __y, float __z) {
  return __ocml_rlen3_f32(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
float rnorm4df(float __x, float __y, float __z, float __w) {
  return __ocml_rlen4_f32(__x, __y, __z, __w);
}

static __attribute__((device)) inline __attribute__((always_inline))
float rnormf(int __dim,
             const float *__a) {
  float __r = 0;
  while (__dim--) {
    __r += __a[0] * __a[0];
    ++__a;
  }

  return __ocml_rsqrt_f32(__r);
}

static __attribute__((device)) inline __attribute__((always_inline))
float roundf(float __x) { return __ocml_round_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float rsqrtf(float __x) { return __ocml_rsqrt_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float scalblnf(float __x, long int __n) {
  return (__n < 2147483647) ? __ocml_scalbn_f32(__x, __n)
                         : __ocml_scalb_f32(__x, __n);
}

static __attribute__((device)) inline __attribute__((always_inline))
float scalbnf(float __x, int __n) { return __ocml_scalbn_f32(__x, __n); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __signbitf(float __x) { return __ocml_signbit_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
void sincosf(float __x, float *__sinptr, float *__cosptr) {
  float __tmp;



  *__sinptr =
      __ocml_sincos_f32(__x, (__attribute__((address_space(5))) float *)&__tmp);
  *__cosptr = __tmp;
}

static __attribute__((device)) inline __attribute__((always_inline))
void sincospif(float __x, float *__sinptr, float *__cosptr) {
  float __tmp;



  *__sinptr = __ocml_sincospi_f32(
      __x, (__attribute__((address_space(5))) float *)&__tmp);
  *__cosptr = __tmp;
}

static __attribute__((device)) inline __attribute__((always_inline))
float sinf(float __x) { return __ocml_sin_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float sinhf(float __x) { return __ocml_sinh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float sinpif(float __x) { return __ocml_sinpi_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float sqrtf(float __x) { return __ocml_sqrt_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float tanf(float __x) { return __ocml_tan_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float tanhf(float __x) { return __ocml_tanh_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float tgammaf(float __x) { return __ocml_tgamma_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float truncf(float __x) { return __ocml_trunc_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float y0f(float __x) { return __ocml_y0_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float y1f(float __x) { return __ocml_y1_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float ynf(int __n, float __x) {




  if (__n == 0)
    return y0f(__x);
  if (__n == 1)
    return y1f(__x);

  float __x0 = y0f(__x);
  float __x1 = y1f(__x);
  for (int __i = 1; __i < __n; ++__i) {
    float __x2 = (2 * __i) / __x * __x1 - __x0;
    __x0 = __x1;
    __x1 = __x2;
  }

  return __x1;
}



static __attribute__((device)) inline __attribute__((always_inline))
float __cosf(float __x) { return __ocml_native_cos_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __exp10f(float __x) { return __ocml_native_exp10_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __expf(float __x) { return __ocml_native_exp_f32(__x); }
# 586 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fadd_rn(float __x, float __y) { return __x + __y; }
# 600 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fdiv_rn(float __x, float __y) { return __x / __y; }


static __attribute__((device)) inline __attribute__((always_inline))
float __fdividef(float __x, float __y) { return __x / __y; }
# 625 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fmaf_rn(float __x, float __y, float __z) {
  return __ocml_fma_f32(__x, __y, __z);
}
# 641 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fmul_rn(float __x, float __y) { return __x * __y; }
# 655 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __frcp_rn(float __x) { return 1.0f / __x; }


static __attribute__((device)) inline __attribute__((always_inline))
float __frsqrt_rn(float __x) { return __llvm_amdgcn_rsq_f32(__x); }
# 672 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fsqrt_rn(float __x) { return __ocml_native_sqrt_f32(__x); }
# 686 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
float __fsub_rn(float __x, float __y) { return __x - __y; }


static __attribute__((device)) inline __attribute__((always_inline))
float __log10f(float __x) { return __ocml_native_log10_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __log2f(float __x) { return __ocml_native_log2_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __logf(float __x) { return __ocml_native_log_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __powf(float __x, float __y) { return __ocml_pow_f32(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float __saturatef(float __x) { return (__x < 0) ? 0 : ((__x > 1) ? 1 : __x); }

static __attribute__((device)) inline __attribute__((always_inline))
void __sincosf(float __x, float *__sinptr, float *__cosptr) {
  *__sinptr = __ocml_native_sin_f32(__x);
  *__cosptr = __ocml_native_cos_f32(__x);
}

static __attribute__((device)) inline __attribute__((always_inline))
float __sinf(float __x) { return __ocml_native_sin_f32(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
float __tanf(float __x) { return __ocml_tan_f32(__x); }




static __attribute__((device)) inline __attribute__((always_inline))
double acos(double __x) { return __ocml_acos_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double acosh(double __x) { return __ocml_acosh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double asin(double __x) { return __ocml_asin_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double asinh(double __x) { return __ocml_asinh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double atan(double __x) { return __ocml_atan_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double atan2(double __x, double __y) { return __ocml_atan2_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double atanh(double __x) { return __ocml_atanh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double cbrt(double __x) { return __ocml_cbrt_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double ceil(double __x) { return __ocml_ceil_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double copysign(double __x, double __y) {
  return __ocml_copysign_f64(__x, __y);
}

static __attribute__((device)) inline __attribute__((always_inline))
double cos(double __x) { return __ocml_cos_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double cosh(double __x) { return __ocml_cosh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double cospi(double __x) { return __ocml_cospi_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double cyl_bessel_i0(double __x) { return __ocml_i0_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double cyl_bessel_i1(double __x) { return __ocml_i1_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double erf(double __x) { return __ocml_erf_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double erfc(double __x) { return __ocml_erfc_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double erfcinv(double __x) { return __ocml_erfcinv_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double erfcx(double __x) { return __ocml_erfcx_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double erfinv(double __x) { return __ocml_erfinv_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double exp(double __x) { return __ocml_exp_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double exp10(double __x) { return __ocml_exp10_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double exp2(double __x) { return __ocml_exp2_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double expm1(double __x) { return __ocml_expm1_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double fabs(double __x) { return __ocml_fabs_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double fdim(double __x, double __y) { return __ocml_fdim_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double floor(double __x) { return __ocml_floor_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double fma(double __x, double __y, double __z) {
  return __ocml_fma_f64(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
double fmax(double __x, double __y) { return __ocml_fmax_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double fmin(double __x, double __y) { return __ocml_fmin_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double fmod(double __x, double __y) { return __ocml_fmod_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double frexp(double __x, int *__nptr) {
  int __tmp;



  double __r =
      __ocml_frexp_f64(__x, (__attribute__((address_space(5))) int *)&__tmp);
  *__nptr = __tmp;
  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
double hypot(double __x, double __y) { return __ocml_hypot_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
int ilogb(double __x) { return __ocml_ilogb_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __finite(double __x) { return __ocml_isfinite_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __isinf(double __x) { return __ocml_isinf_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __isnan(double __x) { return __ocml_isnan_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double j0(double __x) { return __ocml_j0_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double j1(double __x) { return __ocml_j1_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double jn(int __n, double __x) {




  if (__n == 0)
    return j0(__x);
  if (__n == 1)
    return j1(__x);

  double __x0 = j0(__x);
  double __x1 = j1(__x);
  for (int __i = 1; __i < __n; ++__i) {
    double __x2 = (2 * __i) / __x * __x1 - __x0;
    __x0 = __x1;
    __x1 = __x2;
  }
  return __x1;
}

static __attribute__((device)) inline __attribute__((always_inline))
double ldexp(double __x, int __e) { return __ocml_ldexp_f64(__x, __e); }

static __attribute__((device)) inline __attribute__((always_inline))
double lgamma(double __x) { return __ocml_lgamma_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long long int llrint(double __x) { return __ocml_rint_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long long int llround(double __x) { return __ocml_round_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double log(double __x) { return __ocml_log_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double log10(double __x) { return __ocml_log10_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double log1p(double __x) { return __ocml_log1p_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double log2(double __x) { return __ocml_log2_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double logb(double __x) { return __ocml_logb_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long int lrint(double __x) { return __ocml_rint_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
long int lround(double __x) { return __ocml_round_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double modf(double __x, double *__iptr) {
  double __tmp;



  double __r =
      __ocml_modf_f64(__x, (__attribute__((address_space(5))) double *)&__tmp);
  *__iptr = __tmp;

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
double nan(const char *__tagp) {

  union {
    double val;
    struct ieee_double {
      uint64_t mantissa : 51;
      uint32_t quiet : 1;
      uint32_t exponent : 11;
      uint32_t sign : 1;
    } bits;
  } __tmp;
  static_assert((sizeof(__tmp.val)) == (sizeof(__tmp.bits)), "");

  __tmp.bits.sign = 0u;
  __tmp.bits.exponent = ~0u;
  __tmp.bits.quiet = 1u;
  __tmp.bits.mantissa = __make_mantissa(__tagp);

  return __tmp.val;






}

static __attribute__((device)) inline __attribute__((always_inline))
double nearbyint(double __x) { return __ocml_nearbyint_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double nextafter(double __x, double __y) {
  return __ocml_nextafter_f64(__x, __y);
}

static __attribute__((device)) inline __attribute__((always_inline))
double norm(int __dim,
            const double *__a) {
  double __r = 0;
  while (__dim--) {
    __r += __a[0] * __a[0];
    ++__a;
  }

  return __ocml_sqrt_f64(__r);
}

static __attribute__((device)) inline __attribute__((always_inline))
double norm3d(double __x, double __y, double __z) {
  return __ocml_len3_f64(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
double norm4d(double __x, double __y, double __z, double __w) {
  return __ocml_len4_f64(__x, __y, __z, __w);
}

static __attribute__((device)) inline __attribute__((always_inline))
double normcdf(double __x) { return __ocml_ncdf_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double normcdfinv(double __x) { return __ocml_ncdfinv_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double pow(double __x, double __y) { return __ocml_pow_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double powi(double __x, int __y) { return __ocml_pown_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double rcbrt(double __x) { return __ocml_rcbrt_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double remainder(double __x, double __y) {
  return __ocml_remainder_f64(__x, __y);
}

static __attribute__((device)) inline __attribute__((always_inline))
double remquo(double __x, double __y, int *__quo) {
  int __tmp;



  double __r = __ocml_remquo_f64(
      __x, __y, (__attribute__((address_space(5))) int *)&__tmp);
  *__quo = __tmp;

  return __r;
}

static __attribute__((device)) inline __attribute__((always_inline))
double rhypot(double __x, double __y) { return __ocml_rhypot_f64(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double rint(double __x) { return __ocml_rint_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double rnorm(int __dim,
             const double *__a) {
  double __r = 0;
  while (__dim--) {
    __r += __a[0] * __a[0];
    ++__a;
  }

  return __ocml_rsqrt_f64(__r);
}

static __attribute__((device)) inline __attribute__((always_inline))
double rnorm3d(double __x, double __y, double __z) {
  return __ocml_rlen3_f64(__x, __y, __z);
}

static __attribute__((device)) inline __attribute__((always_inline))
double rnorm4d(double __x, double __y, double __z, double __w) {
  return __ocml_rlen4_f64(__x, __y, __z, __w);
}

static __attribute__((device)) inline __attribute__((always_inline))
double round(double __x) { return __ocml_round_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double rsqrt(double __x) { return __ocml_rsqrt_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double scalbln(double __x, long int __n) {
  return (__n < 2147483647) ? __ocml_scalbn_f64(__x, __n)
                         : __ocml_scalb_f64(__x, __n);
}
static __attribute__((device)) inline __attribute__((always_inline))
double scalbn(double __x, int __n) { return __ocml_scalbn_f64(__x, __n); }

static __attribute__((device)) inline __attribute__((always_inline))
bool __signbit(double __x) { return __ocml_signbit_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double sin(double __x) { return __ocml_sin_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
void sincos(double __x, double *__sinptr, double *__cosptr) {
  double __tmp;



  *__sinptr = __ocml_sincos_f64(
      __x, (__attribute__((address_space(5))) double *)&__tmp);
  *__cosptr = __tmp;
}

static __attribute__((device)) inline __attribute__((always_inline))
void sincospi(double __x, double *__sinptr, double *__cosptr) {
  double __tmp;



  *__sinptr = __ocml_sincospi_f64(
      __x, (__attribute__((address_space(5))) double *)&__tmp);
  *__cosptr = __tmp;
}

static __attribute__((device)) inline __attribute__((always_inline))
double sinh(double __x) { return __ocml_sinh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double sinpi(double __x) { return __ocml_sinpi_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double sqrt(double __x) { return __ocml_sqrt_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double tan(double __x) { return __ocml_tan_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double tanh(double __x) { return __ocml_tanh_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double tgamma(double __x) { return __ocml_tgamma_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double trunc(double __x) { return __ocml_trunc_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double y0(double __x) { return __ocml_y0_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double y1(double __x) { return __ocml_y1_f64(__x); }

static __attribute__((device)) inline __attribute__((always_inline))
double yn(int __n, double __x) {




  if (__n == 0)
    return y0(__x);
  if (__n == 1)
    return y1(__x);

  double __x0 = y0(__x);
  double __x1 = y1(__x);
  for (int __i = 1; __i < __n; ++__i) {
    double __x2 = (2 * __i) / __x * __x1 - __x0;
    __x0 = __x1;
    __x1 = __x2;
  }

  return __x1;
}
# 1146 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __dadd_rn(double __x, double __y) { return __x + __y; }
# 1168 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __ddiv_rn(double __x, double __y) { return __x / __y; }
# 1190 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __dmul_rn(double __x, double __y) { return __x * __y; }
# 1204 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __drcp_rn(double __x) { return 1.0 / __x; }
# 1218 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __dsqrt_rn(double __x) { return __ocml_sqrt_f64(__x); }
# 1240 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __dsub_rn(double __x, double __y) { return __x - __y; }
# 1262 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
static __attribute__((device)) inline __attribute__((always_inline))
double __fma_rn(double __x, double __y, double __z) {
  return __ocml_fma_f64(__x, __y, __z);
}
# 1280 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_math.h" 3
template <class T> static __attribute__((device)) inline __attribute__((always_inline)) T min(T __arg1, T __arg2) {
  return (__arg1 < __arg2) ? __arg1 : __arg2;
}

template <class T> static __attribute__((device)) inline __attribute__((always_inline)) T max(T __arg1, T __arg2) {
  return (__arg1 > __arg2) ? __arg1 : __arg2;
}

static __attribute__((device)) inline __attribute__((always_inline)) int min(int __arg1, int __arg2) {
  return (__arg1 < __arg2) ? __arg1 : __arg2;
}
static __attribute__((device)) inline __attribute__((always_inline)) int max(int __arg1, int __arg2) {
  return (__arg1 > __arg2) ? __arg1 : __arg2;
}

static __attribute__((device)) inline __attribute__((always_inline))
float max(float __x, float __y) { return fmaxf(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double max(double __x, double __y) { return fmax(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
float min(float __x, float __y) { return fminf(__x, __y); }

static __attribute__((device)) inline __attribute__((always_inline))
double min(double __x, double __y) { return fmin(__x, __y); }


__attribute__((host)) inline static int min(int __arg1, int __arg2) {
  return std::min(__arg1, __arg2);
}

__attribute__((host)) inline static int max(int __arg1, int __arg2) {
  return std::max(__arg1, __arg2);
}
# 116 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3




# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_cuda_math_forward_declares.h" 1 3
# 26 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_cuda_math_forward_declares.h" 3
static __inline__ __attribute__((always_inline)) __attribute__((device)) long abs(long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long long abs(long long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double abs(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float abs(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) int abs(int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double acos(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float acos(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double acosh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float acosh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double asin(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float asin(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double asinh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float asinh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double atan2(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float atan2(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double atan(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float atan(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double atanh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float atanh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double cbrt(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float cbrt(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double ceil(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float ceil(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double copysign(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float copysign(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double cos(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float cos(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double cosh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float cosh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double erfc(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float erfc(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double erf(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float erf(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double exp2(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float exp2(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double exp(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float exp(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double expm1(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float expm1(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fabs(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fabs(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fdim(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fdim(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double floor(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float floor(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fma(double, double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fma(float, float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fmax(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fmax(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fmin(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fmin(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double fmod(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float fmod(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) int fpclassify(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) int fpclassify(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double frexp(double, int *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float frexp(float, int *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double hypot(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float hypot(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) int ilogb(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) int ilogb(float);



static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isfinite(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isfinite(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isgreater(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isgreaterequal(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isgreaterequal(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isgreater(float, float);



static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isinf(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isinf(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isless(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool islessequal(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool islessequal(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isless(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool islessgreater(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool islessgreater(float, float);



static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isnan(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isnan(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isnormal(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isnormal(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isunordered(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool isunordered(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long labs(long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double ldexp(double, int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float ldexp(float, int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double lgamma(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float lgamma(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long long llabs(long long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long long llrint(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long long llrint(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double log10(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float log10(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double log1p(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float log1p(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double log2(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float log2(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double logb(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float logb(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double log(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float log(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long lrint(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long lrint(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long lround(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long lround(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) long long llround(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double modf(double, double *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float modf(float, float *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double nan(const char *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float nanf(const char *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double nearbyint(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float nearbyint(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double nextafter(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float nextafter(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double pow(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double pow(double, int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float pow(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float pow(float, int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double remainder(double, double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float remainder(float, float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double remquo(double, double, int *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float remquo(float, float, int *);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double rint(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float rint(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double round(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float round(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double scalbln(double, long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float scalbln(float, long);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double scalbn(double, int);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float scalbn(float, int);



static __inline__ __attribute__((always_inline)) __attribute__((device)) bool signbit(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) bool signbit(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double sin(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float sin(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double sinh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float sinh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double sqrt(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float sqrt(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double tan(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float tan(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double tanh(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float tanh(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double tgamma(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float tgamma(float);
static __inline__ __attribute__((always_inline)) __attribute__((device)) double trunc(double);
static __inline__ __attribute__((always_inline)) __attribute__((device)) float trunc(float);
# 194 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_cuda_math_forward_declares.h" 3
namespace std {





using ::abs;
using ::acos;
using ::acosh;
using ::asin;
using ::asinh;
using ::atan;
using ::atan2;
using ::atanh;
using ::cbrt;
using ::ceil;
using ::copysign;
using ::cos;
using ::cosh;
using ::erf;
using ::erfc;
using ::exp;
using ::exp2;
using ::expm1;
using ::fabs;
using ::fdim;
using ::floor;
using ::fma;
using ::fmax;
using ::fmin;
using ::fmod;
using ::fpclassify;
using ::frexp;
using ::hypot;
using ::ilogb;
using ::isfinite;
using ::isgreater;
using ::isgreaterequal;
using ::isinf;
using ::isless;
using ::islessequal;
using ::islessgreater;
using ::isnan;
using ::isnormal;
using ::isunordered;
using ::labs;
using ::ldexp;
using ::lgamma;
using ::llabs;
using ::llrint;
using ::log;
using ::log10;
using ::log1p;
using ::log2;
using ::logb;
using ::lrint;
using ::lround;
using ::llround;
using ::modf;
using ::nan;
using ::nanf;
using ::nearbyint;
using ::nextafter;
using ::pow;
using ::remainder;
using ::remquo;
using ::rint;
using ::round;
using ::scalbln;
using ::scalbn;
using ::signbit;
using ::sin;
using ::sinh;
using ::sqrt;
using ::tan;
using ::tanh;
using ::tgamma;
using ::trunc;







}
# 121 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 1 3
# 19 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 1 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
# 158 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
namespace std __attribute__ ((__visibility__ ("default")))
{







  enum float_round_style
  {
    round_indeterminate = -1,
    round_toward_zero = 0,
    round_to_nearest = 1,
    round_toward_infinity = 2,
    round_toward_neg_infinity = 3
  };







  enum float_denorm_style
  {

    denorm_indeterminate = -1,

    denorm_absent = 0,

    denorm_present = 1
  };
# 202 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  struct __numeric_limits_base
  {


    static constexpr bool is_specialized = false;




    static constexpr int digits = 0;


    static constexpr int digits10 = 0;




    static constexpr int max_digits10 = 0;



    static constexpr bool is_signed = false;


    static constexpr bool is_integer = false;




    static constexpr bool is_exact = false;



    static constexpr int radix = 0;



    static constexpr int min_exponent = 0;



    static constexpr int min_exponent10 = 0;




    static constexpr int max_exponent = 0;



    static constexpr int max_exponent10 = 0;


    static constexpr bool has_infinity = false;



    static constexpr bool has_quiet_NaN = false;



    static constexpr bool has_signaling_NaN = false;


    static constexpr float_denorm_style has_denorm = denorm_absent;



    static constexpr bool has_denorm_loss = false;



    static constexpr bool is_iec559 = false;




    static constexpr bool is_bounded = false;
# 288 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
    static constexpr bool is_modulo = false;


    static constexpr bool traps = false;


    static constexpr bool tinyness_before = false;




    static constexpr float_round_style round_style =
          round_toward_zero;
  };
# 311 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  template<typename _Tp>
    struct numeric_limits : public __numeric_limits_base
    {


      static constexpr _Tp
      min() noexcept { return _Tp(); }


      static constexpr _Tp
      max() noexcept { return _Tp(); }




      static constexpr _Tp
      lowest() noexcept { return _Tp(); }




      static constexpr _Tp
      epsilon() noexcept { return _Tp(); }


      static constexpr _Tp
      round_error() noexcept { return _Tp(); }


      static constexpr _Tp
      infinity() noexcept { return _Tp(); }



      static constexpr _Tp
      quiet_NaN() noexcept { return _Tp(); }



      static constexpr _Tp
      signaling_NaN() noexcept { return _Tp(); }




      static constexpr _Tp
      denorm_min() noexcept { return _Tp(); }
    };




  template<typename _Tp>
    struct numeric_limits<const _Tp>
    : public numeric_limits<_Tp> { };

  template<typename _Tp>
    struct numeric_limits<volatile _Tp>
    : public numeric_limits<_Tp> { };

  template<typename _Tp>
    struct numeric_limits<const volatile _Tp>
    : public numeric_limits<_Tp> { };
# 383 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  template<>
    struct numeric_limits<bool>
    {
      static constexpr bool is_specialized = true;

      static constexpr bool
      min() noexcept { return false; }

      static constexpr bool
      max() noexcept { return true; }


      static constexpr bool
      lowest() noexcept { return min(); }

      static constexpr int digits = 1;
      static constexpr int digits10 = 0;

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr bool
      epsilon() noexcept { return false; }

      static constexpr bool
      round_error() noexcept { return false; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr bool
      infinity() noexcept { return false; }

      static constexpr bool
      quiet_NaN() noexcept { return false; }

      static constexpr bool
      signaling_NaN() noexcept { return false; }

      static constexpr bool
      denorm_min() noexcept { return false; }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;




      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<char>
    {
      static constexpr bool is_specialized = true;

      static constexpr char
      min() noexcept { return (((char)(-1) < 0) ? -(((char)(-1) < 0) ? (((((char)1 << ((sizeof(char) * 8 - ((char)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char)0) - 1 : (char)0); }

      static constexpr char
      max() noexcept { return (((char)(-1) < 0) ? (((((char)1 << ((sizeof(char) * 8 - ((char)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char)0); }


      static constexpr char
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(char) * 8 - ((char)(-1) < 0));
      static constexpr int digits10 = ((sizeof(char) * 8 - ((char)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = ((char)(-1) < 0);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr char
      epsilon() noexcept { return 0; }

      static constexpr char
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr
      char infinity() noexcept { return char(); }

      static constexpr char
      quiet_NaN() noexcept { return char(); }

      static constexpr char
      signaling_NaN() noexcept { return char(); }

      static constexpr char
      denorm_min() noexcept { return static_cast<char>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<signed char>
    {
      static constexpr bool is_specialized = true;

      static constexpr signed char
      min() noexcept { return -127 - 1; }

      static constexpr signed char
      max() noexcept { return 127; }


      static constexpr signed char
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(signed char) * 8 - ((signed char)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(signed char) * 8 - ((signed char)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr signed char
      epsilon() noexcept { return 0; }

      static constexpr signed char
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr signed char
      infinity() noexcept { return static_cast<signed char>(0); }

      static constexpr signed char
      quiet_NaN() noexcept { return static_cast<signed char>(0); }

      static constexpr signed char
      signaling_NaN() noexcept
      { return static_cast<signed char>(0); }

      static constexpr signed char
      denorm_min() noexcept
      { return static_cast<signed char>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<unsigned char>
    {
      static constexpr bool is_specialized = true;

      static constexpr unsigned char
      min() noexcept { return 0; }

      static constexpr unsigned char
      max() noexcept { return 127 * 2U + 1; }


      static constexpr unsigned char
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(unsigned char) * 8 - ((unsigned char)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(unsigned char) * 8 - ((unsigned char)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr unsigned char
      epsilon() noexcept { return 0; }

      static constexpr unsigned char
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr unsigned char
      infinity() noexcept
      { return static_cast<unsigned char>(0); }

      static constexpr unsigned char
      quiet_NaN() noexcept
      { return static_cast<unsigned char>(0); }

      static constexpr unsigned char
      signaling_NaN() noexcept
      { return static_cast<unsigned char>(0); }

      static constexpr unsigned char
      denorm_min() noexcept
      { return static_cast<unsigned char>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = true;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<wchar_t>
    {
      static constexpr bool is_specialized = true;

      static constexpr wchar_t
      min() noexcept { return (((wchar_t)(-1) < 0) ? -(((wchar_t)(-1) < 0) ? (((((wchar_t)1 << ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(wchar_t)0) - 1 : (wchar_t)0); }

      static constexpr wchar_t
      max() noexcept { return (((wchar_t)(-1) < 0) ? (((((wchar_t)1 << ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(wchar_t)0); }


      static constexpr wchar_t
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(wchar_t) * 8 - ((wchar_t)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = ((wchar_t)(-1) < 0);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr wchar_t
      epsilon() noexcept { return 0; }

      static constexpr wchar_t
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr wchar_t
      infinity() noexcept { return wchar_t(); }

      static constexpr wchar_t
      quiet_NaN() noexcept { return wchar_t(); }

      static constexpr wchar_t
      signaling_NaN() noexcept { return wchar_t(); }

      static constexpr wchar_t
      denorm_min() noexcept { return wchar_t(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };
# 796 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  template<>
    struct numeric_limits<char16_t>
    {
      static constexpr bool is_specialized = true;

      static constexpr char16_t
      min() noexcept { return (((char16_t)(-1) < 0) ? -(((char16_t)(-1) < 0) ? (((((char16_t)1 << ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char16_t)0) - 1 : (char16_t)0); }

      static constexpr char16_t
      max() noexcept { return (((char16_t)(-1) < 0) ? (((((char16_t)1 << ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char16_t)0); }

      static constexpr char16_t
      lowest() noexcept { return min(); }

      static constexpr int digits = (sizeof(char16_t) * 8 - ((char16_t)(-1) < 0));
      static constexpr int digits10 = ((sizeof(char16_t) * 8 - ((char16_t)(-1) < 0)) * 643L / 2136);
      static constexpr int max_digits10 = 0;
      static constexpr bool is_signed = ((char16_t)(-1) < 0);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr char16_t
      epsilon() noexcept { return 0; }

      static constexpr char16_t
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr char16_t
      infinity() noexcept { return char16_t(); }

      static constexpr char16_t
      quiet_NaN() noexcept { return char16_t(); }

      static constexpr char16_t
      signaling_NaN() noexcept { return char16_t(); }

      static constexpr char16_t
      denorm_min() noexcept { return char16_t(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style = round_toward_zero;
    };


  template<>
    struct numeric_limits<char32_t>
    {
      static constexpr bool is_specialized = true;

      static constexpr char32_t
      min() noexcept { return (((char32_t)(-1) < 0) ? -(((char32_t)(-1) < 0) ? (((((char32_t)1 << ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char32_t)0) - 1 : (char32_t)0); }

      static constexpr char32_t
      max() noexcept { return (((char32_t)(-1) < 0) ? (((((char32_t)1 << ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(char32_t)0); }

      static constexpr char32_t
      lowest() noexcept { return min(); }

      static constexpr int digits = (sizeof(char32_t) * 8 - ((char32_t)(-1) < 0));
      static constexpr int digits10 = ((sizeof(char32_t) * 8 - ((char32_t)(-1) < 0)) * 643L / 2136);
      static constexpr int max_digits10 = 0;
      static constexpr bool is_signed = ((char32_t)(-1) < 0);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr char32_t
      epsilon() noexcept { return 0; }

      static constexpr char32_t
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr char32_t
      infinity() noexcept { return char32_t(); }

      static constexpr char32_t
      quiet_NaN() noexcept { return char32_t(); }

      static constexpr char32_t
      signaling_NaN() noexcept { return char32_t(); }

      static constexpr char32_t
      denorm_min() noexcept { return char32_t(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style = round_toward_zero;
    };



  template<>
    struct numeric_limits<short>
    {
      static constexpr bool is_specialized = true;

      static constexpr short
      min() noexcept { return -32767 - 1; }

      static constexpr short
      max() noexcept { return 32767; }


      static constexpr short
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(short) * 8 - ((short)(-1) < 0));
      static constexpr int digits10 = ((sizeof(short) * 8 - ((short)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr short
      epsilon() noexcept { return 0; }

      static constexpr short
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr short
      infinity() noexcept { return short(); }

      static constexpr short
      quiet_NaN() noexcept { return short(); }

      static constexpr short
      signaling_NaN() noexcept { return short(); }

      static constexpr short
      denorm_min() noexcept { return short(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<unsigned short>
    {
      static constexpr bool is_specialized = true;

      static constexpr unsigned short
      min() noexcept { return 0; }

      static constexpr unsigned short
      max() noexcept { return 32767 * 2U + 1; }


      static constexpr unsigned short
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(unsigned short) * 8 - ((unsigned short)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(unsigned short) * 8 - ((unsigned short)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr unsigned short
      epsilon() noexcept { return 0; }

      static constexpr unsigned short
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr unsigned short
      infinity() noexcept
      { return static_cast<unsigned short>(0); }

      static constexpr unsigned short
      quiet_NaN() noexcept
      { return static_cast<unsigned short>(0); }

      static constexpr unsigned short
      signaling_NaN() noexcept
      { return static_cast<unsigned short>(0); }

      static constexpr unsigned short
      denorm_min() noexcept
      { return static_cast<unsigned short>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = true;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<int>
    {
      static constexpr bool is_specialized = true;

      static constexpr int
      min() noexcept { return -2147483647 - 1; }

      static constexpr int
      max() noexcept { return 2147483647; }


      static constexpr int
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(int) * 8 - ((int)(-1) < 0));
      static constexpr int digits10 = ((sizeof(int) * 8 - ((int)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr int
      epsilon() noexcept { return 0; }

      static constexpr int
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr int
      infinity() noexcept { return static_cast<int>(0); }

      static constexpr int
      quiet_NaN() noexcept { return static_cast<int>(0); }

      static constexpr int
      signaling_NaN() noexcept { return static_cast<int>(0); }

      static constexpr int
      denorm_min() noexcept { return static_cast<int>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<unsigned int>
    {
      static constexpr bool is_specialized = true;

      static constexpr unsigned int
      min() noexcept { return 0; }

      static constexpr unsigned int
      max() noexcept { return 2147483647 * 2U + 1; }


      static constexpr unsigned int
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(unsigned int) * 8 - ((unsigned int)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(unsigned int) * 8 - ((unsigned int)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr unsigned int
      epsilon() noexcept { return 0; }

      static constexpr unsigned int
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr unsigned int
      infinity() noexcept { return static_cast<unsigned int>(0); }

      static constexpr unsigned int
      quiet_NaN() noexcept
      { return static_cast<unsigned int>(0); }

      static constexpr unsigned int
      signaling_NaN() noexcept
      { return static_cast<unsigned int>(0); }

      static constexpr unsigned int
      denorm_min() noexcept
      { return static_cast<unsigned int>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = true;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<long>
    {
      static constexpr bool is_specialized = true;

      static constexpr long
      min() noexcept { return -9223372036854775807L - 1; }

      static constexpr long
      max() noexcept { return 9223372036854775807L; }


      static constexpr long
      lowest() noexcept { return min(); }


      static constexpr int digits = (sizeof(long) * 8 - ((long)(-1) < 0));
      static constexpr int digits10 = ((sizeof(long) * 8 - ((long)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr long
      epsilon() noexcept { return 0; }

      static constexpr long
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr long
      infinity() noexcept { return static_cast<long>(0); }

      static constexpr long
      quiet_NaN() noexcept { return static_cast<long>(0); }

      static constexpr long
      signaling_NaN() noexcept { return static_cast<long>(0); }

      static constexpr long
      denorm_min() noexcept { return static_cast<long>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<unsigned long>
    {
      static constexpr bool is_specialized = true;

      static constexpr unsigned long
      min() noexcept { return 0; }

      static constexpr unsigned long
      max() noexcept { return 9223372036854775807L * 2UL + 1; }


      static constexpr unsigned long
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(unsigned long) * 8 - ((unsigned long)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(unsigned long) * 8 - ((unsigned long)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr unsigned long
      epsilon() noexcept { return 0; }

      static constexpr unsigned long
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr unsigned long
      infinity() noexcept
      { return static_cast<unsigned long>(0); }

      static constexpr unsigned long
      quiet_NaN() noexcept
      { return static_cast<unsigned long>(0); }

      static constexpr unsigned long
      signaling_NaN() noexcept
      { return static_cast<unsigned long>(0); }

      static constexpr unsigned long
      denorm_min() noexcept
      { return static_cast<unsigned long>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = true;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<long long>
    {
      static constexpr bool is_specialized = true;

      static constexpr long long
      min() noexcept { return -9223372036854775807LL - 1; }

      static constexpr long long
      max() noexcept { return 9223372036854775807LL; }


      static constexpr long long
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(long long) * 8 - ((long long)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(long long) * 8 - ((long long)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr long long
      epsilon() noexcept { return 0; }

      static constexpr long long
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr long long
      infinity() noexcept { return static_cast<long long>(0); }

      static constexpr long long
      quiet_NaN() noexcept { return static_cast<long long>(0); }

      static constexpr long long
      signaling_NaN() noexcept
      { return static_cast<long long>(0); }

      static constexpr long long
      denorm_min() noexcept { return static_cast<long long>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };


  template<>
    struct numeric_limits<unsigned long long>
    {
      static constexpr bool is_specialized = true;

      static constexpr unsigned long long
      min() noexcept { return 0; }

      static constexpr unsigned long long
      max() noexcept { return 9223372036854775807LL * 2ULL + 1; }


      static constexpr unsigned long long
      lowest() noexcept { return min(); }


      static constexpr int digits
       = (sizeof(unsigned long long) * 8 - ((unsigned long long)(-1) < 0));
      static constexpr int digits10
       = ((sizeof(unsigned long long) * 8 - ((unsigned long long)(-1) < 0)) * 643L / 2136);

      static constexpr int max_digits10 = 0;

      static constexpr bool is_signed = false;
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr unsigned long long
      epsilon() noexcept { return 0; }

      static constexpr unsigned long long
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm
       = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr unsigned long long
      infinity() noexcept
      { return static_cast<unsigned long long>(0); }

      static constexpr unsigned long long
      quiet_NaN() noexcept
      { return static_cast<unsigned long long>(0); }

      static constexpr unsigned long long
      signaling_NaN() noexcept
      { return static_cast<unsigned long long>(0); }

      static constexpr unsigned long long
      denorm_min() noexcept
      { return static_cast<unsigned long long>(0); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = true;

      static constexpr bool traps = true;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style
       = round_toward_zero;
    };
# 1658 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  __extension__ template<> struct numeric_limits<__int128> { static constexpr bool is_specialized = true; static constexpr __int128 min() noexcept { return (((__int128)(-1) < 0) ? -(((__int128)(-1) < 0) ? (((((__int128)1 << ((128 - ((__int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(__int128)0) - 1 : (__int128)0); } static constexpr __int128 max() noexcept { return (((__int128)(-1) < 0) ? (((((__int128)1 << ((128 - ((__int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(__int128)0); } static constexpr int digits = 128 - 1; static constexpr int digits10 = (128 - 1) * 643L / 2136; static constexpr bool is_signed = true; static constexpr bool is_integer = true; static constexpr bool is_exact = true; static constexpr int radix = 2; static constexpr __int128 epsilon() noexcept { return 0; } static constexpr __int128 round_error() noexcept { return 0; } static constexpr __int128 lowest() noexcept { return min(); } static constexpr int max_digits10 = 0; static constexpr int min_exponent = 0; static constexpr int min_exponent10 = 0; static constexpr int max_exponent = 0; static constexpr int max_exponent10 = 0; static constexpr bool has_infinity = false; static constexpr bool has_quiet_NaN = false; static constexpr bool has_signaling_NaN = false; static constexpr float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = false; static constexpr __int128 infinity() noexcept { return static_cast<__int128>(0); } static constexpr __int128 quiet_NaN() noexcept { return static_cast<__int128>(0); } static constexpr __int128 signaling_NaN() noexcept { return static_cast<__int128>(0); } static constexpr __int128 denorm_min() noexcept { return static_cast<__int128>(0); } static constexpr bool is_iec559 = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = false; static constexpr bool traps = true; static constexpr bool tinyness_before = false; static constexpr float_round_style round_style = round_toward_zero; }; __extension__ template<> struct numeric_limits<unsigned __int128> { static constexpr bool is_specialized = true; static constexpr unsigned __int128 min() noexcept { return 0; } static constexpr unsigned __int128 max() noexcept { return (((unsigned __int128)(-1) < 0) ? (((((unsigned __int128)1 << ((128 - ((unsigned __int128)(-1) < 0)) - 1)) - 1) << 1) + 1) : ~(unsigned __int128)0); } static constexpr unsigned __int128 lowest() noexcept { return min(); } static constexpr int max_digits10 = 0; static constexpr int digits = 128; static constexpr int digits10 = 128 * 643L / 2136; static constexpr bool is_signed = false; static constexpr bool is_integer = true; static constexpr bool is_exact = true; static constexpr int radix = 2; static constexpr unsigned __int128 epsilon() noexcept { return 0; } static constexpr unsigned __int128 round_error() noexcept { return 0; } static constexpr int min_exponent = 0; static constexpr int min_exponent10 = 0; static constexpr int max_exponent = 0; static constexpr int max_exponent10 = 0; static constexpr bool has_infinity = false; static constexpr bool has_quiet_NaN = false; static constexpr bool has_signaling_NaN = false; static constexpr float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = false; static constexpr unsigned __int128 infinity() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 quiet_NaN() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 signaling_NaN() noexcept { return static_cast<unsigned __int128>(0); } static constexpr unsigned __int128 denorm_min() noexcept { return static_cast<unsigned __int128>(0); } static constexpr bool is_iec559 = false; static constexpr bool is_bounded = true; static constexpr bool is_modulo = true; static constexpr bool traps = true; static constexpr bool tinyness_before = false; static constexpr float_round_style round_style = round_toward_zero; };
# 1669 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/limits" 3
  template<>
    struct numeric_limits<float>
    {
      static constexpr bool is_specialized = true;

      static constexpr float
      min() noexcept { return 1.17549435e-38F; }

      static constexpr float
      max() noexcept { return 3.40282347e+38F; }


      static constexpr float
      lowest() noexcept { return -3.40282347e+38F; }


      static constexpr int digits = 24;
      static constexpr int digits10 = 6;

      static constexpr int max_digits10
  = (2 + (24) * 643L / 2136);

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = false;
      static constexpr bool is_exact = false;
      static constexpr int radix = 2;

      static constexpr float
      epsilon() noexcept { return 1.19209290e-7F; }

      static constexpr float
      round_error() noexcept { return 0.5F; }

      static constexpr int min_exponent = (-125);
      static constexpr int min_exponent10 = (-37);
      static constexpr int max_exponent = 128;
      static constexpr int max_exponent10 = 38;

      static constexpr bool has_infinity = 1;
      static constexpr bool has_quiet_NaN = 1;
      static constexpr bool has_signaling_NaN = has_quiet_NaN;
      static constexpr float_denorm_style has_denorm
 = bool(1) ? denorm_present : denorm_absent;
      static constexpr bool has_denorm_loss
       = false;

      static constexpr float
      infinity() noexcept { return __builtin_huge_valf(); }

      static constexpr float
      quiet_NaN() noexcept { return __builtin_nanf(""); }

      static constexpr float
      signaling_NaN() noexcept { return __builtin_nansf(""); }

      static constexpr float
      denorm_min() noexcept { return 1.40129846e-45F; }

      static constexpr bool is_iec559
 = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = false;
      static constexpr bool tinyness_before
       = false;
      static constexpr float_round_style round_style
       = round_to_nearest;
    };






  template<>
    struct numeric_limits<double>
    {
      static constexpr bool is_specialized = true;

      static constexpr double
      min() noexcept { return 2.2250738585072014e-308; }

      static constexpr double
      max() noexcept { return 1.7976931348623157e+308; }


      static constexpr double
      lowest() noexcept { return -1.7976931348623157e+308; }


      static constexpr int digits = 53;
      static constexpr int digits10 = 15;

      static constexpr int max_digits10
  = (2 + (53) * 643L / 2136);

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = false;
      static constexpr bool is_exact = false;
      static constexpr int radix = 2;

      static constexpr double
      epsilon() noexcept { return 2.2204460492503131e-16; }

      static constexpr double
      round_error() noexcept { return 0.5; }

      static constexpr int min_exponent = (-1021);
      static constexpr int min_exponent10 = (-307);
      static constexpr int max_exponent = 1024;
      static constexpr int max_exponent10 = 308;

      static constexpr bool has_infinity = 1;
      static constexpr bool has_quiet_NaN = 1;
      static constexpr bool has_signaling_NaN = has_quiet_NaN;
      static constexpr float_denorm_style has_denorm
 = bool(1) ? denorm_present : denorm_absent;
      static constexpr bool has_denorm_loss
        = false;

      static constexpr double
      infinity() noexcept { return __builtin_huge_val(); }

      static constexpr double
      quiet_NaN() noexcept { return __builtin_nan(""); }

      static constexpr double
      signaling_NaN() noexcept { return __builtin_nans(""); }

      static constexpr double
      denorm_min() noexcept { return 4.9406564584124654e-324; }

      static constexpr bool is_iec559
 = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = false;
      static constexpr bool tinyness_before
       = false;
      static constexpr float_round_style round_style
       = round_to_nearest;
    };






  template<>
    struct numeric_limits<long double>
    {
      static constexpr bool is_specialized = true;

      static constexpr long double
      min() noexcept { return 3.36210314311209350626e-4932L; }

      static constexpr long double
      max() noexcept { return 1.18973149535723176502e+4932L; }


      static constexpr long double
      lowest() noexcept { return -1.18973149535723176502e+4932L; }


      static constexpr int digits = 64;
      static constexpr int digits10 = 18;

      static constexpr int max_digits10
  = (2 + (64) * 643L / 2136);

      static constexpr bool is_signed = true;
      static constexpr bool is_integer = false;
      static constexpr bool is_exact = false;
      static constexpr int radix = 2;

      static constexpr long double
      epsilon() noexcept { return 1.08420217248550443401e-19L; }

      static constexpr long double
      round_error() noexcept { return 0.5L; }

      static constexpr int min_exponent = (-16381);
      static constexpr int min_exponent10 = (-4931);
      static constexpr int max_exponent = 16384;
      static constexpr int max_exponent10 = 4932;

      static constexpr bool has_infinity = 1;
      static constexpr bool has_quiet_NaN = 1;
      static constexpr bool has_signaling_NaN = has_quiet_NaN;
      static constexpr float_denorm_style has_denorm
 = bool(1) ? denorm_present : denorm_absent;
      static constexpr bool has_denorm_loss
 = false;

      static constexpr long double
      infinity() noexcept { return __builtin_huge_vall(); }

      static constexpr long double
      quiet_NaN() noexcept { return __builtin_nanl(""); }

      static constexpr long double
      signaling_NaN() noexcept { return __builtin_nansl(""); }

      static constexpr long double
      denorm_min() noexcept { return 3.64519953188247460253e-4951L; }

      static constexpr bool is_iec559
 = has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = false;

      static constexpr bool traps = false;
      static constexpr bool tinyness_before =
      false;
      static constexpr float_round_style round_style =
            round_to_nearest;
    };






}
# 20 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 3
# 68 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 1 3
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{


  namespace rel_ops
  {
# 86 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 3
    template <class _Tp>
      inline bool
      operator!=(const _Tp& __x, const _Tp& __y)
      { return !(__x == __y); }
# 99 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 3
    template <class _Tp>
      inline bool
      operator>(const _Tp& __x, const _Tp& __y)
      { return __y < __x; }
# 112 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 3
    template <class _Tp>
      inline bool
      operator<=(const _Tp& __x, const _Tp& __y)
      { return !(__y < __x); }
# 125 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_relops.h" 3
    template <class _Tp>
      inline bool
      operator>=(const _Tp& __x, const _Tp& __y)
      { return !(__x < __y); }
  }


}
# 69 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 2 3
# 82 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 221 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/utility" 3
}
# 22 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 2 3

# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/limits.h" 1 3
# 24 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 2 3
# 44 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
static __attribute__((device)) inline __attribute__((always_inline)) double abs(double __x) { return ::fabs(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float abs(float __x) { return ::fabsf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) long long abs(long long __n) { return ::llabs(__n); }
static __attribute__((device)) inline __attribute__((always_inline)) long abs(long __n) { return ::labs(__n); }
static __attribute__((device)) inline __attribute__((always_inline)) float fma(float __x, float __y, float __z) {
  return ::fmaf(__x, __y, __z);
}



static __attribute__((device)) inline __attribute__((always_inline)) int fpclassify(float __x) {
  return __builtin_fpclassify(0, 1, 4, 3,
                              2, __x);
}
static __attribute__((device)) inline __attribute__((always_inline)) int fpclassify(double __x) {
  return __builtin_fpclassify(0, 1, 4, 3,
                              2, __x);
}


static __attribute__((device)) inline __attribute__((always_inline)) float frexp(float __arg, int *__exp) {
  return ::frexpf(__arg, __exp);
}
# 96 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
static __attribute__((device)) inline __attribute__((always_inline)) bool isinf(float __x) { return ::__isinff(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool isinf(double __x) { return ::__isinf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool isfinite(float __x) { return ::__finitef(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool isfinite(double __x) { return ::__finite(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool isnan(float __x) { return ::__isnanf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool isnan(double __x) { return ::__isnan(__x); }





static __attribute__((device)) inline __attribute__((always_inline)) bool isgreater(float __x, float __y) {
  return __builtin_isgreater(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isgreater(double __x, double __y) {
  return __builtin_isgreater(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isgreaterequal(float __x, float __y) {
  return __builtin_isgreaterequal(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isgreaterequal(double __x, double __y) {
  return __builtin_isgreaterequal(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isless(float __x, float __y) {
  return __builtin_isless(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isless(double __x, double __y) {
  return __builtin_isless(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool islessequal(float __x, float __y) {
  return __builtin_islessequal(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool islessequal(double __x, double __y) {
  return __builtin_islessequal(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool islessgreater(float __x, float __y) {
  return __builtin_islessgreater(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool islessgreater(double __x, double __y) {
  return __builtin_islessgreater(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isnormal(float __x) {
  return __builtin_isnormal(__x);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isnormal(double __x) {
  return __builtin_isnormal(__x);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isunordered(float __x, float __y) {
  return __builtin_isunordered(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool isunordered(double __x, double __y) {
  return __builtin_isunordered(__x, __y);
}
static __attribute__((device)) inline __attribute__((always_inline)) float modf(float __x, float *__iptr) {
  return ::modff(__x, __iptr);
}
static __attribute__((device)) inline __attribute__((always_inline)) float pow(float __base, int __iexp) {
  return ::powif(__base, __iexp);
}
static __attribute__((device)) inline __attribute__((always_inline)) double pow(double __base, int __iexp) {
  return ::powi(__base, __iexp);
}
static __attribute__((device)) inline __attribute__((always_inline)) float remquo(float __x, float __y, int *__quo) {
  return ::remquof(__x, __y, __quo);
}
static __attribute__((device)) inline __attribute__((always_inline)) float scalbln(float __x, long int __n) {
  return ::scalblnf(__x, __n);
}
static __attribute__((device)) inline __attribute__((always_inline)) bool signbit(float __x) { return ::__signbitf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) bool signbit(double __x) { return ::__signbit(__x); }






static __attribute__((device)) inline __attribute__((always_inline)) _Float16 fma(_Float16 __x, _Float16 __y,
                                      _Float16 __z) {
  return __ocml_fma_f16(__x, __y, __z);
}
static __attribute__((device)) inline __attribute__((always_inline)) _Float16 pow(_Float16 __base, int __iexp) {
  return __ocml_pown_f16(__base, __iexp);
}
# 205 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
static __attribute__((device)) inline __attribute__((always_inline)) float acos(float __x) { return acosf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float acosh(float __x) { return acoshf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float asin(float __x) { return asinf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float asinh(float __x) { return asinhf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float atan(float __x) { return atanf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float atan2(float __x, float __y) { return atan2f(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float atanh(float __x) { return atanhf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float cbrt(float __x) { return cbrtf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float ceil(float __x) { return ceilf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float copysign(float __x, float __y) { return copysignf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float cos(float __x) { return cosf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float cosh(float __x) { return coshf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float erf(float __x) { return erff(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float erfc(float __x) { return erfcf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float exp(float __x) { return expf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float exp2(float __x) { return exp2f(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float expm1(float __x) { return expm1f(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float fabs(float __x) { return fabsf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float fdim(float __x, float __y) { return fdimf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float floor(float __x) { return floorf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float fmax(float __x, float __y) { return fmaxf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float fmin(float __x, float __y) { return fminf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float fmod(float __x, float __y) { return fmodf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float hypot(float __x, float __y) { return hypotf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) int ilogb(float __x) { return ilogbf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float ldexp(float __x, int __y) { return ldexpf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float lgamma(float __x) { return lgammaf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float log(float __x) { return logf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float log10(float __x) { return log10f(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float log1p(float __x) { return log1pf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float log2(float __x) { return log2f(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float logb(float __x) { return logbf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) long long llrint(float __x) { return llrintf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) long long llround(float __x) { return llroundf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) long lrint(float __x) { return lrintf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) long lround(float __x) { return lroundf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float nearbyint(float __x) { return nearbyintf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float nextafter(float __x, float __y) { return nextafterf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float pow(float __x, float __y) { return powf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float remainder(float __x, float __y) { return remainderf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float rint(float __x) { return rintf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float round(float __x) { return roundf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float scalbn(float __x, int __y) { return scalbnf(__x, __y); }
static __attribute__((device)) inline __attribute__((always_inline)) float sin(float __x) { return sinf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float sinh(float __x) { return sinhf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float sqrt(float __x) { return sqrtf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float tan(float __x) { return tanf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float tanh(float __x) { return tanhf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float tgamma(float __x) { return tgammaf(__x); }
static __attribute__((device)) inline __attribute__((always_inline)) float trunc(float __x) { return truncf(__x); }
# 268 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
template <bool __B, class __T = void> struct __hip_enable_if {};

template <class __T> struct __hip_enable_if<true, __T> { typedef __T type; };

namespace __hip {
template <class _Tp> struct is_integral {
  enum { value = 0 };
};
template <> struct is_integral<bool> {
  enum { value = 1 };
};
template <> struct is_integral<char> {
  enum { value = 1 };
};
template <> struct is_integral<signed char> {
  enum { value = 1 };
};
template <> struct is_integral<unsigned char> {
  enum { value = 1 };
};
template <> struct is_integral<wchar_t> {
  enum { value = 1 };
};
template <> struct is_integral<short> {
  enum { value = 1 };
};
template <> struct is_integral<unsigned short> {
  enum { value = 1 };
};
template <> struct is_integral<int> {
  enum { value = 1 };
};
template <> struct is_integral<unsigned int> {
  enum { value = 1 };
};
template <> struct is_integral<long> {
  enum { value = 1 };
};
template <> struct is_integral<unsigned long> {
  enum { value = 1 };
};
template <> struct is_integral<long long> {
  enum { value = 1 };
};
template <> struct is_integral<unsigned long long> {
  enum { value = 1 };
};


template <class _Tp> struct is_arithmetic {
  enum { value = 0 };
};
template <> struct is_arithmetic<bool> {
  enum { value = 1 };
};
template <> struct is_arithmetic<char> {
  enum { value = 1 };
};
template <> struct is_arithmetic<signed char> {
  enum { value = 1 };
};
template <> struct is_arithmetic<unsigned char> {
  enum { value = 1 };
};
template <> struct is_arithmetic<wchar_t> {
  enum { value = 1 };
};
template <> struct is_arithmetic<short> {
  enum { value = 1 };
};
template <> struct is_arithmetic<unsigned short> {
  enum { value = 1 };
};
template <> struct is_arithmetic<int> {
  enum { value = 1 };
};
template <> struct is_arithmetic<unsigned int> {
  enum { value = 1 };
};
template <> struct is_arithmetic<long> {
  enum { value = 1 };
};
template <> struct is_arithmetic<unsigned long> {
  enum { value = 1 };
};
template <> struct is_arithmetic<long long> {
  enum { value = 1 };
};
template <> struct is_arithmetic<unsigned long long> {
  enum { value = 1 };
};
template <> struct is_arithmetic<float> {
  enum { value = 1 };
};
template <> struct is_arithmetic<double> {
  enum { value = 1 };
};

struct true_type {
  static const __attribute__((constant)) bool value = true;
};
struct false_type {
  static const __attribute__((constant)) bool value = false;
};

template <typename __T, typename __U> struct is_same : public false_type {};
template <typename __T> struct is_same<__T, __T> : public true_type {};

template <typename __T> struct add_rvalue_reference { typedef __T &&type; };

template <typename __T> typename add_rvalue_reference<__T>::type declval();




template <class _Tp> struct __numeric_type {
  static void __test(...);
  static _Float16 __test(_Float16);
  static float __test(float);
  static double __test(char);
  static double __test(int);
  static double __test(unsigned);
  static double __test(long);
  static double __test(unsigned long);
  static double __test(long long);
  static double __test(unsigned long long);
  static double __test(double);

  static double __test(long double);

  typedef decltype(__test(declval<_Tp>())) type;
  static const bool value = !is_same<type, void>::value;
};

template <> struct __numeric_type<void> { static const bool value = true; };

template <class _A1, class _A2 = void, class _A3 = void,
          bool = __numeric_type<_A1>::value &&__numeric_type<_A2>::value
              &&__numeric_type<_A3>::value>
class __promote_imp {
public:
  static const bool value = false;
};

template <class _A1, class _A2, class _A3>
class __promote_imp<_A1, _A2, _A3, true> {
private:
  typedef typename __promote_imp<_A1>::type __type1;
  typedef typename __promote_imp<_A2>::type __type2;
  typedef typename __promote_imp<_A3>::type __type3;

public:
  typedef decltype(__type1() + __type2() + __type3()) type;
  static const bool value = true;
};

template <class _A1, class _A2> class __promote_imp<_A1, _A2, void, true> {
private:
  typedef typename __promote_imp<_A1>::type __type1;
  typedef typename __promote_imp<_A2>::type __type2;

public:
  typedef decltype(__type1() + __type2()) type;
  static const bool value = true;
};

template <class _A1> class __promote_imp<_A1, void, void, true> {
public:
  typedef typename __numeric_type<_A1>::type type;
  static const bool value = true;
};

template <class _A1, class _A2 = void, class _A3 = void>
class __promote : public __promote_imp<_A1, _A2, _A3> {};

}
# 481 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type acos(__T __x) { return ::acos((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type acosh(__T __x) { return ::acosh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type asin(__T __x) { return ::asin((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type asinh(__T __x) { return ::asinh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type atan(__T __x) { return ::atan((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type atan2(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return atan2((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type atanh(__T __x) { return ::atanh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type cbrt(__T __x) { return ::cbrt((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type ceil(__T __x) { return ::ceil((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type copysign(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return copysign((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type cos(__T __x) { return ::cos((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type cosh(__T __x) { return ::cosh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type erf(__T __x) { return ::erf((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type erfc(__T __x) { return ::erfc((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type exp(__T __x) { return ::exp((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type exp2(__T __x) { return ::exp2((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type expm1(__T __x) { return ::expm1((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type fabs(__T __x) { return ::fabs((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type fdim(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return fdim((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type floor(__T __x) { return ::floor((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type fmax(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return fmax((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type fmin(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return fmin((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type fmod(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return fmod((__result_type)__x, (__result_type)__y); }

template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, int>::type fpclassify(__T __x) { return ::fpclassify((double)__x); }

template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type hypot(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return hypot((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, int>::type ilogb(__T __x) { return ::ilogb((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, bool>::type isfinite(__T __x) { return ::isfinite((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type isgreater(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return isgreater((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type isgreaterequal(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return isgreaterequal((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, bool>::type isinf(__T __x) { return ::isinf((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type isless(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return isless((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type islessequal(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return islessequal((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type islessgreater(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return islessgreater((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, bool>::type isnan(__T __x) { return ::isnan((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, bool>::type isnormal(__T __x) { return ::isnormal((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type isunordered(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return isunordered((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type lgamma(__T __x) { return ::lgamma((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type log(__T __x) { return ::log((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type log10(__T __x) { return ::log10((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type log1p(__T __x) { return ::log1p((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type log2(__T __x) { return ::log2((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type logb(__T __x) { return ::logb((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, long long>::type llrint(__T __x) { return ::llrint((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, long long>::type llround(__T __x) { return ::llround((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, long>::type lrint(__T __x) { return ::lrint((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, long>::type lround(__T __x) { return ::lround((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type nearbyint(__T __x) { return ::nearbyint((double)__x); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type nextafter(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return nextafter((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type pow(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return pow((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type remainder(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return remainder((__result_type)__x, (__result_type)__y); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type rint(__T __x) { return ::rint((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type round(__T __x) { return ::round((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, bool>::type signbit(__T __x) { return ::signbit((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type sin(__T __x) { return ::sin((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type sinh(__T __x) { return ::sinh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type sqrt(__T __x) { return ::sqrt((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type tan(__T __x) { return ::tan((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type tanh(__T __x) { return ::tanh((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type tgamma(__T __x) { return ::tgamma((double)__x); }
template <typename __T> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type trunc(__T __x) { return ::trunc((double)__x); }


template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type max(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return max((__result_type)__x, (__result_type)__y); }
template <typename __T1, typename __T2> static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if< __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value, typename __hip::__promote<__T1, __T2>::type>::type min(__T1 __x, __T2 __y) { typedef typename __hip::__promote<__T1, __T2>::type __result_type; return min((__result_type)__x, (__result_type)__y); }



template <typename __T1, typename __T2, typename __T3>
static __attribute__((device)) inline __attribute__((always_inline)) typename __hip_enable_if<
    __hip::is_arithmetic<__T1>::value && __hip::is_arithmetic<__T2>::value &&
        __hip::is_arithmetic<__T3>::value,
    typename __hip::__promote<__T1, __T2, __T3>::type>::type
fma(__T1 __x, __T2 __y, __T3 __z) {
  typedef typename __hip::__promote<__T1, __T2, __T3>::type __result_type;
  return ::fma((__result_type)__x, (__result_type)__y, (__result_type)__z);
}
# 571 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
template <typename __T>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type
    frexp(__T __x, int *__exp) {
  return ::frexp((double)__x, __exp);
}

template <typename __T>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type
    ldexp(__T __x, int __exp) {
  return ::ldexp((double)__x, __exp);
}

template <typename __T>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type
    modf(__T __x, double *__exp) {
  return ::modf((double)__x, __exp);
}


template <typename __T1, typename __T2>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_arithmetic<__T1>::value &&
                                 __hip::is_arithmetic<__T2>::value,
                             typename __hip::__promote<__T1, __T2>::type>::type
    remquo(__T1 __x, __T2 __y, int *__quo) {
  typedef typename __hip::__promote<__T1, __T2>::type __result_type;
  return ::remquo((__result_type)__x, (__result_type)__y, __quo);
}
# 613 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
template <typename __T>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type
    scalbln(__T __x, long int __exp) {
  return ::scalbln((double)__x, __exp);
}

template <typename __T>
static __attribute__((device)) inline __attribute__((always_inline))
    typename __hip_enable_if<__hip::is_integral<__T>::value, double>::type
    scalbn(__T __x, int __exp) {
  return ::scalbn((double)__x, __exp);
}
# 643 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
namespace std {







using ::acos;
using ::acosh;
using ::asin;
using ::asinh;
using ::atan;
using ::atan2;
using ::atanh;
using ::cbrt;
using ::ceil;
using ::copysign;
using ::cos;
using ::cosh;
using ::erf;
using ::erfc;
using ::exp;
using ::exp2;
using ::expm1;
using ::fabs;
using ::fdim;
using ::floor;
using ::fma;
using ::fmax;
using ::fmin;
using ::fmod;
using ::fpclassify;
using ::frexp;
using ::hypot;
using ::ilogb;
using ::isfinite;
using ::isgreater;
using ::isgreaterequal;
using ::isless;
using ::islessequal;
using ::islessgreater;
using ::isnormal;
using ::isunordered;
using ::ldexp;
using ::lgamma;
using ::llrint;
using ::llround;
using ::log;
using ::log10;
using ::log1p;
using ::log2;
using ::logb;
using ::lrint;
using ::lround;
using ::modf;



using ::nearbyint;
using ::nextafter;

using ::pow;
using ::remainder;
using ::remquo;
using ::rint;
using ::round;
using ::scalbln;
using ::scalbn;
using ::signbit;
using ::sin;
using ::sinh;
using ::sqrt;
using ::tan;
using ::tanh;
using ::tgamma;
using ::trunc;
# 730 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_cmath.h" 3
using ::acosf;
using ::acoshf;
using ::asinf;
using ::asinhf;
using ::atan2f;
using ::atanf;
using ::atanhf;
using ::cbrtf;
using ::ceilf;
using ::copysignf;
using ::cosf;
using ::coshf;
using ::erfcf;
using ::erff;
using ::exp2f;
using ::expf;
using ::expm1f;
using ::fabsf;
using ::fdimf;
using ::floorf;
using ::fmaf;
using ::fmaxf;
using ::fminf;
using ::fmodf;
using ::frexpf;
using ::hypotf;
using ::ilogbf;
using ::ldexpf;
using ::lgammaf;
using ::llrintf;
using ::llroundf;
using ::log10f;
using ::log1pf;
using ::log2f;
using ::logbf;
using ::logf;
using ::lrintf;
using ::lroundf;
using ::modff;
using ::nearbyintf;
using ::nextafterf;

using ::powf;
using ::remainderf;
using ::remquof;
using ::rintf;
using ::roundf;
using ::scalblnf;
using ::scalbnf;
using ::sinf;
using ::sinhf;
using ::sqrtf;
using ::tanf;
using ::tanhf;
using ::tgammaf;
using ::truncf;







}
# 122 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_cuda_complex_builtins.h" 1 3
# 86 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_cuda_complex_builtins.h" 3
extern "C" {


__attribute__((device)) inline double _Complex __muldc3(double __a, double __b, double __c,
                                    double __d) {
  double __ac = __a * __c;
  double __bd = __b * __d;
  double __ad = __a * __d;
  double __bc = __b * __c;
  double _Complex z;
  __real__(z) = __ac - __bd;
  __imag__(z) = __ad + __bc;
  if (std::isnan(__real__(z)) && std::isnan(__imag__(z))) {
    int __recalc = 0;
    if (std::isinf(__a) || std::isinf(__b)) {
      __a = std::copysign(std::isinf(__a) ? 1 : 0, __a);
      __b = std::copysign(std::isinf(__b) ? 1 : 0, __b);
      if (std::isnan(__c))
        __c = std::copysign(0, __c);
      if (std::isnan(__d))
        __d = std::copysign(0, __d);
      __recalc = 1;
    }
    if (std::isinf(__c) || std::isinf(__d)) {
      __c = std::copysign(std::isinf(__c) ? 1 : 0, __c);
      __d = std::copysign(std::isinf(__d) ? 1 : 0, __d);
      if (std::isnan(__a))
        __a = std::copysign(0, __a);
      if (std::isnan(__b))
        __b = std::copysign(0, __b);
      __recalc = 1;
    }
    if (!__recalc &&
        (std::isinf(__ac) || std::isinf(__bd) || std::isinf(__ad) || std::isinf(__bc))) {
      if (std::isnan(__a))
        __a = std::copysign(0, __a);
      if (std::isnan(__b))
        __b = std::copysign(0, __b);
      if (std::isnan(__c))
        __c = std::copysign(0, __c);
      if (std::isnan(__d))
        __d = std::copysign(0, __d);
      __recalc = 1;
    }
    if (__recalc) {


      __real__(z) = __builtin_huge_val() * (__a * __c - __b * __d);
      __imag__(z) = __builtin_huge_val() * (__a * __d + __b * __c);
    }
  }
  return z;
}

__attribute__((device)) inline float _Complex __mulsc3(float __a, float __b, float __c, float __d) {
  float __ac = __a * __c;
  float __bd = __b * __d;
  float __ad = __a * __d;
  float __bc = __b * __c;
  float _Complex z;
  __real__(z) = __ac - __bd;
  __imag__(z) = __ad + __bc;
  if (std::isnan(__real__(z)) && std::isnan(__imag__(z))) {
    int __recalc = 0;
    if (std::isinf(__a) || std::isinf(__b)) {
      __a = std::copysign(std::isinf(__a) ? 1 : 0, __a);
      __b = std::copysign(std::isinf(__b) ? 1 : 0, __b);
      if (std::isnan(__c))
        __c = std::copysign(0, __c);
      if (std::isnan(__d))
        __d = std::copysign(0, __d);
      __recalc = 1;
    }
    if (std::isinf(__c) || std::isinf(__d)) {
      __c = std::copysign(std::isinf(__c) ? 1 : 0, __c);
      __d = std::copysign(std::isinf(__d) ? 1 : 0, __d);
      if (std::isnan(__a))
        __a = std::copysign(0, __a);
      if (std::isnan(__b))
        __b = std::copysign(0, __b);
      __recalc = 1;
    }
    if (!__recalc &&
        (std::isinf(__ac) || std::isinf(__bd) || std::isinf(__ad) || std::isinf(__bc))) {
      if (std::isnan(__a))
        __a = std::copysign(0, __a);
      if (std::isnan(__b))
        __b = std::copysign(0, __b);
      if (std::isnan(__c))
        __c = std::copysign(0, __c);
      if (std::isnan(__d))
        __d = std::copysign(0, __d);
      __recalc = 1;
    }
    if (__recalc) {
      __real__(z) = __builtin_huge_valf() * (__a * __c - __b * __d);
      __imag__(z) = __builtin_huge_valf() * (__a * __d + __b * __c);
    }
  }
  return z;
}

__attribute__((device)) inline double _Complex __divdc3(double __a, double __b, double __c,
                                    double __d) {
  int __ilogbw = 0;



  double __logbw = std::logb(max(std::abs(__c), std::abs(__d)));
  if (std::isfinite(__logbw)) {
    __ilogbw = (int)__logbw;
    __c = std::scalbn(__c, -__ilogbw);
    __d = std::scalbn(__d, -__ilogbw);
  }
  double __denom = __c * __c + __d * __d;
  double _Complex z;
  __real__(z) = std::scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
  __imag__(z) = std::scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
  if (std::isnan(__real__(z)) && std::isnan(__imag__(z))) {
    if ((__denom == 0.0) && (!std::isnan(__a) || !std::isnan(__b))) {
      __real__(z) = std::copysign(__builtin_huge_val(), __c) * __a;
      __imag__(z) = std::copysign(__builtin_huge_val(), __c) * __b;
    } else if ((std::isinf(__a) || std::isinf(__b)) && std::isfinite(__c) &&
               std::isfinite(__d)) {
      __a = std::copysign(std::isinf(__a) ? 1.0 : 0.0, __a);
      __b = std::copysign(std::isinf(__b) ? 1.0 : 0.0, __b);
      __real__(z) = __builtin_huge_val() * (__a * __c + __b * __d);
      __imag__(z) = __builtin_huge_val() * (__b * __c - __a * __d);
    } else if (std::isinf(__logbw) && __logbw > 0.0 && std::isfinite(__a) &&
               std::isfinite(__b)) {
      __c = std::copysign(std::isinf(__c) ? 1.0 : 0.0, __c);
      __d = std::copysign(std::isinf(__d) ? 1.0 : 0.0, __d);
      __real__(z) = 0.0 * (__a * __c + __b * __d);
      __imag__(z) = 0.0 * (__b * __c - __a * __d);
    }
  }
  return z;
}

__attribute__((device)) inline float _Complex __divsc3(float __a, float __b, float __c, float __d) {
  int __ilogbw = 0;
  float __logbw = std::logb(max(std::abs(__c), std::abs(__d)));
  if (std::isfinite(__logbw)) {
    __ilogbw = (int)__logbw;
    __c = std::scalbn(__c, -__ilogbw);
    __d = std::scalbn(__d, -__ilogbw);
  }
  float __denom = __c * __c + __d * __d;
  float _Complex z;
  __real__(z) = std::scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
  __imag__(z) = std::scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
  if (std::isnan(__real__(z)) && std::isnan(__imag__(z))) {
    if ((__denom == 0) && (!std::isnan(__a) || !std::isnan(__b))) {
      __real__(z) = std::copysign(__builtin_huge_valf(), __c) * __a;
      __imag__(z) = std::copysign(__builtin_huge_valf(), __c) * __b;
    } else if ((std::isinf(__a) || std::isinf(__b)) && std::isfinite(__c) &&
               std::isfinite(__d)) {
      __a = std::copysign(std::isinf(__a) ? 1 : 0, __a);
      __b = std::copysign(std::isinf(__b) ? 1 : 0, __b);
      __real__(z) = __builtin_huge_valf() * (__a * __c + __b * __d);
      __imag__(z) = __builtin_huge_valf() * (__b * __c - __a * __d);
    } else if (std::isinf(__logbw) && __logbw > 0 && std::isfinite(__a) &&
               std::isfinite(__b)) {
      __c = std::copysign(std::isinf(__c) ? 1 : 0, __c);
      __d = std::copysign(std::isinf(__d) ? 1 : 0, __d);
      __real__(z) = 0 * (__a * __c + __b * __d);
      __imag__(z) = 0 * (__b * __c - __a * __d);
    }
  }
  return z;
}


}
# 123 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3

# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 1 3
# 35 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdexcept" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdexcept" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 3

#pragma GCC visibility push(default)




extern "C++" {

namespace std
{
# 53 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 3
  class bad_exception : public exception
  {
  public:
    bad_exception() noexcept { }



    virtual ~bad_exception() noexcept;


    virtual const char*
    what() const noexcept;
  };


  typedef void (*terminate_handler) ();


  terminate_handler set_terminate(terminate_handler) noexcept;



  terminate_handler get_terminate() noexcept;




  void terminate() noexcept __attribute__ ((__noreturn__));



  typedef void (*__attribute__ ((__deprecated__)) unexpected_handler) ();





  __attribute__ ((__deprecated__))
  unexpected_handler set_unexpected(unexpected_handler) noexcept;







  __attribute__ ((__deprecated__))
  unexpected_handler get_unexpected() noexcept;







  __attribute__ ((__deprecated__))
  void unexpected() __attribute__ ((__noreturn__));
# 124 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 3
  bool uncaught_exception() noexcept __attribute__ ((__pure__));
# 136 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 3
}

namespace __gnu_cxx
{
# 158 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 3
  void __verbose_terminate_handler();


}

}

#pragma GCC visibility pop


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
#pragma GCC visibility push(default)



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_init_exception.h" 1 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_init_exception.h" 3

#pragma GCC visibility push(default)

# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3
# 35 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 3
typedef long int ptrdiff_t;
# 102 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 3
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__stddef_max_align_t.h" 1 3
# 19 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__stddef_max_align_t.h" 3
typedef struct {
  long long __clang_max_align_nonce1
      __attribute__((__aligned__(__alignof__(long long))));
  long double __clang_max_align_nonce2
      __attribute__((__aligned__(__alignof__(long double))));
} max_align_t;
# 103 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 2 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_init_exception.h" 2 3
# 50 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_init_exception.h" 3
namespace std
{
  class type_info;
}

namespace __cxxabiv1
{
  struct __cxa_refcounted_exception;

  extern "C"
    {

      void*
      __cxa_allocate_exception(size_t) noexcept;

      void
      __cxa_free_exception(void*) noexcept;


      __cxa_refcounted_exception*
      __cxa_init_primary_exception(void *object, std::type_info *tinfo,
                void ( *dest) (void *)) noexcept;

    }
}



#pragma GCC visibility pop
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 3



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/hash_bytes.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/hash_bytes.h" 3



namespace std
{







  size_t
  _Hash_bytes(const void* __ptr, size_t __len, size_t __seed);





  size_t
  _Fnv_hash_bytes(const void* __ptr, size_t __len, size_t __seed);


}
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 2 3


#pragma GCC visibility push(default)





extern "C++" {

namespace __cxxabiv1
{
  class __class_type_info;
}
# 84 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 3
namespace std
{






  class type_info
  {
  public:




    virtual ~type_info();



    const char* name() const noexcept
    { return __name[0] == '*' ? __name + 1 : __name; }



    bool before(const type_info& __arg) const noexcept;


    bool operator==(const type_info& __arg) const noexcept;


    bool operator!=(const type_info& __arg) const noexcept
    { return !operator==(__arg); }



    size_t hash_code() const noexcept
    {

      return _Hash_bytes(name(), __builtin_strlen(name()),
    static_cast<size_t>(0xc70f6907UL));



    }



    virtual bool __is_pointer_p() const;


    virtual bool __is_function_p() const;







    virtual bool __do_catch(const type_info *__thr_type, void **__thr_obj,
       unsigned __outer) const;


    virtual bool __do_upcast(const __cxxabiv1::__class_type_info *__target,
        void **__obj_ptr) const;

  protected:
    const char *__name;

    explicit type_info(const char *__n): __name(__n) { }

  private:


    type_info& operator=(const type_info&) = delete;
    type_info(const type_info&) = delete;
# 167 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 3
  };


  inline bool
  type_info::before(const type_info& __arg) const noexcept
  {




    if (__name[0] != '*' || __arg.__name[0] != '*')
      return __builtin_strcmp (__name, __arg.__name) < 0;
# 187 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 3
    return __name < __arg.__name;
  }



                       inline bool
  type_info::operator==(const type_info& __arg) const noexcept
  {
    if (std::__is_constant_evaluated())
      return this == &__arg;

    if (__name == __arg.__name)
      return true;






    return __name[0] != '*' && __builtin_strcmp (__name, __arg.name()) == 0;



  }
# 220 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/typeinfo" 3
  class bad_cast : public exception
  {
  public:
    bad_cast() noexcept { }



    virtual ~bad_cast() noexcept;


    virtual const char* what() const noexcept;
  };





  class bad_typeid : public exception
  {
  public:
    bad_typeid () noexcept { }



    virtual ~bad_typeid() noexcept;


    virtual const char* what() const noexcept;
  };
}

}

#pragma GCC visibility pop
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 2 3
# 52 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
extern "C++" {

namespace std
{
  class type_info;






  namespace __exception_ptr
  {
    class exception_ptr;
  }

  using __exception_ptr::exception_ptr;





  exception_ptr current_exception() noexcept;

  template<typename _Ex>
  exception_ptr make_exception_ptr(_Ex) noexcept;


  void rethrow_exception(exception_ptr) __attribute__ ((__noreturn__));

  namespace __exception_ptr
  {
    using std::rethrow_exception;





    class exception_ptr
    {
      void* _M_exception_object;

      explicit exception_ptr(void* __e) noexcept;

      void _M_addref() noexcept;
      void _M_release() noexcept;

      void *_M_get() const noexcept __attribute__ ((__pure__));

      friend exception_ptr std::current_exception() noexcept;
      friend void std::rethrow_exception(exception_ptr);
      template<typename _Ex>
      friend exception_ptr std::make_exception_ptr(_Ex) noexcept;

    public:
      exception_ptr() noexcept;

      exception_ptr(const exception_ptr&) noexcept;


      exception_ptr(nullptr_t) noexcept
      : _M_exception_object(nullptr)
      { }

      exception_ptr(exception_ptr&& __o) noexcept
      : _M_exception_object(__o._M_exception_object)
      { __o._M_exception_object = nullptr; }
# 128 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
      exception_ptr&
      operator=(const exception_ptr&) noexcept;


      exception_ptr&
      operator=(exception_ptr&& __o) noexcept
      {
        exception_ptr(static_cast<exception_ptr&&>(__o)).swap(*this);
        return *this;
      }


      ~exception_ptr() noexcept;

      void
      swap(exception_ptr&) noexcept;
# 155 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
      explicit operator bool() const noexcept
      { return _M_exception_object; }







      friend bool
      operator==(const exception_ptr& __x, const exception_ptr& __y)
      noexcept
      { return __x._M_exception_object == __y._M_exception_object; }

      friend bool
      operator!=(const exception_ptr& __x, const exception_ptr& __y)
      noexcept
      { return __x._M_exception_object != __y._M_exception_object; }


      const class std::type_info*
      __cxa_exception_type() const noexcept
 __attribute__ ((__pure__));
    };


    inline
    exception_ptr::exception_ptr() noexcept
    : _M_exception_object(0)
    { }


    inline
    exception_ptr::exception_ptr(const exception_ptr& __other)
    noexcept
    : _M_exception_object(__other._M_exception_object)
    {
      if (_M_exception_object)
 _M_addref();
    }


    inline
    exception_ptr::~exception_ptr() noexcept
    {
      if (_M_exception_object)
 _M_release();
    }


    inline exception_ptr&
    exception_ptr::operator=(const exception_ptr& __other) noexcept
    {
      exception_ptr(__other).swap(*this);
      return *this;
    }


    inline void
    exception_ptr::swap(exception_ptr &__other) noexcept
    {
      void *__tmp = _M_exception_object;
      _M_exception_object = __other._M_exception_object;
      __other._M_exception_object = __tmp;
    }


    inline void
    swap(exception_ptr& __lhs, exception_ptr& __rhs)
    { __lhs.swap(__rhs); }


    template<typename _Ex>

      inline void
      __dest_thunk(void* __x)
      { static_cast<_Ex*>(__x)->~_Ex(); }


  }



  template<typename _Ex>
    exception_ptr
    make_exception_ptr(_Ex __ex) noexcept
    {

      using _Ex2 = typename decay<_Ex>::type;
      void* __e = __cxxabiv1::__cxa_allocate_exception(sizeof(_Ex));
      (void) __cxxabiv1::__cxa_init_primary_exception(
   __e, const_cast<std::type_info*>(&typeid(_Ex)),
   __exception_ptr::__dest_thunk<_Ex2>);
      try
 {
   ::new (__e) _Ex2(__ex);
   return exception_ptr(__e);
 }
      catch(...)
 {
   __cxxabiv1::__cxa_free_exception(__e);
   return current_exception();
 }
# 268 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
    }
# 282 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/exception_ptr.h" 3
}

}

#pragma GCC visibility pop
# 169 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/nested_exception.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/nested_exception.h" 3
#pragma GCC visibility push(default)








extern "C++" {

namespace std
{






  class nested_exception
  {
    exception_ptr _M_ptr;

  public:
    nested_exception() noexcept : _M_ptr(current_exception()) { }

    nested_exception(const nested_exception&) noexcept = default;

    nested_exception& operator=(const nested_exception&) noexcept = default;

    virtual ~nested_exception() noexcept;

    [[noreturn]]
    void
    rethrow_nested() const
    {
      if (_M_ptr)
 rethrow_exception(_M_ptr);
      std::terminate();
    }

    exception_ptr
    nested_ptr() const noexcept
    { return _M_ptr; }
  };



  template<typename _Except>
    struct _Nested_exception : public _Except, public nested_exception
    {
      explicit _Nested_exception(const _Except& __ex)
      : _Except(__ex)
      { }

      explicit _Nested_exception(_Except&& __ex)
      : _Except(static_cast<_Except&&>(__ex))
      { }
    };




  template<typename _Tp>
    [[noreturn]]
    inline void
    __throw_with_nested_impl(_Tp&& __t, true_type)
    {
      using _Up = typename remove_reference<_Tp>::type;
      throw _Nested_exception<_Up>{std::forward<_Tp>(__t)};
    }

  template<typename _Tp>
    [[noreturn]]
    inline void
    __throw_with_nested_impl(_Tp&& __t, false_type)
    { throw std::forward<_Tp>(__t); }





  template<typename _Tp>
    [[noreturn]]
    inline void
    throw_with_nested(_Tp&& __t)
    {
      using _Up = typename decay<_Tp>::type;
      using _CopyConstructible
 = __and_<is_copy_constructible<_Up>, is_move_constructible<_Up>>;
      static_assert(_CopyConstructible::value,
   "throw_with_nested argument must be CopyConstructible");
      using __nest = __and_<is_class<_Up>, __bool_constant<!__is_final(_Up)>,
       __not_<is_base_of<nested_exception, _Up>>>;
      std::__throw_with_nested_impl(std::forward<_Tp>(__t), __nest{});
    }




  template<typename _Tp>
    using __rethrow_if_nested_cond = typename enable_if<
      __and_<is_polymorphic<_Tp>,
      __or_<__not_<is_base_of<nested_exception, _Tp>>,
     is_convertible<_Tp*, nested_exception*>>>::value
    >::type;


  template<typename _Ex>
    inline __rethrow_if_nested_cond<_Ex>
    __rethrow_if_nested_impl(const _Ex* __ptr)
    {
      if (auto __ne_ptr = dynamic_cast<const nested_exception*>(__ptr))
 __ne_ptr->rethrow_nested();
    }


  inline void
  __rethrow_if_nested_impl(const void*)
  { }




  template<typename _Ex>
    inline void
    rethrow_if_nested(const _Ex& __ex)
    { std::__rethrow_if_nested_impl(std::__addressof(__ex)); }


}

}



#pragma GCC visibility pop
# 170 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/exception" 2 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdexcept" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stringfwd.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stringfwd.h" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/memoryfwd.h" 1 3
# 47 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/memoryfwd.h" 3



namespace std __attribute__ ((__visibility__ ("default")))
{
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/memoryfwd.h" 3
  template<typename>
    class allocator;

  template<>
    class allocator<void>;



  template<typename, typename>
    struct uses_allocator;

  template<typename>
    struct allocator_traits;





}
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stringfwd.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{
# 52 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stringfwd.h" 3
  template<class _CharT>
    struct char_traits;

  template<> struct char_traits<char>;

  template<> struct char_traits<wchar_t>;






  template<> struct char_traits<char16_t>;
  template<> struct char_traits<char32_t>;


namespace __cxx11 {

  template<typename _CharT, typename _Traits = char_traits<_CharT>,
           typename _Alloc = allocator<_CharT> >
    class basic_string;

}


  typedef basic_string<char> string;


  typedef basic_string<wchar_t> wstring;
# 89 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stringfwd.h" 3
  typedef basic_string<char16_t> u16string;


  typedef basic_string<char32_t> u32string;





}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 1 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3




# 1 "/usr/include/wchar.h" 1 3 4
# 27 "/usr/include/wchar.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 28 "/usr/include/wchar.h" 2 3 4







# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 36 "/usr/include/wchar.h" 2 3 4


# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdarg.h" 1 3 4
# 14 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdarg.h" 3 4
typedef __builtin_va_list va_list;
# 32 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stdarg.h" 3 4
typedef __builtin_va_list __gnuc_va_list;
# 39 "/usr/include/wchar.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/wint_t.h" 1 3 4
# 20 "/usr/include/x86_64-linux-gnu/bits/types/wint_t.h" 3 4
typedef unsigned int wint_t;
# 42 "/usr/include/wchar.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/mbstate_t.h" 1 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/types/__mbstate_t.h" 1 3 4
# 13 "/usr/include/x86_64-linux-gnu/bits/types/__mbstate_t.h" 3 4
typedef struct
{
  int __count;
  union
  {
    unsigned int __wch;
    char __wchb[4];
  } __value;
} __mbstate_t;
# 5 "/usr/include/x86_64-linux-gnu/bits/types/mbstate_t.h" 2 3 4

typedef __mbstate_t mbstate_t;
# 43 "/usr/include/wchar.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/__FILE.h" 1 3 4



struct _IO_FILE;
typedef struct _IO_FILE __FILE;
# 44 "/usr/include/wchar.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/FILE.h" 1 3 4



struct _IO_FILE;


typedef struct _IO_FILE FILE;
# 47 "/usr/include/wchar.h" 2 3 4
# 79 "/usr/include/wchar.h" 3 4
extern "C" {



struct tm;



extern wchar_t *wcscpy (wchar_t *__restrict __dest,
   const wchar_t *__restrict __src)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern wchar_t *wcsncpy (wchar_t *__restrict __dest,
    const wchar_t *__restrict __src, size_t __n)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern wchar_t *wcscat (wchar_t *__restrict __dest,
   const wchar_t *__restrict __src)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));

extern wchar_t *wcsncat (wchar_t *__restrict __dest,
    const wchar_t *__restrict __src, size_t __n)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int wcscmp (const wchar_t *__s1, const wchar_t *__s2)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));

extern int wcsncmp (const wchar_t *__s1, const wchar_t *__s2, size_t __n)
     noexcept (true) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));



extern int wcscasecmp (const wchar_t *__s1, const wchar_t *__s2) noexcept (true);


extern int wcsncasecmp (const wchar_t *__s1, const wchar_t *__s2,
   size_t __n) noexcept (true);



extern int wcscasecmp_l (const wchar_t *__s1, const wchar_t *__s2,
    locale_t __loc) noexcept (true);

extern int wcsncasecmp_l (const wchar_t *__s1, const wchar_t *__s2,
     size_t __n, locale_t __loc) noexcept (true);




extern int wcscoll (const wchar_t *__s1, const wchar_t *__s2) noexcept (true);



extern size_t wcsxfrm (wchar_t *__restrict __s1,
         const wchar_t *__restrict __s2, size_t __n) noexcept (true);







extern int wcscoll_l (const wchar_t *__s1, const wchar_t *__s2,
        locale_t __loc) noexcept (true);




extern size_t wcsxfrm_l (wchar_t *__s1, const wchar_t *__s2,
    size_t __n, locale_t __loc) noexcept (true);


extern wchar_t *wcsdup (const wchar_t *__s) noexcept (true)
  __attribute__ ((__malloc__)) ;
# 165 "/usr/include/wchar.h" 3 4
extern wchar_t *wcschr (const wchar_t *__wcs, wchar_t __wc)
     noexcept (true) __attribute__ ((__pure__));
# 175 "/usr/include/wchar.h" 3 4
extern wchar_t *wcsrchr (const wchar_t *__wcs, wchar_t __wc)
     noexcept (true) __attribute__ ((__pure__));





extern wchar_t *wcschrnul (const wchar_t *__s, wchar_t __wc)
     noexcept (true) __attribute__ ((__pure__));




extern size_t wcscspn (const wchar_t *__wcs, const wchar_t *__reject)
     noexcept (true) __attribute__ ((__pure__));


extern size_t wcsspn (const wchar_t *__wcs, const wchar_t *__accept)
     noexcept (true) __attribute__ ((__pure__));
# 202 "/usr/include/wchar.h" 3 4
extern wchar_t *wcspbrk (const wchar_t *__wcs, const wchar_t *__accept)
     noexcept (true) __attribute__ ((__pure__));
# 213 "/usr/include/wchar.h" 3 4
extern wchar_t *wcsstr (const wchar_t *__haystack, const wchar_t *__needle)
     noexcept (true) __attribute__ ((__pure__));



extern wchar_t *wcstok (wchar_t *__restrict __s,
   const wchar_t *__restrict __delim,
   wchar_t **__restrict __ptr) noexcept (true);


extern size_t wcslen (const wchar_t *__s) noexcept (true) __attribute__ ((__pure__));
# 234 "/usr/include/wchar.h" 3 4
extern wchar_t *wcswcs (const wchar_t *__haystack, const wchar_t *__needle)
     noexcept (true) __attribute__ ((__pure__));





extern size_t wcsnlen (const wchar_t *__s, size_t __maxlen)
     noexcept (true) __attribute__ ((__pure__));
# 254 "/usr/include/wchar.h" 3 4
extern wchar_t *wmemchr (const wchar_t *__s, wchar_t __c, size_t __n)
     noexcept (true) __attribute__ ((__pure__));



extern int wmemcmp (const wchar_t *__s1, const wchar_t *__s2, size_t __n)
     noexcept (true) __attribute__ ((__pure__));


extern wchar_t *wmemcpy (wchar_t *__restrict __s1,
    const wchar_t *__restrict __s2, size_t __n) noexcept (true);



extern wchar_t *wmemmove (wchar_t *__s1, const wchar_t *__s2, size_t __n)
     noexcept (true);


extern wchar_t *wmemset (wchar_t *__s, wchar_t __c, size_t __n) noexcept (true);




extern wchar_t *wmempcpy (wchar_t *__restrict __s1,
     const wchar_t *__restrict __s2, size_t __n)
     noexcept (true);





extern wint_t btowc (int __c) noexcept (true);



extern int wctob (wint_t __c) noexcept (true);



extern int mbsinit (const mbstate_t *__ps) noexcept (true) __attribute__ ((__pure__));



extern size_t mbrtowc (wchar_t *__restrict __pwc,
         const char *__restrict __s, size_t __n,
         mbstate_t *__restrict __p) noexcept (true);


extern size_t wcrtomb (char *__restrict __s, wchar_t __wc,
         mbstate_t *__restrict __ps) noexcept (true);


extern size_t __mbrlen (const char *__restrict __s, size_t __n,
   mbstate_t *__restrict __ps) noexcept (true);
extern size_t mbrlen (const char *__restrict __s, size_t __n,
        mbstate_t *__restrict __ps) noexcept (true);
# 338 "/usr/include/wchar.h" 3 4
extern size_t mbsrtowcs (wchar_t *__restrict __dst,
    const char **__restrict __src, size_t __len,
    mbstate_t *__restrict __ps) noexcept (true);



extern size_t wcsrtombs (char *__restrict __dst,
    const wchar_t **__restrict __src, size_t __len,
    mbstate_t *__restrict __ps) noexcept (true);





extern size_t mbsnrtowcs (wchar_t *__restrict __dst,
     const char **__restrict __src, size_t __nmc,
     size_t __len, mbstate_t *__restrict __ps) noexcept (true);



extern size_t wcsnrtombs (char *__restrict __dst,
     const wchar_t **__restrict __src,
     size_t __nwc, size_t __len,
     mbstate_t *__restrict __ps) noexcept (true);






extern int wcwidth (wchar_t __c) noexcept (true);



extern int wcswidth (const wchar_t *__s, size_t __n) noexcept (true);





extern double wcstod (const wchar_t *__restrict __nptr,
        wchar_t **__restrict __endptr) noexcept (true);



extern float wcstof (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr) noexcept (true);
extern long double wcstold (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr) noexcept (true);
# 397 "/usr/include/wchar.h" 3 4
extern _Float32 wcstof32 (const wchar_t *__restrict __nptr,
     wchar_t **__restrict __endptr) noexcept (true);



extern _Float64 wcstof64 (const wchar_t *__restrict __nptr,
     wchar_t **__restrict __endptr) noexcept (true);
# 412 "/usr/include/wchar.h" 3 4
extern _Float32x wcstof32x (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr) noexcept (true);



extern _Float64x wcstof64x (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr) noexcept (true);
# 429 "/usr/include/wchar.h" 3 4
extern long int wcstol (const wchar_t *__restrict __nptr,
   wchar_t **__restrict __endptr, int __base) noexcept (true);



extern unsigned long int wcstoul (const wchar_t *__restrict __nptr,
      wchar_t **__restrict __endptr, int __base)
     noexcept (true);




__extension__
extern long long int wcstoll (const wchar_t *__restrict __nptr,
         wchar_t **__restrict __endptr, int __base)
     noexcept (true);



__extension__
extern unsigned long long int wcstoull (const wchar_t *__restrict __nptr,
     wchar_t **__restrict __endptr,
     int __base) noexcept (true);





__extension__
extern long long int wcstoq (const wchar_t *__restrict __nptr,
        wchar_t **__restrict __endptr, int __base)
     noexcept (true);



__extension__
extern unsigned long long int wcstouq (const wchar_t *__restrict __nptr,
           wchar_t **__restrict __endptr,
           int __base) noexcept (true);






extern long int wcstol_l (const wchar_t *__restrict __nptr,
     wchar_t **__restrict __endptr, int __base,
     locale_t __loc) noexcept (true);

extern unsigned long int wcstoul_l (const wchar_t *__restrict __nptr,
        wchar_t **__restrict __endptr,
        int __base, locale_t __loc) noexcept (true);

__extension__
extern long long int wcstoll_l (const wchar_t *__restrict __nptr,
    wchar_t **__restrict __endptr,
    int __base, locale_t __loc) noexcept (true);

__extension__
extern unsigned long long int wcstoull_l (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr,
       int __base, locale_t __loc)
     noexcept (true);

extern double wcstod_l (const wchar_t *__restrict __nptr,
   wchar_t **__restrict __endptr, locale_t __loc)
     noexcept (true);

extern float wcstof_l (const wchar_t *__restrict __nptr,
         wchar_t **__restrict __endptr, locale_t __loc)
     noexcept (true);

extern long double wcstold_l (const wchar_t *__restrict __nptr,
         wchar_t **__restrict __endptr,
         locale_t __loc) noexcept (true);
# 512 "/usr/include/wchar.h" 3 4
extern _Float32 wcstof32_l (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr,
       locale_t __loc) noexcept (true);



extern _Float64 wcstof64_l (const wchar_t *__restrict __nptr,
       wchar_t **__restrict __endptr,
       locale_t __loc) noexcept (true);
# 530 "/usr/include/wchar.h" 3 4
extern _Float32x wcstof32x_l (const wchar_t *__restrict __nptr,
         wchar_t **__restrict __endptr,
         locale_t __loc) noexcept (true);



extern _Float64x wcstof64x_l (const wchar_t *__restrict __nptr,
         wchar_t **__restrict __endptr,
         locale_t __loc) noexcept (true);
# 552 "/usr/include/wchar.h" 3 4
extern wchar_t *wcpcpy (wchar_t *__restrict __dest,
   const wchar_t *__restrict __src) noexcept (true);



extern wchar_t *wcpncpy (wchar_t *__restrict __dest,
    const wchar_t *__restrict __src, size_t __n)
     noexcept (true);
# 581 "/usr/include/wchar.h" 3 4
extern __FILE *open_wmemstream (wchar_t **__bufloc, size_t *__sizeloc) noexcept (true)
  __attribute__ ((__malloc__)) ;





extern int fwide (__FILE *__fp, int __mode) noexcept (true);






extern int fwprintf (__FILE *__restrict __stream,
       const wchar_t *__restrict __format, ...)
                                                           ;




extern int wprintf (const wchar_t *__restrict __format, ...)
                                                           ;

extern int swprintf (wchar_t *__restrict __s, size_t __n,
       const wchar_t *__restrict __format, ...)
     noexcept (true) ;





extern int vfwprintf (__FILE *__restrict __s,
        const wchar_t *__restrict __format,
        __gnuc_va_list __arg)
                                                           ;




extern int vwprintf (const wchar_t *__restrict __format,
       __gnuc_va_list __arg)
                                                           ;


extern int vswprintf (wchar_t *__restrict __s, size_t __n,
        const wchar_t *__restrict __format,
        __gnuc_va_list __arg)
     noexcept (true) ;






extern int fwscanf (__FILE *__restrict __stream,
      const wchar_t *__restrict __format, ...)
                                                          ;




extern int wscanf (const wchar_t *__restrict __format, ...)
                                                          ;

extern int swscanf (const wchar_t *__restrict __s,
      const wchar_t *__restrict __format, ...)
     noexcept (true) ;
# 657 "/usr/include/wchar.h" 3 4
extern int fwscanf (__FILE *__restrict __stream, const wchar_t *__restrict __format, ...) __asm__ ("" "__isoc99_fwscanf")


                                                          ;
extern int wscanf (const wchar_t *__restrict __format, ...) __asm__ ("" "__isoc99_wscanf")

                                                          ;
extern int swscanf (const wchar_t *__restrict __s, const wchar_t *__restrict __format, ...) noexcept (true) __asm__ ("" "__isoc99_swscanf")


                                                          ;
# 688 "/usr/include/wchar.h" 3 4
extern int vfwscanf (__FILE *__restrict __s,
       const wchar_t *__restrict __format,
       __gnuc_va_list __arg)
                                                          ;




extern int vwscanf (const wchar_t *__restrict __format,
      __gnuc_va_list __arg)
                                                          ;

extern int vswscanf (const wchar_t *__restrict __s,
       const wchar_t *__restrict __format,
       __gnuc_va_list __arg)
     noexcept (true) ;







extern int vfwscanf (__FILE *__restrict __s, const wchar_t *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vfwscanf")


                                                          ;
extern int vwscanf (const wchar_t *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vwscanf")

                                                          ;
extern int vswscanf (const wchar_t *__restrict __s, const wchar_t *__restrict __format, __gnuc_va_list __arg) noexcept (true) __asm__ ("" "__isoc99_vswscanf")


                                                          ;
# 744 "/usr/include/wchar.h" 3 4
extern wint_t fgetwc (__FILE *__stream);
extern wint_t getwc (__FILE *__stream);





extern wint_t getwchar (void);






extern wint_t fputwc (wchar_t __wc, __FILE *__stream);
extern wint_t putwc (wchar_t __wc, __FILE *__stream);





extern wint_t putwchar (wchar_t __wc);







extern wchar_t *fgetws (wchar_t *__restrict __ws, int __n,
   __FILE *__restrict __stream);





extern int fputws (const wchar_t *__restrict __ws,
     __FILE *__restrict __stream);






extern wint_t ungetwc (wint_t __wc, __FILE *__stream);
# 799 "/usr/include/wchar.h" 3 4
extern wint_t getwc_unlocked (__FILE *__stream);
extern wint_t getwchar_unlocked (void);







extern wint_t fgetwc_unlocked (__FILE *__stream);







extern wint_t fputwc_unlocked (wchar_t __wc, __FILE *__stream);
# 825 "/usr/include/wchar.h" 3 4
extern wint_t putwc_unlocked (wchar_t __wc, __FILE *__stream);
extern wint_t putwchar_unlocked (wchar_t __wc);
# 835 "/usr/include/wchar.h" 3 4
extern wchar_t *fgetws_unlocked (wchar_t *__restrict __ws, int __n,
     __FILE *__restrict __stream);







extern int fputws_unlocked (const wchar_t *__restrict __ws,
       __FILE *__restrict __stream);






extern size_t wcsftime (wchar_t *__restrict __s, size_t __maxsize,
   const wchar_t *__restrict __format,
   const struct tm *__restrict __tp) noexcept (true);




extern size_t wcsftime_l (wchar_t *__restrict __s, size_t __maxsize,
     const wchar_t *__restrict __format,
     const struct tm *__restrict __tp,
     locale_t __loc) noexcept (true);
# 882 "/usr/include/wchar.h" 3 4
}
# 45 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 2 3
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
namespace std
{
  using ::mbstate_t;
}
# 135 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
extern "C++"
{
namespace std __attribute__ ((__visibility__ ("default")))
{


  using ::wint_t;

  using ::btowc;
  using ::fgetwc;
  using ::fgetws;
  using ::fputwc;
  using ::fputws;
  using ::fwide;
  using ::fwprintf;
  using ::fwscanf;
  using ::getwc;
  using ::getwchar;
  using ::mbrlen;
  using ::mbrtowc;
  using ::mbsinit;
  using ::mbsrtowcs;
  using ::putwc;
  using ::putwchar;

  using ::swprintf;

  using ::swscanf;
  using ::ungetwc;
  using ::vfwprintf;

  using ::vfwscanf;


  using ::vswprintf;


  using ::vswscanf;

  using ::vwprintf;

  using ::vwscanf;

  using ::wcrtomb;
  using ::wcscat;
  using ::wcscmp;
  using ::wcscoll;
  using ::wcscpy;
  using ::wcscspn;
  using ::wcsftime;
  using ::wcslen;
  using ::wcsncat;
  using ::wcsncmp;
  using ::wcsncpy;
  using ::wcsrtombs;
  using ::wcsspn;
  using ::wcstod;

  using ::wcstof;

  using ::wcstok;
  using ::wcstol;
  using ::wcstoul;
  using ::wcsxfrm;
  using ::wctob;
  using ::wmemcmp;
  using ::wmemcpy;
  using ::wmemmove;
  using ::wmemset;
  using ::wprintf;
  using ::wscanf;
  using ::wcschr;
  using ::wcspbrk;
  using ::wcsrchr;
  using ::wcsstr;
  using ::wmemchr;


  inline wchar_t*
  wcschr(wchar_t* __p, wchar_t __c)
  { return wcschr(const_cast<const wchar_t*>(__p), __c); }

  inline wchar_t*
  wcspbrk(wchar_t* __s1, const wchar_t* __s2)
  { return wcspbrk(const_cast<const wchar_t*>(__s1), __s2); }

  inline wchar_t*
  wcsrchr(wchar_t* __p, wchar_t __c)
  { return wcsrchr(const_cast<const wchar_t*>(__p), __c); }

  inline wchar_t*
  wcsstr(wchar_t* __s1, const wchar_t* __s2)
  { return wcsstr(const_cast<const wchar_t*>(__s1), __s2); }

  inline wchar_t*
  wmemchr(wchar_t* __p, wchar_t __c, size_t __n)
  { return wmemchr(const_cast<const wchar_t*>(__p), __c, __n); }



}
}







namespace __gnu_cxx
{





  using ::wcstold;
# 260 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
  using ::wcstoll;
  using ::wcstoull;

}

namespace std
{
  using ::__gnu_cxx::wcstold;
  using ::__gnu_cxx::wcstoll;
  using ::__gnu_cxx::wcstoull;
}
# 280 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
namespace std
{

  using std::wcstof;


  using std::vfwscanf;


  using std::vswscanf;


  using std::vwscanf;



  using std::wcstold;
  using std::wcstoll;
  using std::wcstoull;

}
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 3
  typedef long int streamoff;





  typedef ptrdiff_t streamsize;
# 81 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 3
  template<typename _StateT>
    class fpos
    {
    private:
      streamoff _M_off;
      _StateT _M_state;

    public:




      fpos()
      : _M_off(0), _M_state() { }
# 103 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 3
      fpos(streamoff __off)
      : _M_off(__off), _M_state() { }


      fpos(const fpos&) = default;
      fpos& operator=(const fpos&) = default;
      ~fpos() = default;



      operator streamoff() const { return _M_off; }


      void
      state(_StateT __st)
      { _M_state = __st; }


      _StateT
      state() const
      { return _M_state; }





      fpos&
      operator+=(streamoff __off)
      {
 _M_off += __off;
 return *this;
      }





      fpos&
      operator-=(streamoff __off)
      {
 _M_off -= __off;
 return *this;
      }







      fpos
      operator+(streamoff __off) const
      {
 fpos __pos(*this);
 __pos += __off;
 return __pos;
      }







      fpos
      operator-(streamoff __off) const
      {
 fpos __pos(*this);
 __pos -= __off;
 return __pos;
      }






      streamoff
      operator-(const fpos& __other) const
      { return _M_off - __other._M_off; }
    };






  template<typename _StateT>
    inline bool
    operator==(const fpos<_StateT>& __lhs, const fpos<_StateT>& __rhs)
    { return streamoff(__lhs) == streamoff(__rhs); }

  template<typename _StateT>
    inline bool
    operator!=(const fpos<_StateT>& __lhs, const fpos<_StateT>& __rhs)
    { return streamoff(__lhs) != streamoff(__rhs); }





  typedef fpos<mbstate_t> streampos;

  typedef fpos<mbstate_t> wstreampos;
# 215 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/postypes.h" 3
  typedef fpos<mbstate_t> u16streampos;

  typedef fpos<mbstate_t> u32streampos;



}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 2 3
# 53 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{


#pragma GCC diagnostic push


#pragma GCC diagnostic ignored "-Warray-bounds"
# 72 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
  template<typename _CharT>
    struct _Char_types
    {
      typedef unsigned long int_type;
      typedef std::streampos pos_type;
      typedef std::streamoff off_type;
      typedef std::mbstate_t state_type;
    };
# 97 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
  template<typename _CharT>
    struct char_traits
    {
      typedef _CharT char_type;
      typedef typename _Char_types<_CharT>::int_type int_type;
      typedef typename _Char_types<_CharT>::pos_type pos_type;
      typedef typename _Char_types<_CharT>::off_type off_type;
      typedef typename _Char_types<_CharT>::state_type state_type;




      static void
      assign(char_type& __c1, const char_type& __c2)
      {





 __c1 = __c2;
      }

      static constexpr bool
      eq(const char_type& __c1, const char_type& __c2)
      { return __c1 == __c2; }

      static constexpr bool
      lt(const char_type& __c1, const char_type& __c2)
      { return __c1 < __c2; }

      static int
      compare(const char_type* __s1, const char_type* __s2, std::size_t __n);

      static std::size_t
      length(const char_type* __s);

      static const char_type*
      find(const char_type* __s, std::size_t __n, const char_type& __a);

      static char_type*
      move(char_type* __s1, const char_type* __s2, std::size_t __n);

      static char_type*
      copy(char_type* __s1, const char_type* __s2, std::size_t __n);

      static char_type*
      assign(char_type* __s, std::size_t __n, char_type __a);

      static constexpr char_type
      to_char_type(const int_type& __c)
      { return static_cast<char_type>(__c); }

      static constexpr int_type
      to_int_type(const char_type& __c)
      { return static_cast<int_type>(__c); }

      static constexpr bool
      eq_int_type(const int_type& __c1, const int_type& __c2)
      { return __c1 == __c2; }

      static constexpr int_type
      eof()
      { return static_cast<int_type>(-1); }

      static constexpr int_type
      not_eof(const int_type& __c)
      { return !eq_int_type(__c, eof()) ? __c : to_int_type(char_type()); }
    };

  template<typename _CharT>
                         int
    char_traits<_CharT>::
    compare(const char_type* __s1, const char_type* __s2, std::size_t __n)
    {
      for (std::size_t __i = 0; __i < __n; ++__i)
 if (lt(__s1[__i], __s2[__i]))
   return -1;
 else if (lt(__s2[__i], __s1[__i]))
   return 1;
      return 0;
    }

  template<typename _CharT>
                         std::size_t
    char_traits<_CharT>::
    length(const char_type* __p)
    {
      std::size_t __i = 0;
      while (!eq(__p[__i], char_type()))
        ++__i;
      return __i;
    }

  template<typename _CharT>
                         const typename char_traits<_CharT>::char_type*
    char_traits<_CharT>::
    find(const char_type* __s, std::size_t __n, const char_type& __a)
    {
      for (std::size_t __i = 0; __i < __n; ++__i)
        if (eq(__s[__i], __a))
          return __s + __i;
      return 0;
    }

  template<typename _CharT>

    typename char_traits<_CharT>::char_type*
    char_traits<_CharT>::
    move(char_type* __s1, const char_type* __s2, std::size_t __n)
    {
      if (__n == 0)
 return __s1;
# 248 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
      __builtin_memmove(__s1, __s2, __n * sizeof(char_type));
      return __s1;
    }

  template<typename _CharT>

    typename char_traits<_CharT>::char_type*
    char_traits<_CharT>::
    copy(char_type* __s1, const char_type* __s2, std::size_t __n)
    {
# 267 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
      __builtin_memcpy(__s1, __s2, __n * sizeof(char_type));
      return __s1;
    }

  template<typename _CharT>

    typename char_traits<_CharT>::char_type*
    char_traits<_CharT>::
    assign(char_type* __s, std::size_t __n, char_type __a)
    {
# 286 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
      if (sizeof(_CharT) == 1 && __is_trivial(_CharT))
 {
   unsigned char __c;
   __builtin_memcpy(&__c, __builtin_addressof(__a), 1);
   __builtin_memset(__s, __c, __n);
 }
      else
 {
   for (std::size_t __i = 0; __i < __n; ++__i)
     __s[__i] = __a;
 }
      return __s;
    }


}

namespace std __attribute__ ((__visibility__ ("default")))
{
# 328 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
  template<typename _CharT>
    struct char_traits : public __gnu_cxx::char_traits<_CharT>
    { };



  template<>
    struct char_traits<char>
    {
      typedef char char_type;
      typedef int int_type;
      typedef streampos pos_type;
      typedef streamoff off_type;
      typedef mbstate_t state_type;




      static void
      assign(char_type& __c1, const char_type& __c2) noexcept
      {





 __c1 = __c2;
      }

      static constexpr bool
      eq(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr bool
      lt(const char_type& __c1, const char_type& __c2) noexcept
      {

 return (static_cast<unsigned char>(__c1)
  < static_cast<unsigned char>(__c2));
      }

      static int
      compare(const char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return 0;
# 385 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
 return __builtin_memcmp(__s1, __s2, __n);
      }

      static size_t
      length(const char_type* __s)
      {




 return __builtin_strlen(__s);
      }

      static const char_type*
      find(const char_type* __s, size_t __n, const char_type& __a)
      {
 if (__n == 0)
   return 0;




 return static_cast<const char_type*>(__builtin_memchr(__s, __a, __n));
      }

      static char_type*
      move(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return static_cast<char_type*>(__builtin_memmove(__s1, __s2, __n));
      }

      static char_type*
      copy(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return static_cast<char_type*>(__builtin_memcpy(__s1, __s2, __n));
      }

      static char_type*
      assign(char_type* __s, size_t __n, char_type __a)
      {
 if (__n == 0)
   return __s;




 return static_cast<char_type*>(__builtin_memset(__s, __a, __n));
      }

      static constexpr char_type
      to_char_type(const int_type& __c) noexcept
      { return static_cast<char_type>(__c); }



      static constexpr int_type
      to_int_type(const char_type& __c) noexcept
      { return static_cast<int_type>(static_cast<unsigned char>(__c)); }

      static constexpr bool
      eq_int_type(const int_type& __c1, const int_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr int_type
      eof() noexcept
      { return static_cast<int_type>(-1); }

      static constexpr int_type
      not_eof(const int_type& __c) noexcept
      { return (__c == eof()) ? 0 : __c; }
  };




  template<>
    struct char_traits<wchar_t>
    {
      typedef wchar_t char_type;
      typedef wint_t int_type;
      typedef streamoff off_type;
      typedef wstreampos pos_type;
      typedef mbstate_t state_type;




      static void
      assign(char_type& __c1, const char_type& __c2) noexcept
      {





 __c1 = __c2;
      }

      static constexpr bool
      eq(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr bool
      lt(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 < __c2; }

      static int
      compare(const char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return 0;




 return wmemcmp(__s1, __s2, __n);
      }

      static size_t
      length(const char_type* __s)
      {




 return wcslen(__s);
      }

      static const char_type*
      find(const char_type* __s, size_t __n, const char_type& __a)
      {
 if (__n == 0)
   return 0;




 return wmemchr(__s, __a, __n);
      }

      static char_type*
      move(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return wmemmove(__s1, __s2, __n);
      }

      static char_type*
      copy(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return wmemcpy(__s1, __s2, __n);
      }

      static char_type*
      assign(char_type* __s, size_t __n, char_type __a)
      {
 if (__n == 0)
   return __s;




 return wmemset(__s, __a, __n);
      }

      static constexpr char_type
      to_char_type(const int_type& __c) noexcept
      { return char_type(__c); }

      static constexpr int_type
      to_int_type(const char_type& __c) noexcept
      { return int_type(__c); }

      static constexpr bool
      eq_int_type(const int_type& __c1, const int_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr int_type
      eof() noexcept
      { return static_cast<int_type>((0xffffffffu)); }

      static constexpr int_type
      not_eof(const int_type& __c) noexcept
      { return eq_int_type(__c, eof()) ? 0 : __c; }
  };
# 727 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
}



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdint" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdint" 3
# 44 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdint" 3
namespace std
{

  using ::int8_t;
  using ::int16_t;
  using ::int32_t;
  using ::int64_t;

  using ::int_fast8_t;
  using ::int_fast16_t;
  using ::int_fast32_t;
  using ::int_fast64_t;

  using ::int_least8_t;
  using ::int_least16_t;
  using ::int_least32_t;
  using ::int_least64_t;

  using ::intmax_t;
  using ::intptr_t;

  using ::uint8_t;
  using ::uint16_t;
  using ::uint32_t;
  using ::uint64_t;

  using ::uint_fast8_t;
  using ::uint_fast16_t;
  using ::uint_fast32_t;
  using ::uint_fast64_t;

  using ::uint_least8_t;
  using ::uint_least16_t;
  using ::uint_least32_t;
  using ::uint_least64_t;

  using ::uintmax_t;
  using ::uintptr_t;





}
# 732 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  template<>
    struct char_traits<char16_t>
    {
      typedef char16_t char_type;

      typedef uint_least16_t int_type;





      typedef streamoff off_type;
      typedef u16streampos pos_type;
      typedef mbstate_t state_type;




      static void
      assign(char_type& __c1, const char_type& __c2) noexcept
      {





 __c1 = __c2;
      }

      static constexpr bool
      eq(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr bool
      lt(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 < __c2; }

      static int
      compare(const char_type* __s1, const char_type* __s2, size_t __n)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   if (lt(__s1[__i], __s2[__i]))
     return -1;
   else if (lt(__s2[__i], __s1[__i]))
     return 1;
 return 0;
      }

      static size_t
      length(const char_type* __s)
      {
 size_t __i = 0;
 while (!eq(__s[__i], char_type()))
   ++__i;
 return __i;
      }

      static const char_type*
      find(const char_type* __s, size_t __n, const char_type& __a)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   if (eq(__s[__i], __a))
     return __s + __i;
 return 0;
      }

      static char_type*
      move(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return (static_cast<char_type*>
  (__builtin_memmove(__s1, __s2, __n * sizeof(char_type))));
      }

      static char_type*
      copy(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return (static_cast<char_type*>
  (__builtin_memcpy(__s1, __s2, __n * sizeof(char_type))));
      }

      static char_type*
      assign(char_type* __s, size_t __n, char_type __a)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   assign(__s[__i], __a);
 return __s;
      }

      static constexpr char_type
      to_char_type(const int_type& __c) noexcept
      { return char_type(__c); }

      static constexpr int_type
      to_int_type(const char_type& __c) noexcept
      { return __c == eof() ? int_type(0xfffd) : int_type(__c); }

      static constexpr bool
      eq_int_type(const int_type& __c1, const int_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr int_type
      eof() noexcept
      { return static_cast<int_type>(-1); }

      static constexpr int_type
      not_eof(const int_type& __c) noexcept
      { return eq_int_type(__c, eof()) ? 0 : __c; }
    };

  template<>
    struct char_traits<char32_t>
    {
      typedef char32_t char_type;

      typedef uint_least32_t int_type;





      typedef streamoff off_type;
      typedef u32streampos pos_type;
      typedef mbstate_t state_type;




      static void
      assign(char_type& __c1, const char_type& __c2) noexcept
      {





 __c1 = __c2;
      }

      static constexpr bool
      eq(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr bool
      lt(const char_type& __c1, const char_type& __c2) noexcept
      { return __c1 < __c2; }

      static int
      compare(const char_type* __s1, const char_type* __s2, size_t __n)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   if (lt(__s1[__i], __s2[__i]))
     return -1;
   else if (lt(__s2[__i], __s1[__i]))
     return 1;
 return 0;
      }

      static size_t
      length(const char_type* __s)
      {
 size_t __i = 0;
 while (!eq(__s[__i], char_type()))
   ++__i;
 return __i;
      }

      static const char_type*
      find(const char_type* __s, size_t __n, const char_type& __a)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   if (eq(__s[__i], __a))
     return __s + __i;
 return 0;
      }

      static char_type*
      move(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return (static_cast<char_type*>
  (__builtin_memmove(__s1, __s2, __n * sizeof(char_type))));
      }

      static char_type*
      copy(char_type* __s1, const char_type* __s2, size_t __n)
      {
 if (__n == 0)
   return __s1;




 return (static_cast<char_type*>
  (__builtin_memcpy(__s1, __s2, __n * sizeof(char_type))));
      }

      static char_type*
      assign(char_type* __s, size_t __n, char_type __a)
      {
 for (size_t __i = 0; __i < __n; ++__i)
   assign(__s[__i], __a);
 return __s;
      }

      static constexpr char_type
      to_char_type(const int_type& __c) noexcept
      { return char_type(__c); }

      static constexpr int_type
      to_int_type(const char_type& __c) noexcept
      { return int_type(__c); }

      static constexpr bool
      eq_int_type(const int_type& __c1, const int_type& __c2) noexcept
      { return __c1 == __c2; }

      static constexpr int_type
      eof() noexcept
      { return static_cast<int_type>(-1); }

      static constexpr int_type
      not_eof(const int_type& __c) noexcept
      { return eq_int_type(__c, eof()) ? 0 : __c; }
    };
# 998 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/char_traits.h" 3
#pragma GCC diagnostic pop


}
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 1 3
# 46 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++allocator.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++allocator.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 1 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 55 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
  template<typename _Tp>
    class __new_allocator
    {
    public:
      typedef _Tp value_type;
      typedef std::size_t size_type;
      typedef std::ptrdiff_t difference_type;

      typedef _Tp* pointer;
      typedef const _Tp* const_pointer;
      typedef _Tp& reference;
      typedef const _Tp& const_reference;

      template<typename _Tp1>
 struct rebind
 { typedef __new_allocator<_Tp1> other; };





      typedef std::true_type propagate_on_container_move_assignment;



      __new_allocator() noexcept { }


      __new_allocator(const __new_allocator&) noexcept { }

      template<typename _Tp1>

 __new_allocator(const __new_allocator<_Tp1>&) noexcept { }


      ~__new_allocator() noexcept { }

      pointer
      address(reference __x) const noexcept
      { return std::__addressof(__x); }

      const_pointer
      address(const_reference __x) const noexcept
      { return std::__addressof(__x); }
# 111 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
                         _Tp*
      allocate(size_type __n, const void* = static_cast<const void*>(0))
      {



 static_assert(sizeof(_Tp) != 0, "cannot allocate incomplete types");


 if (__builtin_expect(__n > this->_M_max_size(), false))
   {


     if (__n > (std::size_t(-1) / sizeof(_Tp)))
       std::__throw_bad_array_new_length();
     std::__throw_bad_alloc();
   }
# 137 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
 return static_cast<_Tp*>(__builtin_operator_new(__n * sizeof(_Tp)));
      }


      void
      deallocate(_Tp* __p, size_type __n __attribute__ ((__unused__)))
      {
# 158 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
 __builtin_operator_delete((__p));
      }






      size_type
      max_size() const noexcept
      { return _M_max_size(); }


      template<typename _Up, typename... _Args>
 void
 construct(_Up* __p, _Args&&... __args)
 noexcept(std::is_nothrow_constructible<_Up, _Args...>::value)
 { ::new((void *)__p) _Up(std::forward<_Args>(__args)...); }

      template<typename _Up>
 void
 destroy(_Up* __p)
 noexcept(std::is_nothrow_destructible<_Up>::value)
 { __p->~_Up(); }
# 194 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/new_allocator.h" 3
      template<typename _Up>
 friend bool
 operator==(const __new_allocator&, const __new_allocator<_Up>&)
 noexcept
 { return true; }


      template<typename _Up>
 friend bool
 operator!=(const __new_allocator&, const __new_allocator<_Up>&)
 noexcept
 { return false; }


    private:
      constexpr size_type
      _M_max_size() const noexcept
      {

 return std::size_t(9223372036854775807L) / sizeof(_Tp);



      }
    };


}
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++allocator.h" 2 3


namespace std
{
# 46 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++allocator.h" 3
  template<typename _Tp>
    using __allocator_base = __new_allocator<_Tp>;
}
# 47 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 2 3







namespace std __attribute__ ((__visibility__ ("default")))
{
# 71 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 3
  template<>
    class allocator<void>
    {
    public:
      typedef void value_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;



      typedef void* pointer;
      typedef const void* const_pointer;

      template<typename _Tp1>
 struct rebind
 { typedef allocator<_Tp1> other; };





      using propagate_on_container_move_assignment = true_type;

      using is_always_equal

 = true_type;
# 113 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 3
    };
# 123 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 3
  template<typename _Tp>
    class allocator : public __allocator_base<_Tp>
    {
    public:
      typedef _Tp value_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;



      typedef _Tp* pointer;
      typedef const _Tp* const_pointer;
      typedef _Tp& reference;
      typedef const _Tp& const_reference;

      template<typename _Tp1>
 struct rebind
 { typedef allocator<_Tp1> other; };





      using propagate_on_container_move_assignment = true_type;

      using is_always_equal

 = true_type;





      allocator() noexcept { }


      allocator(const allocator& __a) noexcept
      : __allocator_base<_Tp>(__a) { }



      allocator& operator=(const allocator&) = default;


      template<typename _Tp1>

 allocator(const allocator<_Tp1>&) noexcept { }




      ~allocator() noexcept { }
# 204 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/allocator.h" 3
      friend bool
      operator==(const allocator&, const allocator&) noexcept
      { return true; }


      friend bool
      operator!=(const allocator&, const allocator&) noexcept
      { return false; }



    };

  template<typename _T1, typename _T2>
    inline bool
    operator==(const allocator<_T1>&, const allocator<_T2>&)
    noexcept
    { return true; }


  template<typename _T1, typename _T2>
    inline bool
    operator!=(const allocator<_T1>&, const allocator<_T2>&)
    noexcept
    { return false; }




  template<typename _Tp>
    class allocator<const _Tp>
    {
    public:
      typedef _Tp value_type;
      template<typename _Up> allocator(const allocator<_Up>&) { }
    };

  template<typename _Tp>
    class allocator<volatile _Tp>
    {
    public:
      typedef _Tp value_type;
      template<typename _Up> allocator(const allocator<_Up>&) { }
    };

  template<typename _Tp>
    class allocator<const volatile _Tp>
    {
    public:
      typedef _Tp value_type;
      template<typename _Up> allocator(const allocator<_Up>&) { }
    };






  extern template class allocator<char>;
  extern template class allocator<wchar_t>;






  template<typename _Alloc, bool = __is_empty(_Alloc)>
    struct __alloc_swap
    { static void _S_do_it(_Alloc&, _Alloc&) noexcept { } };

  template<typename _Alloc>
    struct __alloc_swap<_Alloc, false>
    {
      static void
      _S_do_it(_Alloc& __one, _Alloc& __two) noexcept
      {

 if (__one != __two)
   swap(__one, __two);
      }
    };


  template<typename _Alloc, bool = __is_empty(_Alloc)>
    struct __alloc_neq
    {
      static bool
      _S_do_it(const _Alloc&, const _Alloc&)
      { return false; }
    };

  template<typename _Alloc>
    struct __alloc_neq<_Alloc, false>
    {
      static bool
      _S_do_it(const _Alloc& __one, const _Alloc& __two)
      { return __one != __two; }
    };


  template<typename _Tp, bool
    = __or_<is_copy_constructible<typename _Tp::value_type>,
            is_nothrow_move_constructible<typename _Tp::value_type>>::value>
    struct __shrink_to_fit_aux
    { static bool _S_do_it(_Tp&) noexcept { return false; } };

  template<typename _Tp>
    struct __shrink_to_fit_aux<_Tp, true>
    {

      static bool
      _S_do_it(_Tp& __c) noexcept
      {

 try
   {
     _Tp(__make_move_if_noexcept_iterator(__c.begin()),
  __make_move_if_noexcept_iterator(__c.end()),
  __c.get_allocator()).swap(__c);
     return true;
   }
 catch(...)
   { return false; }



      }
    };



}
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++locale.h" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++locale.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/clocale" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/clocale" 3


# 1 "/usr/include/locale.h" 1 3 4
# 28 "/usr/include/locale.h" 3 4
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 29 "/usr/include/locale.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/locale.h" 1 3 4
# 30 "/usr/include/locale.h" 2 3 4

extern "C" {
# 51 "/usr/include/locale.h" 3 4
struct lconv
{


  char *decimal_point;
  char *thousands_sep;





  char *grouping;





  char *int_curr_symbol;
  char *currency_symbol;
  char *mon_decimal_point;
  char *mon_thousands_sep;
  char *mon_grouping;
  char *positive_sign;
  char *negative_sign;
  char int_frac_digits;
  char frac_digits;

  char p_cs_precedes;

  char p_sep_by_space;

  char n_cs_precedes;

  char n_sep_by_space;






  char p_sign_posn;
  char n_sign_posn;


  char int_p_cs_precedes;

  char int_p_sep_by_space;

  char int_n_cs_precedes;

  char int_n_sep_by_space;






  char int_p_sign_posn;
  char int_n_sign_posn;
# 118 "/usr/include/locale.h" 3 4
};



extern char *setlocale (int __category, const char *__locale) noexcept (true);


extern struct lconv *localeconv (void) noexcept (true);
# 141 "/usr/include/locale.h" 3 4
extern locale_t newlocale (int __category_mask, const char *__locale,
      locale_t __base) noexcept (true);
# 176 "/usr/include/locale.h" 3 4
extern locale_t duplocale (locale_t __dataset) noexcept (true);



extern void freelocale (locale_t __dataset) noexcept (true);






extern locale_t uselocale (locale_t __dataset) noexcept (true);







}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/clocale" 2 3








namespace std
{
  using ::lconv;
  using ::setlocale;
  using ::localeconv;
}
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++locale.h" 2 3






namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{


  extern "C" __typeof(uselocale) __uselocale;


}


namespace std __attribute__ ((__visibility__ ("default")))
{


  typedef __locale_t __c_locale;
# 73 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++locale.h" 3
  inline int
  __convert_from_v(const __c_locale& __cloc __attribute__ ((__unused__)),
     char* __out,
     const int __size __attribute__ ((__unused__)),
     const char* __fmt, ...)
  {

    __c_locale __old = __gnu_cxx::__uselocale(__cloc);
# 93 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/c++locale.h" 3
    __builtin_va_list __args;
    __builtin_va_start(__args, __fmt);


    const int __ret = __builtin_vsnprintf(__out, __size, __fmt, __args);




    __builtin_va_end(__args);


    __gnu_cxx::__uselocale(__old);







    return __ret;
  }







}
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iosfwd" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iosfwd" 3





namespace std __attribute__ ((__visibility__ ("default")))
{
# 74 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iosfwd" 3
  class ios_base;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_ios;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_streambuf;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_istream;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_ostream;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_iostream;


namespace __cxx11 {

  template<typename _CharT, typename _Traits = char_traits<_CharT>,
     typename _Alloc = allocator<_CharT> >
    class basic_stringbuf;

  template<typename _CharT, typename _Traits = char_traits<_CharT>,
    typename _Alloc = allocator<_CharT> >
    class basic_istringstream;

  template<typename _CharT, typename _Traits = char_traits<_CharT>,
    typename _Alloc = allocator<_CharT> >
    class basic_ostringstream;

  template<typename _CharT, typename _Traits = char_traits<_CharT>,
    typename _Alloc = allocator<_CharT> >
    class basic_stringstream;

}

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_filebuf;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_ifstream;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_ofstream;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class basic_fstream;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class istreambuf_iterator;

  template<typename _CharT, typename _Traits = char_traits<_CharT> >
    class ostreambuf_iterator;



  typedef basic_ios<char> ios;


  typedef basic_streambuf<char> streambuf;


  typedef basic_istream<char> istream;


  typedef basic_ostream<char> ostream;


  typedef basic_iostream<char> iostream;


  typedef basic_stringbuf<char> stringbuf;


  typedef basic_istringstream<char> istringstream;


  typedef basic_ostringstream<char> ostringstream;


  typedef basic_stringstream<char> stringstream;


  typedef basic_filebuf<char> filebuf;


  typedef basic_ifstream<char> ifstream;


  typedef basic_ofstream<char> ofstream;


  typedef basic_fstream<char> fstream;



  typedef basic_ios<wchar_t> wios;


  typedef basic_streambuf<wchar_t> wstreambuf;


  typedef basic_istream<wchar_t> wistream;


  typedef basic_ostream<wchar_t> wostream;


  typedef basic_iostream<wchar_t> wiostream;


  typedef basic_stringbuf<wchar_t> wstringbuf;


  typedef basic_istringstream<wchar_t> wistringstream;


  typedef basic_ostringstream<wchar_t> wostringstream;


  typedef basic_stringstream<wchar_t> wstringstream;


  typedef basic_filebuf<wchar_t> wfilebuf;


  typedef basic_ifstream<wchar_t> wifstream;


  typedef basic_ofstream<wchar_t> wofstream;


  typedef basic_fstream<wchar_t> wfstream;
# 254 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iosfwd" 3
}
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 3


# 1 "/usr/include/ctype.h" 1 3 4
# 28 "/usr/include/ctype.h" 3 4
extern "C" {
# 46 "/usr/include/ctype.h" 3 4
enum
{
  _ISupper = ((0) < 8 ? ((1 << (0)) << 8) : ((1 << (0)) >> 8)),
  _ISlower = ((1) < 8 ? ((1 << (1)) << 8) : ((1 << (1)) >> 8)),
  _ISalpha = ((2) < 8 ? ((1 << (2)) << 8) : ((1 << (2)) >> 8)),
  _ISdigit = ((3) < 8 ? ((1 << (3)) << 8) : ((1 << (3)) >> 8)),
  _ISxdigit = ((4) < 8 ? ((1 << (4)) << 8) : ((1 << (4)) >> 8)),
  _ISspace = ((5) < 8 ? ((1 << (5)) << 8) : ((1 << (5)) >> 8)),
  _ISprint = ((6) < 8 ? ((1 << (6)) << 8) : ((1 << (6)) >> 8)),
  _ISgraph = ((7) < 8 ? ((1 << (7)) << 8) : ((1 << (7)) >> 8)),
  _ISblank = ((8) < 8 ? ((1 << (8)) << 8) : ((1 << (8)) >> 8)),
  _IScntrl = ((9) < 8 ? ((1 << (9)) << 8) : ((1 << (9)) >> 8)),
  _ISpunct = ((10) < 8 ? ((1 << (10)) << 8) : ((1 << (10)) >> 8)),
  _ISalnum = ((11) < 8 ? ((1 << (11)) << 8) : ((1 << (11)) >> 8))
};
# 79 "/usr/include/ctype.h" 3 4
extern const unsigned short int **__ctype_b_loc (void)
     noexcept (true) __attribute__ ((__const__));
extern const __int32_t **__ctype_tolower_loc (void)
     noexcept (true) __attribute__ ((__const__));
extern const __int32_t **__ctype_toupper_loc (void)
     noexcept (true) __attribute__ ((__const__));
# 108 "/usr/include/ctype.h" 3 4
extern int isalnum (int) noexcept (true);
extern int isalpha (int) noexcept (true);
extern int iscntrl (int) noexcept (true);
extern int isdigit (int) noexcept (true);
extern int islower (int) noexcept (true);
extern int isgraph (int) noexcept (true);
extern int isprint (int) noexcept (true);
extern int ispunct (int) noexcept (true);
extern int isspace (int) noexcept (true);
extern int isupper (int) noexcept (true);
extern int isxdigit (int) noexcept (true);



extern int tolower (int __c) noexcept (true);


extern int toupper (int __c) noexcept (true);




extern int isblank (int) noexcept (true);




extern int isctype (int __c, int __mask) noexcept (true);






extern int isascii (int __c) noexcept (true);



extern int toascii (int __c) noexcept (true);



extern int _toupper (int) noexcept (true);
extern int _tolower (int) noexcept (true);
# 251 "/usr/include/ctype.h" 3 4
extern int isalnum_l (int, locale_t) noexcept (true);
extern int isalpha_l (int, locale_t) noexcept (true);
extern int iscntrl_l (int, locale_t) noexcept (true);
extern int isdigit_l (int, locale_t) noexcept (true);
extern int islower_l (int, locale_t) noexcept (true);
extern int isgraph_l (int, locale_t) noexcept (true);
extern int isprint_l (int, locale_t) noexcept (true);
extern int ispunct_l (int, locale_t) noexcept (true);
extern int isspace_l (int, locale_t) noexcept (true);
extern int isupper_l (int, locale_t) noexcept (true);
extern int isxdigit_l (int, locale_t) noexcept (true);

extern int isblank_l (int, locale_t) noexcept (true);



extern int __tolower_l (int __c, locale_t __l) noexcept (true);
extern int tolower_l (int __c, locale_t __l) noexcept (true);


extern int __toupper_l (int __c, locale_t __l) noexcept (true);
extern int toupper_l (int __c, locale_t __l) noexcept (true);
# 327 "/usr/include/ctype.h" 3 4
}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 2 3
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 3
namespace std
{
  using ::isalnum;
  using ::isalpha;
  using ::iscntrl;
  using ::isdigit;
  using ::isgraph;
  using ::islower;
  using ::isprint;
  using ::ispunct;
  using ::isspace;
  using ::isupper;
  using ::isxdigit;
  using ::tolower;
  using ::toupper;
}







namespace std
{
  using ::isblank;
}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{
# 55 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/localefwd.h" 3
  class locale;

  template<typename _Facet>
    bool
    has_facet(const locale&) throw();

  template<typename _Facet>
    const _Facet&
    use_facet(const locale&);


  template<typename _CharT>
    bool
    isspace(_CharT, const locale&);

  template<typename _CharT>
    bool
    isprint(_CharT, const locale&);

  template<typename _CharT>
    bool
    iscntrl(_CharT, const locale&);

  template<typename _CharT>
    bool
    isupper(_CharT, const locale&);

  template<typename _CharT>
    bool
    islower(_CharT, const locale&);

  template<typename _CharT>
    bool
    isalpha(_CharT, const locale&);

  template<typename _CharT>
    bool
    isdigit(_CharT, const locale&);

  template<typename _CharT>
    bool
    ispunct(_CharT, const locale&);

  template<typename _CharT>
    bool
    isxdigit(_CharT, const locale&);

  template<typename _CharT>
    bool
    isalnum(_CharT, const locale&);

  template<typename _CharT>
    bool
    isgraph(_CharT, const locale&);


  template<typename _CharT>
    bool
    isblank(_CharT, const locale&);


  template<typename _CharT>
    _CharT
    toupper(_CharT, const locale&);

  template<typename _CharT>
    _CharT
    tolower(_CharT, const locale&);


  struct ctype_base;
  template<typename _CharT>
    class ctype;
  template<> class ctype<char>;

  template<> class ctype<wchar_t>;

  template<typename _CharT>
    class ctype_byname;


  class codecvt_base;
  template<typename _InternT, typename _ExternT, typename _StateT>
    class codecvt;
  template<> class codecvt<char, char, mbstate_t>;

  template<> class codecvt<wchar_t, char, mbstate_t>;


  template<> class codecvt<char16_t, char, mbstate_t>;
  template<> class codecvt<char32_t, char, mbstate_t>;





  template<typename _InternT, typename _ExternT, typename _StateT>
    class codecvt_byname;



  template<typename _CharT, typename _InIter = istreambuf_iterator<_CharT> >
    class num_get;
  template<typename _CharT, typename _OutIter = ostreambuf_iterator<_CharT> >
    class num_put;

namespace __cxx11 {
  template<typename _CharT> class numpunct;
  template<typename _CharT> class numpunct_byname;
}

namespace __cxx11 {

  template<typename _CharT>
    class collate;
  template<typename _CharT>
    class collate_byname;
}


  class time_base;
namespace __cxx11 {
  template<typename _CharT, typename _InIter = istreambuf_iterator<_CharT> >
    class time_get;
  template<typename _CharT, typename _InIter = istreambuf_iterator<_CharT> >
    class time_get_byname;
}
  template<typename _CharT, typename _OutIter = ostreambuf_iterator<_CharT> >
    class time_put;
  template<typename _CharT, typename _OutIter = ostreambuf_iterator<_CharT> >
    class time_put_byname;


  class money_base;
namespace __cxx11 {
  template<typename _CharT, typename _InIter = istreambuf_iterator<_CharT> >
    class money_get;
  template<typename _CharT, typename _OutIter = ostreambuf_iterator<_CharT> >
    class money_put;
}
namespace __cxx11 {
  template<typename _CharT, bool _Intl = false>
    class moneypunct;
  template<typename _CharT, bool _Intl = false>
    class moneypunct_byname;
}


  struct messages_base;
namespace __cxx11 {
  template<typename _CharT>
    class messages;
  template<typename _CharT>
    class messages_byname;
}


}
# 44 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ostream_insert.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ostream_insert.h" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_forced.h" 1 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/cxxabi_forced.h" 3

#pragma GCC visibility push(default)


namespace __cxxabiv1
{







  class __forced_unwind
  {
    virtual ~__forced_unwind() throw();


    virtual void __pure_dummy() = 0;
  };
}


#pragma GCC visibility pop
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ostream_insert.h" 2 3


namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _CharT, typename _Traits>
    inline void
    __ostream_write(basic_ostream<_CharT, _Traits>& __out,
      const _CharT* __s, streamsize __n)
    {
      typedef basic_ostream<_CharT, _Traits> __ostream_type;
      typedef typename __ostream_type::ios_base __ios_base;

      const streamsize __put = __out.rdbuf()->sputn(__s, __n);
      if (__put != __n)
 __out.setstate(__ios_base::badbit);
    }

  template<typename _CharT, typename _Traits>
    inline void
    __ostream_fill(basic_ostream<_CharT, _Traits>& __out, streamsize __n)
    {
      typedef basic_ostream<_CharT, _Traits> __ostream_type;
      typedef typename __ostream_type::ios_base __ios_base;

      const _CharT __c = __out.fill();
      for (; __n > 0; --__n)
 {
   const typename _Traits::int_type __put = __out.rdbuf()->sputc(__c);
   if (_Traits::eq_int_type(__put, _Traits::eof()))
     {
       __out.setstate(__ios_base::badbit);
       break;
     }
 }
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    __ostream_insert(basic_ostream<_CharT, _Traits>& __out,
       const _CharT* __s, streamsize __n)
    {
      typedef basic_ostream<_CharT, _Traits> __ostream_type;
      typedef typename __ostream_type::ios_base __ios_base;

      typename __ostream_type::sentry __cerb(__out);
      if (__cerb)
 {
   try
     {
       const streamsize __w = __out.width();
       if (__w > __n)
  {
    const bool __left = ((__out.flags()
     & __ios_base::adjustfield)
           == __ios_base::left);
    if (!__left)
      __ostream_fill(__out, __w - __n);
    if (__out.good())
      __ostream_write(__out, __s, __n);
    if (__left && __out.good())
      __ostream_fill(__out, __w - __n);
  }
       else
  __ostream_write(__out, __s, __n);
       __out.width(0);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __out._M_setstate(__ios_base::badbit);
       throw;
     }
   catch(...)
     { __out._M_setstate(__ios_base::badbit); }
 }
      return __out;
    }




  extern template ostream& __ostream_insert(ostream&, const char*, streamsize);


  extern template wostream& __ostream_insert(wostream&, const wchar_t*,
          streamsize);




}
# 45 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 1 3
# 63 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 116 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
  template<typename _Arg, typename _Result>
    struct unary_function
    {

      typedef _Arg argument_type;


      typedef _Result result_type;
    } __attribute__ ((__deprecated__));





  template<typename _Arg1, typename _Arg2, typename _Result>
    struct binary_function
    {

      typedef _Arg1 first_argument_type;


      typedef _Arg2 second_argument_type;


      typedef _Result result_type;
    } __attribute__ ((__deprecated__));
# 179 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _Tp>
    struct plus : public binary_function<_Tp, _Tp, _Tp>
    {


      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x + __y; }
    };


  template<typename _Tp>
    struct minus : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x - __y; }
    };


  template<typename _Tp>
    struct multiplies : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x * __y; }
    };


  template<typename _Tp>
    struct divides : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x / __y; }
    };


  template<typename _Tp>
    struct modulus : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x % __y; }
    };


  template<typename _Tp>
    struct negate : public unary_function<_Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x) const
      { return -__x; }
    };
#pragma GCC diagnostic pop
# 368 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _Tp>
    struct equal_to : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x == __y; }
    };


  template<typename _Tp>
    struct not_equal_to : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x != __y; }
    };


  template<typename _Tp>
    struct greater : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x > __y; }
    };


  template<typename _Tp>
    struct less : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x < __y; }
    };


  template<typename _Tp>
    struct greater_equal : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x >= __y; }
    };


  template<typename _Tp>
    struct less_equal : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x <= __y; }
    };


  template<typename _Tp>
    struct greater<_Tp*> : public binary_function<_Tp*, _Tp*, bool>
    {
                           bool
      operator()(_Tp* __x, _Tp* __y) const noexcept
      {




 return (long unsigned int)__x > (long unsigned int)__y;
      }
    };


  template<typename _Tp>
    struct less<_Tp*> : public binary_function<_Tp*, _Tp*, bool>
    {
                           bool
      operator()(_Tp* __x, _Tp* __y) const noexcept
      {




 return (long unsigned int)__x < (long unsigned int)__y;
      }
    };


  template<typename _Tp>
    struct greater_equal<_Tp*> : public binary_function<_Tp*, _Tp*, bool>
    {
                           bool
      operator()(_Tp* __x, _Tp* __y) const noexcept
      {




 return (long unsigned int)__x >= (long unsigned int)__y;
      }
    };


  template<typename _Tp>
    struct less_equal<_Tp*> : public binary_function<_Tp*, _Tp*, bool>
    {
                           bool
      operator()(_Tp* __x, _Tp* __y) const noexcept
      {




 return (long unsigned int)__x <= (long unsigned int)__y;
      }
    };
#pragma GCC diagnostic pop
# 791 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _Tp>
    struct logical_and : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x && __y; }
    };


  template<typename _Tp>
    struct logical_or : public binary_function<_Tp, _Tp, bool>
    {

      bool
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x || __y; }
    };


  template<typename _Tp>
    struct logical_not : public unary_function<_Tp, bool>
    {

      bool
      operator()(const _Tp& __x) const
      { return !__x; }
    };
#pragma GCC diagnostic pop
# 887 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"



  template<typename _Tp>
    struct bit_and : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x & __y; }
    };

  template<typename _Tp>
    struct bit_or : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x | __y; }
    };

  template<typename _Tp>
    struct bit_xor : public binary_function<_Tp, _Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x, const _Tp& __y) const
      { return __x ^ __y; }
    };

  template<typename _Tp>
    struct bit_not : public unary_function<_Tp, _Tp>
    {

      _Tp
      operator()(const _Tp& __x) const
      { return ~__x; }
    };
#pragma GCC diagnostic pop
# 987 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
# 1023 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
  template<typename _Predicate>
    class unary_negate
    : public unary_function<typename _Predicate::argument_type, bool>
    {
    protected:
      _Predicate _M_pred;

    public:

      explicit
      unary_negate(const _Predicate& __x) : _M_pred(__x) { }


      bool
      operator()(const typename _Predicate::argument_type& __x) const
      { return !_M_pred(__x); }
    };


  template<typename _Predicate>


    inline unary_negate<_Predicate>
    not1(const _Predicate& __pred)
    { return unary_negate<_Predicate>(__pred); }


  template<typename _Predicate>
    class binary_negate
    : public binary_function<typename _Predicate::first_argument_type,
        typename _Predicate::second_argument_type, bool>
    {
    protected:
      _Predicate _M_pred;

    public:

      explicit
      binary_negate(const _Predicate& __x) : _M_pred(__x) { }


      bool
      operator()(const typename _Predicate::first_argument_type& __x,
   const typename _Predicate::second_argument_type& __y) const
      { return !_M_pred(__x, __y); }
    };


  template<typename _Predicate>


    inline binary_negate<_Predicate>
    not2(const _Predicate& __pred)
    { return binary_negate<_Predicate>(__pred); }
# 1104 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
  template<typename _Arg, typename _Result>
    class pointer_to_unary_function : public unary_function<_Arg, _Result>
    {
    protected:
      _Result (*_M_ptr)(_Arg);

    public:
      pointer_to_unary_function() { }

      explicit
      pointer_to_unary_function(_Result (*__x)(_Arg))
      : _M_ptr(__x) { }

      _Result
      operator()(_Arg __x) const
      { return _M_ptr(__x); }
    } __attribute__ ((__deprecated__));


  template<typename _Arg, typename _Result>
    __attribute__ ((__deprecated__ ("use '" "std::function" "' instead")))
    inline pointer_to_unary_function<_Arg, _Result>
    ptr_fun(_Result (*__x)(_Arg))
    { return pointer_to_unary_function<_Arg, _Result>(__x); }


  template<typename _Arg1, typename _Arg2, typename _Result>
    class pointer_to_binary_function
    : public binary_function<_Arg1, _Arg2, _Result>
    {
    protected:
      _Result (*_M_ptr)(_Arg1, _Arg2);

    public:
      pointer_to_binary_function() { }

      explicit
      pointer_to_binary_function(_Result (*__x)(_Arg1, _Arg2))
      : _M_ptr(__x) { }

      _Result
      operator()(_Arg1 __x, _Arg2 __y) const
      { return _M_ptr(__x, __y); }
    } __attribute__ ((__deprecated__));


  template<typename _Arg1, typename _Arg2, typename _Result>
    __attribute__ ((__deprecated__ ("use '" "std::function" "' instead")))
    inline pointer_to_binary_function<_Arg1, _Arg2, _Result>
    ptr_fun(_Result (*__x)(_Arg1, _Arg2))
    { return pointer_to_binary_function<_Arg1, _Arg2, _Result>(__x); }


  template<typename _Tp>
    struct _Identity
    : public unary_function<_Tp, _Tp>
    {
      _Tp&
      operator()(_Tp& __x) const
      { return __x; }

      const _Tp&
      operator()(const _Tp& __x) const
      { return __x; }
    };


  template<typename _Tp> struct _Identity<const _Tp> : _Identity<_Tp> { };

  template<typename _Pair>
    struct _Select1st
    : public unary_function<_Pair, typename _Pair::first_type>
    {
      typename _Pair::first_type&
      operator()(_Pair& __x) const
      { return __x.first; }

      const typename _Pair::first_type&
      operator()(const _Pair& __x) const
      { return __x.first; }


      template<typename _Pair2>
        typename _Pair2::first_type&
        operator()(_Pair2& __x) const
        { return __x.first; }

      template<typename _Pair2>
        const typename _Pair2::first_type&
        operator()(const _Pair2& __x) const
        { return __x.first; }

    };

  template<typename _Pair>
    struct _Select2nd
    : public unary_function<_Pair, typename _Pair::second_type>
    {
      typename _Pair::second_type&
      operator()(_Pair& __x) const
      { return __x.second; }

      const typename _Pair::second_type&
      operator()(const _Pair& __x) const
      { return __x.second; }
    };
# 1231 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
  template<typename _Ret, typename _Tp>
    class mem_fun_t : public unary_function<_Tp*, _Ret>
    {
    public:
      explicit
      mem_fun_t(_Ret (_Tp::*__pf)())
      : _M_f(__pf) { }

      _Ret
      operator()(_Tp* __p) const
      { return (__p->*_M_f)(); }

    private:
      _Ret (_Tp::*_M_f)();
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp>
    class const_mem_fun_t : public unary_function<const _Tp*, _Ret>
    {
    public:
      explicit
      const_mem_fun_t(_Ret (_Tp::*__pf)() const)
      : _M_f(__pf) { }

      _Ret
      operator()(const _Tp* __p) const
      { return (__p->*_M_f)(); }

    private:
      _Ret (_Tp::*_M_f)() const;
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp>
    class mem_fun_ref_t : public unary_function<_Tp, _Ret>
    {
    public:
      explicit
      mem_fun_ref_t(_Ret (_Tp::*__pf)())
      : _M_f(__pf) { }

      _Ret
      operator()(_Tp& __r) const
      { return (__r.*_M_f)(); }

    private:
      _Ret (_Tp::*_M_f)();
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp>
    class const_mem_fun_ref_t : public unary_function<_Tp, _Ret>
    {
    public:
      explicit
      const_mem_fun_ref_t(_Ret (_Tp::*__pf)() const)
      : _M_f(__pf) { }

      _Ret
      operator()(const _Tp& __r) const
      { return (__r.*_M_f)(); }

    private:
      _Ret (_Tp::*_M_f)() const;
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp, typename _Arg>
    class mem_fun1_t : public binary_function<_Tp*, _Arg, _Ret>
    {
    public:
      explicit
      mem_fun1_t(_Ret (_Tp::*__pf)(_Arg))
      : _M_f(__pf) { }

      _Ret
      operator()(_Tp* __p, _Arg __x) const
      { return (__p->*_M_f)(__x); }

    private:
      _Ret (_Tp::*_M_f)(_Arg);
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp, typename _Arg>
    class const_mem_fun1_t : public binary_function<const _Tp*, _Arg, _Ret>
    {
    public:
      explicit
      const_mem_fun1_t(_Ret (_Tp::*__pf)(_Arg) const)
      : _M_f(__pf) { }

      _Ret
      operator()(const _Tp* __p, _Arg __x) const
      { return (__p->*_M_f)(__x); }

    private:
      _Ret (_Tp::*_M_f)(_Arg) const;
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp, typename _Arg>
    class mem_fun1_ref_t : public binary_function<_Tp, _Arg, _Ret>
    {
    public:
      explicit
      mem_fun1_ref_t(_Ret (_Tp::*__pf)(_Arg))
      : _M_f(__pf) { }

      _Ret
      operator()(_Tp& __r, _Arg __x) const
      { return (__r.*_M_f)(__x); }

    private:
      _Ret (_Tp::*_M_f)(_Arg);
    } __attribute__ ((__deprecated__));


  template<typename _Ret, typename _Tp, typename _Arg>
    class const_mem_fun1_ref_t : public binary_function<_Tp, _Arg, _Ret>
    {
    public:
      explicit
      const_mem_fun1_ref_t(_Ret (_Tp::*__pf)(_Arg) const)
      : _M_f(__pf) { }

      _Ret
      operator()(const _Tp& __r, _Arg __x) const
      { return (__r.*_M_f)(__x); }

    private:
      _Ret (_Tp::*_M_f)(_Arg) const;
    } __attribute__ ((__deprecated__));



  template<typename _Ret, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline mem_fun_t<_Ret, _Tp>
    mem_fun(_Ret (_Tp::*__f)())
    { return mem_fun_t<_Ret, _Tp>(__f); }

  template<typename _Ret, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline const_mem_fun_t<_Ret, _Tp>
    mem_fun(_Ret (_Tp::*__f)() const)
    { return const_mem_fun_t<_Ret, _Tp>(__f); }

  template<typename _Ret, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline mem_fun_ref_t<_Ret, _Tp>
    mem_fun_ref(_Ret (_Tp::*__f)())
    { return mem_fun_ref_t<_Ret, _Tp>(__f); }

  template<typename _Ret, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline const_mem_fun_ref_t<_Ret, _Tp>
    mem_fun_ref(_Ret (_Tp::*__f)() const)
    { return const_mem_fun_ref_t<_Ret, _Tp>(__f); }

  template<typename _Ret, typename _Tp, typename _Arg>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline mem_fun1_t<_Ret, _Tp, _Arg>
    mem_fun(_Ret (_Tp::*__f)(_Arg))
    { return mem_fun1_t<_Ret, _Tp, _Arg>(__f); }

  template<typename _Ret, typename _Tp, typename _Arg>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline const_mem_fun1_t<_Ret, _Tp, _Arg>
    mem_fun(_Ret (_Tp::*__f)(_Arg) const)
    { return const_mem_fun1_t<_Ret, _Tp, _Arg>(__f); }

  template<typename _Ret, typename _Tp, typename _Arg>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline mem_fun1_ref_t<_Ret, _Tp, _Arg>
    mem_fun_ref(_Ret (_Tp::*__f)(_Arg))
    { return mem_fun1_ref_t<_Ret, _Tp, _Arg>(__f); }

  template<typename _Ret, typename _Tp, typename _Arg>
    __attribute__ ((__deprecated__ ("use '" "std::mem_fn" "' instead")))
    inline const_mem_fun1_ref_t<_Ret, _Tp, _Arg>
    mem_fun_ref(_Ret (_Tp::*__f)(_Arg) const)
    { return const_mem_fun1_ref_t<_Ret, _Tp, _Arg>(__f); }
#pragma GCC diagnostic pop
# 1435 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 3
}


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/backward/binders.h" 1 3
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/backward/binders.h" 3
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"

namespace std __attribute__ ((__visibility__ ("default")))
{
# 107 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/backward/binders.h" 3
  template<typename _Operation>
    class binder1st
    : public unary_function<typename _Operation::second_argument_type,
       typename _Operation::result_type>
    {
    protected:
      _Operation op;
      typename _Operation::first_argument_type value;

    public:
      binder1st(const _Operation& __x,
  const typename _Operation::first_argument_type& __y)
      : op(__x), value(__y) { }

      typename _Operation::result_type
      operator()(const typename _Operation::second_argument_type& __x) const
      { return op(value, __x); }



      typename _Operation::result_type
      operator()(typename _Operation::second_argument_type& __x) const
      { return op(value, __x); }
    } __attribute__ ((__deprecated__ ("use '" "std::bind" "' instead")));


  template<typename _Operation, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::bind" "' instead")))
    inline binder1st<_Operation>
    bind1st(const _Operation& __fn, const _Tp& __x)
    {
      typedef typename _Operation::first_argument_type _Arg1_type;
      return binder1st<_Operation>(__fn, _Arg1_type(__x));
    }


  template<typename _Operation>
    class binder2nd
    : public unary_function<typename _Operation::first_argument_type,
       typename _Operation::result_type>
    {
    protected:
      _Operation op;
      typename _Operation::second_argument_type value;

    public:
      binder2nd(const _Operation& __x,
  const typename _Operation::second_argument_type& __y)
      : op(__x), value(__y) { }

      typename _Operation::result_type
      operator()(const typename _Operation::first_argument_type& __x) const
      { return op(__x, value); }



      typename _Operation::result_type
      operator()(typename _Operation::first_argument_type& __x) const
      { return op(__x, value); }
    } __attribute__ ((__deprecated__ ("use '" "std::bind" "' instead")));


  template<typename _Operation, typename _Tp>
    __attribute__ ((__deprecated__ ("use '" "std::bind" "' instead")))
    inline binder2nd<_Operation>
    bind2nd(const _Operation& __fn, const _Tp& __x)
    {
      typedef typename _Operation::second_argument_type _Arg2_type;
      return binder2nd<_Operation>(__fn, _Arg2_type(__x));
    }



}

#pragma GCC diagnostic pop
# 1439 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_function.h" 2 3
# 49 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 3




# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/invoke.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/invoke.h" 3








namespace std __attribute__ ((__visibility__ ("default")))
{
# 53 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/invoke.h" 3
  template<typename _Tp, typename _Up = typename __inv_unwrap<_Tp>::type>
    constexpr _Up&&
    __invfwd(typename remove_reference<_Tp>::type& __t) noexcept
    { return static_cast<_Up&&>(__t); }

  template<typename _Res, typename _Fn, typename... _Args>
    constexpr _Res
    __invoke_impl(__invoke_other, _Fn&& __f, _Args&&... __args)
    { return std::forward<_Fn>(__f)(std::forward<_Args>(__args)...); }

  template<typename _Res, typename _MemFun, typename _Tp, typename... _Args>
    constexpr _Res
    __invoke_impl(__invoke_memfun_ref, _MemFun&& __f, _Tp&& __t,
    _Args&&... __args)
    { return (__invfwd<_Tp>(__t).*__f)(std::forward<_Args>(__args)...); }

  template<typename _Res, typename _MemFun, typename _Tp, typename... _Args>
    constexpr _Res
    __invoke_impl(__invoke_memfun_deref, _MemFun&& __f, _Tp&& __t,
    _Args&&... __args)
    {
      return ((*std::forward<_Tp>(__t)).*__f)(std::forward<_Args>(__args)...);
    }

  template<typename _Res, typename _MemPtr, typename _Tp>
    constexpr _Res
    __invoke_impl(__invoke_memobj_ref, _MemPtr&& __f, _Tp&& __t)
    { return __invfwd<_Tp>(__t).*__f; }

  template<typename _Res, typename _MemPtr, typename _Tp>
    constexpr _Res
    __invoke_impl(__invoke_memobj_deref, _MemPtr&& __f, _Tp&& __t)
    { return (*std::forward<_Tp>(__t)).*__f; }


  template<typename _Callable, typename... _Args>
    constexpr typename __invoke_result<_Callable, _Args...>::type
    __invoke(_Callable&& __fn, _Args&&... __args)
    noexcept(__is_nothrow_invocable<_Callable, _Args...>::value)
    {
      using __result = __invoke_result<_Callable, _Args...>;
      using __type = typename __result::type;
      using __tag = typename __result::__invoke_type;
      return std::__invoke_impl<__type>(__tag{}, std::forward<_Callable>(__fn),
     std::forward<_Args>(__args)...);
    }
# 119 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/invoke.h" 3
  template<typename _Res, typename _Callable, typename... _Args>
    using __can_invoke_as_void = __enable_if_t<
      __and_<is_void<_Res>, __is_invocable<_Callable, _Args...>>::value,
      _Res
    >;

  template<typename _Res, typename _Callable, typename... _Args>
    using __can_invoke_as_nonvoid = __enable_if_t<
      __and_<__not_<is_void<_Res>>,
      is_convertible<typename __invoke_result<_Callable, _Args...>::type,
       _Res>
      >::value,
      _Res
    >;


  template<typename _Res, typename _Callable, typename... _Args>
    constexpr __can_invoke_as_nonvoid<_Res, _Callable, _Args...>
    __invoke_r(_Callable&& __fn, _Args&&... __args)
    {
      using __result = __invoke_result<_Callable, _Args...>;
      using __type = typename __result::type;
      using __tag = typename __result::__invoke_type;
      return std::__invoke_impl<__type>(__tag{}, std::forward<_Callable>(__fn),
     std::forward<_Args>(__args)...);
    }


  template<typename _Res, typename _Callable, typename... _Args>
                         __can_invoke_as_void<_Res, _Callable, _Args...>
    __invoke_r(_Callable&& __fn, _Args&&... __args)
    {
      using __result = __invoke_result<_Callable, _Args...>;
      using __type = typename __result::type;
      using __tag = typename __result::__invoke_type;
      std::__invoke_impl<__type>(__tag{}, std::forward<_Callable>(__fn),
     std::forward<_Args>(__args)...);
    }



}
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 2 3


namespace std __attribute__ ((__visibility__ ("default")))
{
# 52 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 3
  template<typename _Res, typename... _ArgTypes>
    struct _Maybe_unary_or_binary_function { };


#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _Res, typename _T1>
    struct _Maybe_unary_or_binary_function<_Res, _T1>
    : std::unary_function<_T1, _Res> { };


  template<typename _Res, typename _T1, typename _T2>
    struct _Maybe_unary_or_binary_function<_Res, _T1, _T2>
    : std::binary_function<_T1, _T2, _Res> { };

#pragma GCC diagnostic pop

  template<typename _Signature>
    struct _Mem_fn_traits;

  template<typename _Res, typename _Class, typename... _ArgTypes>
    struct _Mem_fn_traits_base
    {
      using __result_type = _Res;
      using __maybe_type
 = _Maybe_unary_or_binary_function<_Res, _Class*, _ArgTypes...>;
      using __arity = integral_constant<size_t, sizeof...(_ArgTypes)>;
    };
# 103 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 3
template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) > : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) > : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const > : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const > : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) volatile > : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) volatile > : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const volatile > : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const volatile > : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = true_type; };
template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) &> : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) &> : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const &> : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const &> : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) volatile &> : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) volatile &> : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const volatile &> : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const volatile &> : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = true_type; };
template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) &&> : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) &&> : _Mem_fn_traits_base<_Res, _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const &&> : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const &&> : _Mem_fn_traits_base<_Res, const _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) volatile &&> : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) volatile &&> : _Mem_fn_traits_base<_Res, volatile _Class, _ArgTypes...> { using __vararg = true_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes...) const volatile &&> : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = false_type; }; template<typename _Res, typename _Class, typename... _ArgTypes> struct _Mem_fn_traits<_Res (_Class::*)(_ArgTypes... ...) const volatile &&> : _Mem_fn_traits_base<_Res, const volatile _Class, _ArgTypes...> { using __vararg = true_type; };
# 117 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 3
  template<typename _Functor, typename = __void_t<>>
    struct _Maybe_get_result_type
    { };

  template<typename _Functor>
    struct _Maybe_get_result_type<_Functor,
      __void_t<typename _Functor::result_type>>
    { typedef typename _Functor::result_type result_type; };





  template<typename _Functor>
    struct _Weak_result_type_impl
    : _Maybe_get_result_type<_Functor>
    { };


  template<typename _Res, typename... _ArgTypes >
    struct _Weak_result_type_impl<_Res(_ArgTypes...) >
    { typedef _Res result_type; };


  template<typename _Res, typename... _ArgTypes >
    struct _Weak_result_type_impl<_Res(_ArgTypes......) >
    { typedef _Res result_type; };


  template<typename _Res, typename... _ArgTypes >
    struct _Weak_result_type_impl<_Res(*)(_ArgTypes...) >
    { typedef _Res result_type; };


  template<typename _Res, typename... _ArgTypes >
    struct
    _Weak_result_type_impl<_Res(*)(_ArgTypes......) >
    { typedef _Res result_type; };


  template<typename _Functor,
    bool = is_member_function_pointer<_Functor>::value>
    struct _Weak_result_type_memfun
    : _Weak_result_type_impl<_Functor>
    { };


  template<typename _MemFunPtr>
    struct _Weak_result_type_memfun<_MemFunPtr, true>
    {
      using result_type = typename _Mem_fn_traits<_MemFunPtr>::__result_type;
    };


  template<typename _Func, typename _Class>
    struct _Weak_result_type_memfun<_Func _Class::*, false>
    { };





  template<typename _Functor>
    struct _Weak_result_type
    : _Weak_result_type_memfun<typename remove_cv<_Functor>::type>
    { };



  template<typename _Tp, typename = __void_t<>>
    struct _Refwrap_base_arg1
    { };


  template<typename _Tp>
    struct _Refwrap_base_arg1<_Tp,
         __void_t<typename _Tp::argument_type>>
    {
      typedef typename _Tp::argument_type argument_type;
    };


  template<typename _Tp, typename = __void_t<>>
    struct _Refwrap_base_arg2
    { };


  template<typename _Tp>
    struct _Refwrap_base_arg2<_Tp,
         __void_t<typename _Tp::first_argument_type,
           typename _Tp::second_argument_type>>
    {
      typedef typename _Tp::first_argument_type first_argument_type;
      typedef typename _Tp::second_argument_type second_argument_type;
    };







  template<typename _Tp>
    struct _Reference_wrapper_base
    : _Weak_result_type<_Tp>, _Refwrap_base_arg1<_Tp>, _Refwrap_base_arg2<_Tp>
    { };


#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _Res, typename _T1 >
    struct _Reference_wrapper_base<_Res(_T1) >
    : unary_function<_T1, _Res>
    { };

  template<typename _Res, typename _T1>
    struct _Reference_wrapper_base<_Res(_T1) const>
    : unary_function<_T1, _Res>
    { };

  template<typename _Res, typename _T1>
    struct _Reference_wrapper_base<_Res(_T1) volatile>
    : unary_function<_T1, _Res>
    { };

  template<typename _Res, typename _T1>
    struct _Reference_wrapper_base<_Res(_T1) const volatile>
    : unary_function<_T1, _Res>
    { };


  template<typename _Res, typename _T1, typename _T2 >
    struct _Reference_wrapper_base<_Res(_T1, _T2) >
    : binary_function<_T1, _T2, _Res>
    { };

  template<typename _Res, typename _T1, typename _T2>
    struct _Reference_wrapper_base<_Res(_T1, _T2) const>
    : binary_function<_T1, _T2, _Res>
    { };

  template<typename _Res, typename _T1, typename _T2>
    struct _Reference_wrapper_base<_Res(_T1, _T2) volatile>
    : binary_function<_T1, _T2, _Res>
    { };

  template<typename _Res, typename _T1, typename _T2>
    struct _Reference_wrapper_base<_Res(_T1, _T2) const volatile>
    : binary_function<_T1, _T2, _Res>
    { };


  template<typename _Res, typename _T1 >
    struct _Reference_wrapper_base<_Res(*)(_T1) >
    : unary_function<_T1, _Res>
    { };


  template<typename _Res, typename _T1, typename _T2 >
    struct _Reference_wrapper_base<_Res(*)(_T1, _T2) >
    : binary_function<_T1, _T2, _Res>
    { };

  template<typename _Tp, bool = is_member_function_pointer<_Tp>::value>
    struct _Reference_wrapper_base_memfun
    : _Reference_wrapper_base<_Tp>
    { };

  template<typename _MemFunPtr>
    struct _Reference_wrapper_base_memfun<_MemFunPtr, true>
    : _Mem_fn_traits<_MemFunPtr>::__maybe_type
    {
      using result_type = typename _Mem_fn_traits<_MemFunPtr>::__result_type;
    };
#pragma GCC diagnostic pop








  template<typename _Tp>
    class reference_wrapper



    : public _Reference_wrapper_base_memfun<typename remove_cv<_Tp>::type>

    {
      _Tp* _M_data;


      static _Tp* _S_fun(_Tp& __r) noexcept { return std::__addressof(__r); }

      static void _S_fun(_Tp&&) = delete;

      template<typename _Up, typename _Up2 = __remove_cvref_t<_Up>>
 using __not_same
   = typename enable_if<!is_same<reference_wrapper, _Up2>::value>::type;

    public:
      typedef _Tp type;




      template<typename _Up, typename = __not_same<_Up>, typename
  = decltype(reference_wrapper::_S_fun(std::declval<_Up>()))>

 reference_wrapper(_Up&& __uref)
 noexcept(noexcept(reference_wrapper::_S_fun(std::declval<_Up>())))
 : _M_data(reference_wrapper::_S_fun(std::forward<_Up>(__uref)))
 { }

      reference_wrapper(const reference_wrapper&) = default;

      reference_wrapper&
      operator=(const reference_wrapper&) = default;


      operator _Tp&() const noexcept
      { return this->get(); }


      _Tp&
      get() const noexcept
      { return *_M_data; }

      template<typename... _Args>

 typename result_of<_Tp&(_Args&&...)>::type
 operator()(_Args&&... __args) const
 {




   return std::__invoke(get(), std::forward<_Args>(__args)...);
 }
    };
# 370 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/refwrap.h" 3
  template<typename _Tp>

    inline reference_wrapper<_Tp>
    ref(_Tp& __t) noexcept
    { return reference_wrapper<_Tp>(__t); }


  template<typename _Tp>

    inline reference_wrapper<const _Tp>
    cref(const _Tp& __t) noexcept
    { return reference_wrapper<const _Tp>(__t); }

  template<typename _Tp>
    void ref(const _Tp&&) = delete;

  template<typename _Tp>
    void cref(const _Tp&&) = delete;


  template<typename _Tp>

    inline reference_wrapper<_Tp>
    ref(reference_wrapper<_Tp> __t) noexcept
    { return __t; }


  template<typename _Tp>

    inline reference_wrapper<const _Tp>
    cref(reference_wrapper<_Tp> __t) noexcept
    { return { __t.get() }; }




}
# 52 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/range_access.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/range_access.h" 3






namespace std __attribute__ ((__visibility__ ("default")))
{







  template<typename _Container>
    [[__nodiscard__]]
    inline auto
    begin(_Container& __cont) -> decltype(__cont.begin())
    { return __cont.begin(); }






  template<typename _Container>
    [[__nodiscard__]]
    inline auto
    begin(const _Container& __cont) -> decltype(__cont.begin())
    { return __cont.begin(); }






  template<typename _Container>
    [[__nodiscard__]]
    inline auto
    end(_Container& __cont) -> decltype(__cont.end())
    { return __cont.end(); }






  template<typename _Container>
    [[__nodiscard__]]
    inline auto
    end(const _Container& __cont) -> decltype(__cont.end())
    { return __cont.end(); }





  template<typename _Tp, size_t _Nm>
    [[__nodiscard__]]
    inline _Tp*
    begin(_Tp (&__arr)[_Nm]) noexcept
    { return __arr; }






  template<typename _Tp, size_t _Nm>
    [[__nodiscard__]]
    inline _Tp*
    end(_Tp (&__arr)[_Nm]) noexcept
    { return __arr + _Nm; }
# 368 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/range_access.h" 3
}
# 53 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/alloc_traits.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/alloc_traits.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 1 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{






  struct __allocator_traits_base
  {
    template<typename _Tp, typename _Up, typename = void>
      struct __rebind : __replace_first_arg<_Tp, _Up> { };

    template<typename _Tp, typename _Up>
      struct __rebind<_Tp, _Up,
        __void_t<typename _Tp::template rebind<_Up>::other>>
      { using type = typename _Tp::template rebind<_Up>::other; };

  protected:
    template<typename _Tp>
      using __pointer = typename _Tp::pointer;
    template<typename _Tp>
      using __c_pointer = typename _Tp::const_pointer;
    template<typename _Tp>
      using __v_pointer = typename _Tp::void_pointer;
    template<typename _Tp>
      using __cv_pointer = typename _Tp::const_void_pointer;
    template<typename _Tp>
      using __pocca = typename _Tp::propagate_on_container_copy_assignment;
    template<typename _Tp>
      using __pocma = typename _Tp::propagate_on_container_move_assignment;
    template<typename _Tp>
      using __pocs = typename _Tp::propagate_on_container_swap;
    template<typename _Tp>
      using __equal = typename _Tp::is_always_equal;
  };

  template<typename _Alloc, typename _Up>
    using __alloc_rebind
      = typename __allocator_traits_base::template __rebind<_Alloc, _Up>::type;
# 89 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
  template<typename _Alloc>
    struct allocator_traits : __allocator_traits_base
    {

      typedef _Alloc allocator_type;

      typedef typename _Alloc::value_type value_type;






      using pointer = __detected_or_t<value_type*, __pointer, _Alloc>;

    private:

      template<template<typename> class _Func, typename _Tp, typename = void>
 struct _Ptr
 {
   using type = typename pointer_traits<pointer>::template rebind<_Tp>;
 };

      template<template<typename> class _Func, typename _Tp>
 struct _Ptr<_Func, _Tp, __void_t<_Func<_Alloc>>>
 {
   using type = _Func<_Alloc>;
 };


      template<typename _A2, typename _PtrT, typename = void>
 struct _Diff
 { using type = typename pointer_traits<_PtrT>::difference_type; };

      template<typename _A2, typename _PtrT>
 struct _Diff<_A2, _PtrT, __void_t<typename _A2::difference_type>>
 { using type = typename _A2::difference_type; };


      template<typename _A2, typename _DiffT, typename = void>
 struct _Size : make_unsigned<_DiffT> { };

      template<typename _A2, typename _DiffT>
 struct _Size<_A2, _DiffT, __void_t<typename _A2::size_type>>
 { using type = typename _A2::size_type; };

    public:






      using const_pointer = typename _Ptr<__c_pointer, const value_type>::type;







      using void_pointer = typename _Ptr<__v_pointer, void>::type;







      using const_void_pointer = typename _Ptr<__cv_pointer, const void>::type;







      using difference_type = typename _Diff<_Alloc, pointer>::type;







      using size_type = typename _Size<_Alloc, difference_type>::type;







      using propagate_on_container_copy_assignment
 = __detected_or_t<false_type, __pocca, _Alloc>;







      using propagate_on_container_move_assignment
 = __detected_or_t<false_type, __pocma, _Alloc>;







      using propagate_on_container_swap
 = __detected_or_t<false_type, __pocs, _Alloc>;







      using is_always_equal
 = __detected_or_t<typename is_empty<_Alloc>::type, __equal, _Alloc>;

      template<typename _Tp>
 using rebind_alloc = __alloc_rebind<_Alloc, _Tp>;
      template<typename _Tp>
 using rebind_traits = allocator_traits<rebind_alloc<_Tp>>;

    private:
      template<typename _Alloc2>
 static constexpr auto
 _S_allocate(_Alloc2& __a, size_type __n, const_void_pointer __hint, int)
 -> decltype(__a.allocate(__n, __hint))
 { return __a.allocate(__n, __hint); }

      template<typename _Alloc2>
 static constexpr pointer
 _S_allocate(_Alloc2& __a, size_type __n, const_void_pointer, ...)
 { return __a.allocate(__n); }

      template<typename _Tp, typename... _Args>
 struct __construct_helper
 {
   template<typename _Alloc2,
     typename = decltype(std::declval<_Alloc2*>()->construct(
    std::declval<_Tp*>(), std::declval<_Args>()...))>
     static true_type __test(int);

   template<typename>
     static false_type __test(...);

   using type = decltype(__test<_Alloc>(0));
 };

      template<typename _Tp, typename... _Args>
 using __has_construct
   = typename __construct_helper<_Tp, _Args...>::type;

      template<typename _Tp, typename... _Args>
 static _Require<__has_construct<_Tp, _Args...>>
 _S_construct(_Alloc& __a, _Tp* __p, _Args&&... __args)
 noexcept(noexcept(__a.construct(__p, std::forward<_Args>(__args)...)))
 { __a.construct(__p, std::forward<_Args>(__args)...); }

      template<typename _Tp, typename... _Args>
 static
 _Require<__and_<__not_<__has_construct<_Tp, _Args...>>,
          is_constructible<_Tp, _Args...>>>
 _S_construct(_Alloc&, _Tp* __p, _Args&&... __args)
 noexcept(std::is_nothrow_constructible<_Tp, _Args...>::value)
 {

   ::new((void*)__p) _Tp(std::forward<_Args>(__args)...);



 }

      template<typename _Alloc2, typename _Tp>
 static auto
 _S_destroy(_Alloc2& __a, _Tp* __p, int)
 noexcept(noexcept(__a.destroy(__p)))
 -> decltype(__a.destroy(__p))
 { __a.destroy(__p); }

      template<typename _Alloc2, typename _Tp>
 static void
 _S_destroy(_Alloc2&, _Tp* __p, ...)
 noexcept(std::is_nothrow_destructible<_Tp>::value)
 { std::_Destroy(__p); }

      template<typename _Alloc2>
 static constexpr auto
 _S_max_size(_Alloc2& __a, int)
 -> decltype(__a.max_size())
 { return __a.max_size(); }

      template<typename _Alloc2>
 static constexpr size_type
 _S_max_size(_Alloc2&, ...)
 {


   return __gnu_cxx::__numeric_traits<size_type>::__max
     / sizeof(value_type);
 }

      template<typename _Alloc2>
 static constexpr auto
 _S_select(_Alloc2& __a, int)
 -> decltype(__a.select_on_container_copy_construction())
 { return __a.select_on_container_copy_construction(); }

      template<typename _Alloc2>
 static constexpr _Alloc2
 _S_select(_Alloc2& __a, ...)
 { return __a; }

    public:
# 316 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
                         static pointer
      allocate(_Alloc& __a, size_type __n)
      { return __a.allocate(__n); }
# 331 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
                         static pointer
      allocate(_Alloc& __a, size_type __n, const_void_pointer __hint)
      { return _S_allocate(__a, __n, __hint, 0); }
# 343 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      static void
      deallocate(_Alloc& __a, pointer __p, size_type __n)
      { __a.deallocate(__p, __n); }
# 358 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Tp, typename... _Args>
 static auto
 construct(_Alloc& __a, _Tp* __p, _Args&&... __args)
 noexcept(noexcept(_S_construct(__a, __p,
           std::forward<_Args>(__args)...)))
 -> decltype(_S_construct(__a, __p, std::forward<_Args>(__args)...))
 { _S_construct(__a, __p, std::forward<_Args>(__args)...); }
# 374 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Tp>
 static void
 destroy(_Alloc& __a, _Tp* __p)
 noexcept(noexcept(_S_destroy(__a, __p, 0)))
 { _S_destroy(__a, __p, 0); }
# 388 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      static size_type
      max_size(const _Alloc& __a) noexcept
      { return _S_max_size(__a, 0); }
# 400 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      static _Alloc
      select_on_container_copy_construction(const _Alloc& __rhs)
      { return _S_select(__rhs, 0); }
    };






  template<typename _Tp>
    struct allocator_traits<allocator<_Tp>>
    {

      using allocator_type = allocator<_Tp>;


      using value_type = _Tp;


      using pointer = _Tp*;


      using const_pointer = const _Tp*;


      using void_pointer = void*;


      using const_void_pointer = const void*;


      using difference_type = std::ptrdiff_t;


      using size_type = std::size_t;


      using propagate_on_container_copy_assignment = false_type;


      using propagate_on_container_move_assignment = true_type;


      using propagate_on_container_swap = false_type;


      using is_always_equal = true_type;

      template<typename _Up>
 using rebind_alloc = allocator<_Up>;

      template<typename _Up>
 using rebind_traits = allocator_traits<allocator<_Up>>;
# 462 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
                         static pointer
      allocate(allocator_type& __a, size_type __n)
      { return __a.allocate(__n); }
# 476 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
                         static pointer
      allocate(allocator_type& __a, size_type __n, const_void_pointer __hint)
      {

 return __a.allocate(__n, __hint);



      }
# 494 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      static void
      deallocate(allocator_type& __a, pointer __p, size_type __n)
      { __a.deallocate(__p, __n); }
# 509 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Up, typename... _Args>
 static void
 construct(allocator_type& __a __attribute__((__unused__)), _Up* __p,
    _Args&&... __args)
 noexcept(std::is_nothrow_constructible<_Up, _Args...>::value)
 {

   __a.construct(__p, std::forward<_Args>(__args)...);



 }
# 529 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Up>
 static void
 destroy(allocator_type& __a __attribute__((__unused__)), _Up* __p)
 noexcept(is_nothrow_destructible<_Up>::value)
 {

   __a.destroy(__p);



 }






      static size_type
      max_size(const allocator_type& __a __attribute__((__unused__))) noexcept
      {

 return __a.max_size();



      }






      static allocator_type
      select_on_container_copy_construction(const allocator_type& __rhs)
      { return __rhs; }
    };


  template<>
    struct allocator_traits<allocator<void>>
    {

      using allocator_type = allocator<void>;


      using value_type = void;


      using pointer = void*;


      using const_pointer = const void*;


      using void_pointer = void*;


      using const_void_pointer = const void*;


      using difference_type = std::ptrdiff_t;


      using size_type = std::size_t;


      using propagate_on_container_copy_assignment = false_type;


      using propagate_on_container_move_assignment = true_type;


      using propagate_on_container_swap = false_type;


      using is_always_equal = true_type;

      template<typename _Up>
 using rebind_alloc = allocator<_Up>;

      template<typename _Up>
 using rebind_traits = allocator_traits<allocator<_Up>>;


      static void*
      allocate(allocator_type&, size_type, const void* = nullptr) = delete;


      static void
      deallocate(allocator_type&, void*, size_type) = delete;
# 631 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Up, typename... _Args>
 static void
 construct(allocator_type&, _Up* __p, _Args&&... __args)
 noexcept(std::is_nothrow_constructible<_Up, _Args...>::value)
 { std::_Construct(__p, std::forward<_Args>(__args)...); }
# 644 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
      template<typename _Up>
 static void
 destroy(allocator_type&, _Up* __p)
 noexcept(is_nothrow_destructible<_Up>::value)
 { std::_Destroy(__p); }


      static size_type
      max_size(const allocator_type&) = delete;






      static allocator_type
      select_on_container_copy_construction(const allocator_type& __rhs)
      { return __rhs; }
    };


  template<typename _Alloc>
    inline void
    __do_alloc_on_copy(_Alloc& __one, const _Alloc& __two, true_type)
    { __one = __two; }

  template<typename _Alloc>
    inline void
    __do_alloc_on_copy(_Alloc&, const _Alloc&, false_type)
    { }


  template<typename _Alloc>
                         inline void
    __alloc_on_copy(_Alloc& __one, const _Alloc& __two)
    {
      typedef allocator_traits<_Alloc> __traits;
      typedef typename __traits::propagate_on_container_copy_assignment __pocca;




      __do_alloc_on_copy(__one, __two, __pocca());

    }

  template<typename _Alloc>
    constexpr _Alloc
    __alloc_on_copy(const _Alloc& __a)
    {
      typedef allocator_traits<_Alloc> __traits;
      return __traits::select_on_container_copy_construction(__a);
    }


  template<typename _Alloc>
    inline void __do_alloc_on_move(_Alloc& __one, _Alloc& __two, true_type)
    { __one = std::move(__two); }

  template<typename _Alloc>
    inline void __do_alloc_on_move(_Alloc&, _Alloc&, false_type)
    { }


  template<typename _Alloc>
                         inline void
    __alloc_on_move(_Alloc& __one, _Alloc& __two)
    {
      typedef allocator_traits<_Alloc> __traits;
      typedef typename __traits::propagate_on_container_move_assignment __pocma;




      __do_alloc_on_move(__one, __two, __pocma());

    }


  template<typename _Alloc>
    inline void __do_alloc_on_swap(_Alloc& __one, _Alloc& __two, true_type)
    {
      using std::swap;
      swap(__one, __two);
    }

  template<typename _Alloc>
    inline void __do_alloc_on_swap(_Alloc&, _Alloc&, false_type)
    { }


  template<typename _Alloc>
                         inline void
    __alloc_on_swap(_Alloc& __one, _Alloc& __two)
    {
      typedef allocator_traits<_Alloc> __traits;
      typedef typename __traits::propagate_on_container_swap __pocs;







      __do_alloc_on_swap(__one, __two, __pocs());

    }

  template<typename _Alloc, typename _Tp,
    typename _ValueT = __remove_cvref_t<typename _Alloc::value_type>,
    typename = void>
    struct __is_alloc_insertable_impl
    : false_type
    { };

  template<typename _Alloc, typename _Tp, typename _ValueT>
    struct __is_alloc_insertable_impl<_Alloc, _Tp, _ValueT,
      __void_t<decltype(allocator_traits<_Alloc>::construct(
     std::declval<_Alloc&>(), std::declval<_ValueT*>(),
     std::declval<_Tp>()))>>
    : true_type
    { };




  template<typename _Alloc>
    struct __is_copy_insertable
    : __is_alloc_insertable_impl<_Alloc,
     typename _Alloc::value_type const&>::type
    { };


  template<typename _Tp>
    struct __is_copy_insertable<allocator<_Tp>>
    : is_copy_constructible<_Tp>
    { };




  template<typename _Alloc>
    struct __is_move_insertable
    : __is_alloc_insertable_impl<_Alloc, typename _Alloc::value_type>::type
    { };


  template<typename _Tp>
    struct __is_move_insertable<allocator<_Tp>>
    : is_move_constructible<_Tp>
    { };


  template<typename _Alloc, typename = void>
    struct __is_allocator : false_type { };

  template<typename _Alloc>
    struct __is_allocator<_Alloc,
      __void_t<typename _Alloc::value_type,
        decltype(std::declval<_Alloc&>().allocate(size_t{}))>>
    : true_type { };

  template<typename _Alloc>
    using _RequireAllocator
      = typename enable_if<__is_allocator<_Alloc>::value, _Alloc>::type;

  template<typename _Alloc>
    using _RequireNotAllocator
      = typename enable_if<!__is_allocator<_Alloc>::value, _Alloc>::type;
# 829 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/alloc_traits.h" 3
  template<typename _ForwardIterator, typename _Allocator>

    void
    _Destroy(_ForwardIterator __first, _ForwardIterator __last,
      _Allocator& __alloc)
    {
      for (; __first != __last; ++__first)



 allocator_traits<_Allocator>::destroy(__alloc,
           std::__addressof(*__first));

    }

  template<typename _ForwardIterator, typename _Tp>

    inline void
    _Destroy(_ForwardIterator __first, _ForwardIterator __last,
      allocator<_Tp>&)
    {
      _Destroy(__first, __last);
    }


}
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/alloc_traits.h" 2 3




namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{






template<typename _Alloc, typename = typename _Alloc::value_type>
  struct __alloc_traits

  : std::allocator_traits<_Alloc>

  {
    typedef _Alloc allocator_type;

    typedef std::allocator_traits<_Alloc> _Base_type;
    typedef typename _Base_type::value_type value_type;
    typedef typename _Base_type::pointer pointer;
    typedef typename _Base_type::const_pointer const_pointer;
    typedef typename _Base_type::size_type size_type;
    typedef typename _Base_type::difference_type difference_type;

    typedef value_type& reference;
    typedef const value_type& const_reference;
    using _Base_type::allocate;
    using _Base_type::deallocate;
    using _Base_type::construct;
    using _Base_type::destroy;
    using _Base_type::max_size;

  private:
    template<typename _Ptr>
      using __is_custom_pointer
 = std::__and_<std::is_same<pointer, _Ptr>,
        std::__not_<std::is_pointer<_Ptr>>>;

  public:

    template<typename _Ptr, typename... _Args>
      static
      std::__enable_if_t<__is_custom_pointer<_Ptr>::value>
      construct(_Alloc& __a, _Ptr __p, _Args&&... __args)
      noexcept(noexcept(_Base_type::construct(__a, std::__to_address(__p),
           std::forward<_Args>(__args)...)))
      {
 _Base_type::construct(__a, std::__to_address(__p),
         std::forward<_Args>(__args)...);
      }


    template<typename _Ptr>
      static
      std::__enable_if_t<__is_custom_pointer<_Ptr>::value>
      destroy(_Alloc& __a, _Ptr __p)
      noexcept(noexcept(_Base_type::destroy(__a, std::__to_address(__p))))
      { _Base_type::destroy(__a, std::__to_address(__p)); }

    static constexpr _Alloc _S_select_on_copy(const _Alloc& __a)
    { return _Base_type::select_on_container_copy_construction(__a); }

    static void _S_on_swap(_Alloc& __a, _Alloc& __b)
    { std::__alloc_on_swap(__a, __b); }

    static constexpr bool _S_propagate_on_copy_assign()
    { return _Base_type::propagate_on_container_copy_assignment::value; }

    static constexpr bool _S_propagate_on_move_assign()
    { return _Base_type::propagate_on_container_move_assignment::value; }

    static constexpr bool _S_propagate_on_swap()
    { return _Base_type::propagate_on_container_swap::value; }

    static constexpr bool _S_always_equal()
    { return _Base_type::is_always_equal::value; }

    static constexpr bool _S_nothrow_move()
    { return _S_propagate_on_move_assign() || _S_always_equal(); }

    template<typename _Tp>
      struct rebind
      { typedef typename _Base_type::template rebind_alloc<_Tp> other; };
# 166 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/alloc_traits.h" 3
  };


}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 2 3
# 53 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{

namespace __cxx11 {
# 84 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    class basic_string
    {
      typedef typename __gnu_cxx::__alloc_traits<_Alloc>::template
 rebind<_CharT>::other _Char_alloc_type;


      typedef __gnu_cxx::__alloc_traits<_Char_alloc_type> _Alloc_traits;
# 122 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
    public:
      typedef _Traits traits_type;
      typedef typename _Traits::char_type value_type;
      typedef _Char_alloc_type allocator_type;
      typedef typename _Alloc_traits::size_type size_type;
      typedef typename _Alloc_traits::difference_type difference_type;
      typedef typename _Alloc_traits::reference reference;
      typedef typename _Alloc_traits::const_reference const_reference;
      typedef typename _Alloc_traits::pointer pointer;
      typedef typename _Alloc_traits::const_pointer const_pointer;
      typedef __gnu_cxx::__normal_iterator<pointer, basic_string> iterator;
      typedef __gnu_cxx::__normal_iterator<const_pointer, basic_string>
       const_iterator;
      typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
      typedef std::reverse_iterator<iterator> reverse_iterator;


      static const size_type npos = static_cast<size_type>(-1);

    protected:




      typedef const_iterator __const_iterator;


    private:
# 192 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      struct _Alloc_hider : allocator_type
      {





 _Alloc_hider(pointer __dat, const _Alloc& __a)
 : allocator_type(__a), _M_p(__dat) { }


 _Alloc_hider(pointer __dat, _Alloc&& __a = _Alloc())
 : allocator_type(std::move(__a)), _M_p(__dat) { }


 pointer _M_p;
      };

      _Alloc_hider _M_dataplus;
      size_type _M_string_length;

      enum { _S_local_capacity = 15 / sizeof(_CharT) };

      union
      {
 _CharT _M_local_buf[_S_local_capacity + 1];
 size_type _M_allocated_capacity;
      };


      void
      _M_data(pointer __p)
      { _M_dataplus._M_p = __p; }


      void
      _M_length(size_type __length)
      { _M_string_length = __length; }


      pointer
      _M_data() const
      { return _M_dataplus._M_p; }


      pointer
      _M_local_data()
      {

 return std::pointer_traits<pointer>::pointer_to(*_M_local_buf);



      }


      const_pointer
      _M_local_data() const
      {

 return std::pointer_traits<const_pointer>::pointer_to(*_M_local_buf);



      }


      void
      _M_capacity(size_type __capacity)
      { _M_allocated_capacity = __capacity; }


      void
      _M_set_length(size_type __n)
      {
 _M_length(__n);
 traits_type::assign(_M_data()[__n], _CharT());
      }


      bool
      _M_is_local() const
      { return _M_data() == _M_local_data(); }



      pointer
      _M_create(size_type&, size_type);


      void
      _M_dispose()
      {
 if (!_M_is_local())
   _M_destroy(_M_allocated_capacity);
      }


      void
      _M_destroy(size_type __size) throw()
      { _Alloc_traits::deallocate(_M_get_allocator(), _M_data(), __size + 1); }
# 319 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<typename _InIterator>

        void
        _M_construct(_InIterator __beg, _InIterator __end,
       std::input_iterator_tag);



      template<typename _FwdIterator>

        void
        _M_construct(_FwdIterator __beg, _FwdIterator __end,
       std::forward_iterator_tag);


      void
      _M_construct(size_type __req, _CharT __c);


      allocator_type&
      _M_get_allocator()
      { return _M_dataplus; }


      const allocator_type&
      _M_get_allocator() const
      { return _M_dataplus; }


      __attribute__((__always_inline__))

      pointer
      _M_use_local_data() noexcept
      {





 return _M_local_data();
      }

    private:
# 378 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      _M_check(size_type __pos, const char* __s) const
      {
 if (__pos > this->size())
   __throw_out_of_range_fmt(("%s: __pos (which is %zu) > " "this->size() (which is %zu)"),

       __s, __pos, this->size());
 return __pos;
      }


      void
      _M_check_length(size_type __n1, size_type __n2, const char* __s) const
      {
 if (this->max_size() - (this->size() - __n1) < __n2)
   __throw_length_error((__s));
      }




      size_type
      _M_limit(size_type __pos, size_type __off) const noexcept
      {
 const bool __testoff = __off < this->size() - __pos;
 return __testoff ? __off : this->size() - __pos;
      }


      bool
      _M_disjunct(const _CharT* __s) const noexcept
      {
 return (less<const _CharT*>()(__s, _M_data())
  || less<const _CharT*>()(_M_data() + this->size(), __s));
      }




      static void
      _S_copy(_CharT* __d, const _CharT* __s, size_type __n)
      {
 if (__n == 1)
   traits_type::assign(*__d, *__s);
 else
   traits_type::copy(__d, __s, __n);
      }


      static void
      _S_move(_CharT* __d, const _CharT* __s, size_type __n)
      {
 if (__n == 1)
   traits_type::assign(*__d, *__s);
 else
   traits_type::move(__d, __s, __n);
      }


      static void
      _S_assign(_CharT* __d, size_type __n, _CharT __c)
      {
 if (__n == 1)
   traits_type::assign(*__d, __c);
 else
   traits_type::assign(__d, __n, __c);
      }



      template<class _Iterator>

        static void
        _S_copy_chars(_CharT* __p, _Iterator __k1, _Iterator __k2)
        {
   for (; __k1 != __k2; ++__k1, (void)++__p)
     traits_type::assign(*__p, *__k1);
 }


      static void
      _S_copy_chars(_CharT* __p, iterator __k1, iterator __k2) noexcept
      { _S_copy_chars(__p, __k1.base(), __k2.base()); }


      static void
      _S_copy_chars(_CharT* __p, const_iterator __k1, const_iterator __k2)
      noexcept
      { _S_copy_chars(__p, __k1.base(), __k2.base()); }


      static void
      _S_copy_chars(_CharT* __p, _CharT* __k1, _CharT* __k2) noexcept
      { _S_copy(__p, __k1, __k2 - __k1); }


      static void
      _S_copy_chars(_CharT* __p, const _CharT* __k1, const _CharT* __k2)
      noexcept
      { _S_copy(__p, __k1, __k2 - __k1); }


      static int
      _S_compare(size_type __n1, size_type __n2) noexcept
      {
 const difference_type __d = difference_type(__n1 - __n2);

 if (__d > __gnu_cxx::__numeric_traits<int>::__max)
   return __gnu_cxx::__numeric_traits<int>::__max;
 else if (__d < __gnu_cxx::__numeric_traits<int>::__min)
   return __gnu_cxx::__numeric_traits<int>::__min;
 else
   return int(__d);
      }


      void
      _M_assign(const basic_string&);


      void
      _M_mutate(size_type __pos, size_type __len1, const _CharT* __s,
  size_type __len2);


      void
      _M_erase(size_type __pos, size_type __n);

    public:
# 515 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string()
      noexcept(is_nothrow_default_constructible<_Alloc>::value)
      : _M_dataplus(_M_local_data())
      {
 _M_use_local_data();
 _M_set_length(0);
      }





      explicit
      basic_string(const _Alloc& __a) noexcept
      : _M_dataplus(_M_local_data(), __a)
      {
 _M_use_local_data();
 _M_set_length(0);
      }






      basic_string(const basic_string& __str)
      : _M_dataplus(_M_local_data(),
      _Alloc_traits::_S_select_on_copy(__str._M_get_allocator()))
      {
 _M_construct(__str._M_data(), __str._M_data() + __str.length(),
       std::forward_iterator_tag());
      }
# 557 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(const basic_string& __str, size_type __pos,
     const _Alloc& __a = _Alloc())
      : _M_dataplus(_M_local_data(), __a)
      {
 const _CharT* __start = __str._M_data()
   + __str._M_check(__pos, "basic_string::basic_string");
 _M_construct(__start, __start + __str._M_limit(__pos, npos),
       std::forward_iterator_tag());
      }
# 574 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(const basic_string& __str, size_type __pos,
     size_type __n)
      : _M_dataplus(_M_local_data())
      {
 const _CharT* __start = __str._M_data()
   + __str._M_check(__pos, "basic_string::basic_string");
 _M_construct(__start, __start + __str._M_limit(__pos, __n),
       std::forward_iterator_tag());
      }
# 592 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(const basic_string& __str, size_type __pos,
     size_type __n, const _Alloc& __a)
      : _M_dataplus(_M_local_data(), __a)
      {
 const _CharT* __start
   = __str._M_data() + __str._M_check(__pos, "string::string");
 _M_construct(__start, __start + __str._M_limit(__pos, __n),
       std::forward_iterator_tag());
      }
# 612 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(const _CharT* __s, size_type __n,
     const _Alloc& __a = _Alloc())
      : _M_dataplus(_M_local_data(), __a)
      {

 if (__s == 0 && __n > 0)
   std::__throw_logic_error(("basic_string: " "construction from null is not valid"));

 _M_construct(__s, __s + __n, std::forward_iterator_tag());
      }
# 634 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(const _CharT* __s, const _Alloc& __a = _Alloc())
      : _M_dataplus(_M_local_data(), __a)
      {

 if (__s == 0)
   std::__throw_logic_error(("basic_string: " "construction from null is not valid"));

 const _CharT* __end = __s + traits_type::length(__s);
 _M_construct(__s, __end, forward_iterator_tag());
      }
# 657 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(size_type __n, _CharT __c, const _Alloc& __a = _Alloc())
      : _M_dataplus(_M_local_data(), __a)
      { _M_construct(__n, __c); }
# 670 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string(basic_string&& __str) noexcept
      : _M_dataplus(_M_local_data(), std::move(__str._M_get_allocator()))
      {
 if (__str._M_is_local())
   {
     traits_type::copy(_M_local_buf, __str._M_local_buf,
         __str.length() + 1);
   }
 else
   {
     _M_data(__str._M_data());
     _M_capacity(__str._M_allocated_capacity);
   }




 _M_length(__str.length());
 __str._M_data(__str._M_local_data());
 __str._M_set_length(0);
      }







      basic_string(initializer_list<_CharT> __l, const _Alloc& __a = _Alloc())
      : _M_dataplus(_M_local_data(), __a)
      { _M_construct(__l.begin(), __l.end(), std::forward_iterator_tag()); }


      basic_string(const basic_string& __str, const _Alloc& __a)
      : _M_dataplus(_M_local_data(), __a)
      { _M_construct(__str.begin(), __str.end(), std::forward_iterator_tag()); }


      basic_string(basic_string&& __str, const _Alloc& __a)
      noexcept(_Alloc_traits::_S_always_equal())
      : _M_dataplus(_M_local_data(), __a)
      {
 if (__str._M_is_local())
   {
     traits_type::copy(_M_local_buf, __str._M_local_buf,
         __str.length() + 1);
     _M_length(__str.length());
     __str._M_set_length(0);
   }
 else if (_Alloc_traits::_S_always_equal()
     || __str.get_allocator() == __a)
   {
     _M_data(__str._M_data());
     _M_length(__str.length());
     _M_capacity(__str._M_allocated_capacity);
     __str._M_data(__str._M_local_buf);
     __str._M_set_length(0);
   }
 else
   _M_construct(__str.begin(), __str.end(), std::forward_iterator_tag());
      }
# 745 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>




        basic_string(_InputIterator __beg, _InputIterator __end,
       const _Alloc& __a = _Alloc())
 : _M_dataplus(_M_local_data(), __a)
 {

   _M_construct(__beg, __end, std::__iterator_category(__beg));




 }
# 794 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      ~basic_string()
      { _M_dispose(); }






      basic_string&
      operator=(const basic_string& __str)
      {
 return this->assign(__str);
      }






      basic_string&
      operator=(const _CharT* __s)
      { return this->assign(__s); }
# 825 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      operator=(_CharT __c)
      {
 this->assign(1, __c);
 return *this;
      }
# 843 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      operator=(basic_string&& __str)
      noexcept(_Alloc_traits::_S_nothrow_move())
      {
 if (!_M_is_local() && _Alloc_traits::_S_propagate_on_move_assign()
     && !_Alloc_traits::_S_always_equal()
     && _M_get_allocator() != __str._M_get_allocator())
   {

     _M_destroy(_M_allocated_capacity);
     _M_data(_M_local_data());
     _M_set_length(0);
   }

 std::__alloc_on_move(_M_get_allocator(), __str._M_get_allocator());

 if (__str._M_is_local())
   {



     if (__builtin_expect(std::__addressof(__str) != this, true))
       {
  if (__str.size())
    this->_S_copy(_M_data(), __str._M_data(), __str.size());
  _M_set_length(__str.size());
       }
   }
 else if (_Alloc_traits::_S_propagate_on_move_assign()
     || _Alloc_traits::_S_always_equal()
     || _M_get_allocator() == __str._M_get_allocator())
   {

     pointer __data = nullptr;
     size_type __capacity;
     if (!_M_is_local())
       {
  if (_Alloc_traits::_S_always_equal())
    {

      __data = _M_data();
      __capacity = _M_allocated_capacity;
    }
  else
    _M_destroy(_M_allocated_capacity);
       }

     _M_data(__str._M_data());
     _M_length(__str.length());
     _M_capacity(__str._M_allocated_capacity);
     if (__data)
       {
  __str._M_data(__data);
  __str._M_capacity(__capacity);
       }
     else
       __str._M_data(__str._M_local_buf);
   }
 else
   assign(__str);
 __str.clear();
 return *this;
      }






      basic_string&
      operator=(initializer_list<_CharT> __l)
      {
 this->assign(__l.begin(), __l.size());
 return *this;
      }
# 946 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      begin() noexcept
      { return iterator(_M_data()); }






      const_iterator
      begin() const noexcept
      { return const_iterator(_M_data()); }






      iterator
      end() noexcept
      { return iterator(_M_data() + this->size()); }






      const_iterator
      end() const noexcept
      { return const_iterator(_M_data() + this->size()); }







      reverse_iterator
      rbegin() noexcept
      { return reverse_iterator(this->end()); }







      const_reverse_iterator
      rbegin() const noexcept
      { return const_reverse_iterator(this->end()); }







      reverse_iterator
      rend() noexcept
      { return reverse_iterator(this->begin()); }







      const_reverse_iterator
      rend() const noexcept
      { return const_reverse_iterator(this->begin()); }







      const_iterator
      cbegin() const noexcept
      { return const_iterator(this->_M_data()); }






      const_iterator
      cend() const noexcept
      { return const_iterator(this->_M_data() + this->size()); }







      const_reverse_iterator
      crbegin() const noexcept
      { return const_reverse_iterator(this->end()); }







      const_reverse_iterator
      crend() const noexcept
      { return const_reverse_iterator(this->begin()); }


    public:




      size_type
      size() const noexcept
      { return _M_string_length; }




      size_type
      length() const noexcept
      { return _M_string_length; }



      size_type
      max_size() const noexcept
      { return (_Alloc_traits::max_size(_M_get_allocator()) - 1) / 2; }
# 1090 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      resize(size_type __n, _CharT __c);
# 1104 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      resize(size_type __n)
      { this->resize(__n, _CharT()); }


#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


      void
      shrink_to_fit() noexcept
      { reserve(); }
#pragma GCC diagnostic pop
# 1131 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      capacity() const noexcept
      {
 return _M_is_local() ? size_type(_S_local_capacity)
                      : _M_allocated_capacity;
      }
# 1156 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      reserve(size_type __res_arg);
# 1166 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      reserve();





      void
      clear() noexcept
      { _M_set_length(0); }






      bool
      empty() const noexcept
      { return this->size() == 0; }
# 1198 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      const_reference
      operator[] (size_type __pos) const noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(__pos <= size())) __builtin_unreachable(); } while (false);
 return _M_data()[__pos];
      }
# 1216 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      reference
      operator[](size_type __pos)
      {


 do { if (std::__is_constant_evaluated() && !bool(__pos <= size())) __builtin_unreachable(); } while (false);

                                                                   ;
 return _M_data()[__pos];
      }
# 1238 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      const_reference
      at(size_type __n) const
      {
 if (__n >= this->size())
   __throw_out_of_range_fmt(("basic_string::at: __n " "(which is %zu) >= this->size() " "(which is %zu)"),


       __n, this->size());
 return _M_data()[__n];
      }
# 1260 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      reference
      at(size_type __n)
      {
 if (__n >= size())
   __throw_out_of_range_fmt(("basic_string::at: __n " "(which is %zu) >= this->size() " "(which is %zu)"),


       __n, this->size());
 return _M_data()[__n];
      }







      reference
      front() noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(!empty())) __builtin_unreachable(); } while (false);
 return operator[](0);
      }






      const_reference
      front() const noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(!empty())) __builtin_unreachable(); } while (false);
 return operator[](0);
      }






      reference
      back() noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(!empty())) __builtin_unreachable(); } while (false);
 return operator[](this->size() - 1);
      }






      const_reference
      back() const noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(!empty())) __builtin_unreachable(); } while (false);
 return operator[](this->size() - 1);
      }
# 1328 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      operator+=(const basic_string& __str)
      { return this->append(__str); }







      basic_string&
      operator+=(const _CharT* __s)
      { return this->append(__s); }







      basic_string&
      operator+=(_CharT __c)
      {
 this->push_back(__c);
 return *this;
      }
# 1362 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      operator+=(initializer_list<_CharT> __l)
      { return this->append(__l.begin(), __l.size()); }
# 1386 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      append(const basic_string& __str)
      { return this->append(__str._M_data(), __str.size()); }
# 1404 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      append(const basic_string& __str, size_type __pos, size_type __n = npos)
      { return this->append(__str._M_data()
       + __str._M_check(__pos, "basic_string::append"),
       __str._M_limit(__pos, __n)); }
# 1417 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      append(const _CharT* __s, size_type __n)
      {
                                        ;
 _M_check_length(size_type(0), __n, "basic_string::append");
 return _M_append(__s, __n);
      }







      basic_string&
      append(const _CharT* __s)
      {
                               ;
 const size_type __n = traits_type::length(__s);
 _M_check_length(size_type(0), __n, "basic_string::append");
 return _M_append(__s, __n);
      }
# 1449 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      append(size_type __n, _CharT __c)
      { return _M_replace_aux(this->size(), size_type(0), __n, __c); }
# 1460 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      append(initializer_list<_CharT> __l)
      { return this->append(__l.begin(), __l.size()); }
# 1474 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<class _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>




        basic_string&
        append(_InputIterator __first, _InputIterator __last)
        { return this->replace(end(), end(), __first, __last); }
# 1523 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      push_back(_CharT __c)
      {
 const size_type __size = this->size();
 if (__size + 1 > this->capacity())
   this->_M_mutate(__size, size_type(0), 0, size_type(1));
 traits_type::assign(this->_M_data()[__size], __c);
 this->_M_set_length(__size + 1);
      }







      basic_string&
      assign(const basic_string& __str)
      {

 if (_Alloc_traits::_S_propagate_on_copy_assign())
   {
     if (!_Alloc_traits::_S_always_equal() && !_M_is_local()
  && _M_get_allocator() != __str._M_get_allocator())
       {


  if (__str.size() <= _S_local_capacity)
    {
      _M_destroy(_M_allocated_capacity);
      _M_data(_M_use_local_data());
      _M_set_length(0);
    }
  else
    {
      const auto __len = __str.size();
      auto __alloc = __str._M_get_allocator();

      auto __ptr = _Alloc_traits::allocate(__alloc, __len + 1);
      _M_destroy(_M_allocated_capacity);
      _M_data(__ptr);
      _M_capacity(__len);
      _M_set_length(__len);
    }
       }
     std::__alloc_on_copy(_M_get_allocator(), __str._M_get_allocator());
   }

 this->_M_assign(__str);
 return *this;
      }
# 1585 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(basic_string&& __str)
      noexcept(_Alloc_traits::_S_nothrow_move())
      {


 return *this = std::move(__str);
      }
# 1609 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(const basic_string& __str, size_type __pos, size_type __n = npos)
      { return _M_replace(size_type(0), this->size(), __str._M_data()
     + __str._M_check(__pos, "basic_string::assign"),
     __str._M_limit(__pos, __n)); }
# 1626 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(const _CharT* __s, size_type __n)
      {
                                        ;
 return _M_replace(size_type(0), this->size(), __s, __n);
      }
# 1643 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(const _CharT* __s)
      {
                               ;
 return _M_replace(size_type(0), this->size(), __s,
     traits_type::length(__s));
      }
# 1661 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(size_type __n, _CharT __c)
      { return _M_replace_aux(size_type(0), this->size(), __n, __c); }
# 1674 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<class _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>




        basic_string&
        assign(_InputIterator __first, _InputIterator __last)
        { return this->replace(begin(), end(), __first, __last); }
# 1691 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      assign(initializer_list<_CharT> __l)
      { return this->assign(__l.begin(), __l.size()); }
# 1748 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      insert(const_iterator __p, size_type __n, _CharT __c)
      {
                                                         ;
 const size_type __pos = __p - begin();
 this->replace(__p, __p, __n, __c);
 return iterator(this->_M_data() + __pos);
      }
# 1790 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<class _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 iterator
        insert(const_iterator __p, _InputIterator __beg, _InputIterator __end)
        {
                                                           ;
   const size_type __pos = __p - begin();
   this->replace(__p, __p, __beg, __end);
   return iterator(this->_M_data() + __pos);
 }
# 1828 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      insert(const_iterator __p, initializer_list<_CharT> __l)
      { return this->insert(__p, __l.begin(), __l.end()); }
# 1856 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      insert(size_type __pos1, const basic_string& __str)
      { return this->replace(__pos1, size_type(0),
        __str._M_data(), __str.size()); }
# 1880 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      insert(size_type __pos1, const basic_string& __str,
      size_type __pos2, size_type __n = npos)
      { return this->replace(__pos1, size_type(0), __str._M_data()
        + __str._M_check(__pos2, "basic_string::insert"),
        __str._M_limit(__pos2, __n)); }
# 1904 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      insert(size_type __pos, const _CharT* __s, size_type __n)
      { return this->replace(__pos, size_type(0), __s, __n); }
# 1924 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      insert(size_type __pos, const _CharT* __s)
      {
                               ;
 return this->replace(__pos, size_type(0), __s,
        traits_type::length(__s));
      }
# 1949 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      insert(size_type __pos, size_type __n, _CharT __c)
      { return _M_replace_aux(_M_check(__pos, "basic_string::insert"),
         size_type(0), __n, __c); }
# 1968 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      insert(__const_iterator __p, _CharT __c)
      {
                                                         ;
 const size_type __pos = __p - begin();
 _M_replace_aux(__pos, size_type(0), size_type(1), __c);
 return iterator(_M_data() + __pos);
      }
# 2031 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      erase(size_type __pos = 0, size_type __n = npos)
      {
 _M_check(__pos, "basic_string::erase");
 if (__n == npos)
   this->_M_set_length(__pos);
 else if (__n != 0)
   this->_M_erase(__pos, _M_limit(__pos, __n));
 return *this;
      }
# 2051 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      erase(__const_iterator __position)
      {

                           ;
 const size_type __pos = __position - begin();
 this->_M_erase(__pos, size_type(1));
 return iterator(_M_data() + __pos);
      }
# 2071 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      iterator
      erase(__const_iterator __first, __const_iterator __last)
      {

                        ;
        const size_type __pos = __first - begin();
 if (__last == end())
   this->_M_set_length(__pos);
 else
   this->_M_erase(__pos, __last - __first);
 return iterator(this->_M_data() + __pos);
      }
# 2091 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      pop_back() noexcept
      {
 do { if (std::__is_constant_evaluated() && !bool(!empty())) __builtin_unreachable(); } while (false);
 _M_erase(size() - 1, 1);
      }
# 2117 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(size_type __pos, size_type __n, const basic_string& __str)
      { return this->replace(__pos, __n, __str._M_data(), __str.size()); }
# 2140 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(size_type __pos1, size_type __n1, const basic_string& __str,
       size_type __pos2, size_type __n2 = npos)
      { return this->replace(__pos1, __n1, __str._M_data()
        + __str._M_check(__pos2, "basic_string::replace"),
        __str._M_limit(__pos2, __n2)); }
# 2166 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(size_type __pos, size_type __n1, const _CharT* __s,
       size_type __n2)
      {
                                         ;
 return _M_replace(_M_check(__pos, "basic_string::replace"),
     _M_limit(__pos, __n1), __s, __n2);
      }
# 2192 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(size_type __pos, size_type __n1, const _CharT* __s)
      {
                               ;
 return this->replace(__pos, __n1, __s, traits_type::length(__s));
      }
# 2217 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(size_type __pos, size_type __n1, size_type __n2, _CharT __c)
      { return _M_replace_aux(_M_check(__pos, "basic_string::replace"),
         _M_limit(__pos, __n1), __n2, __c); }
# 2236 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       const basic_string& __str)
      { return this->replace(__i1, __i2, __str._M_data(), __str.size()); }
# 2257 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       const _CharT* __s, size_type __n)
      {

                      ;
 return this->replace(__i1 - begin(), __i2 - __i1, __s, __n);
      }
# 2280 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2, const _CharT* __s)
      {
                               ;
 return this->replace(__i1, __i2, __s, traits_type::length(__s));
      }
# 2302 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2, size_type __n,
       _CharT __c)
      {

                      ;
 return _M_replace_aux(__i1 - begin(), __i2 - __i1, __n, __c);
      }
# 2327 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<class _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

        basic_string&
        replace(const_iterator __i1, const_iterator __i2,
  _InputIterator __k1, _InputIterator __k2)
        {

                        ;
                                             ;
   return this->_M_replace_dispatch(__i1, __i2, __k1, __k2,
        std::__false_type());
 }
# 2361 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       _CharT* __k1, _CharT* __k2)
      {

                      ;
                                           ;
 return this->replace(__i1 - begin(), __i2 - __i1,
        __k1, __k2 - __k1);
      }


      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       const _CharT* __k1, const _CharT* __k2)
      {

                      ;
                                           ;
 return this->replace(__i1 - begin(), __i2 - __i1,
        __k1, __k2 - __k1);
      }


      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       iterator __k1, iterator __k2)
      {

                      ;
                                           ;
 return this->replace(__i1 - begin(), __i2 - __i1,
        __k1.base(), __k2 - __k1);
      }


      basic_string&
      replace(__const_iterator __i1, __const_iterator __i2,
       const_iterator __k1, const_iterator __k2)
      {

                      ;
                                           ;
 return this->replace(__i1 - begin(), __i2 - __i1,
        __k1.base(), __k2 - __k1);
      }
# 2424 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string& replace(const_iterator __i1, const_iterator __i2,
       initializer_list<_CharT> __l)
      { return this->replace(__i1, __i2, __l.begin(), __l.size()); }
# 2487 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
    private:
      template<class _Integer>

 basic_string&
 _M_replace_dispatch(const_iterator __i1, const_iterator __i2,
       _Integer __n, _Integer __val, __true_type)
        { return _M_replace_aux(__i1 - begin(), __i2 - __i1, __n, __val); }

      template<class _InputIterator>

 basic_string&
 _M_replace_dispatch(const_iterator __i1, const_iterator __i2,
       _InputIterator __k1, _InputIterator __k2,
       __false_type);


      basic_string&
      _M_replace_aux(size_type __pos1, size_type __n1, size_type __n2,
       _CharT __c);


      basic_string&
      _M_replace(size_type __pos, size_type __len1, const _CharT* __s,
   const size_type __len2);


      basic_string&
      _M_append(const _CharT* __s, size_type __n);

    public:
# 2531 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      copy(_CharT* __s, size_type __n, size_type __pos = 0) const;
# 2542 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      void
      swap(basic_string& __s) noexcept;
# 2553 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      const _CharT*
      c_str() const noexcept
      { return _M_data(); }
# 2566 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      const _CharT*
      data() const noexcept
      { return _M_data(); }
# 2587 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      allocator_type
      get_allocator() const noexcept
      { return _M_get_allocator(); }
# 2604 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find(const _CharT* __s, size_type __pos, size_type __n) const
      noexcept;
# 2619 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find(const basic_string& __str, size_type __pos = 0) const
      noexcept
      { return this->find(__str.data(), __pos, __str.size()); }
# 2653 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find(const _CharT* __s, size_type __pos = 0) const noexcept
      {
                               ;
 return this->find(__s, __pos, traits_type::length(__s));
      }
# 2671 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find(_CharT __c, size_type __pos = 0) const noexcept;
# 2685 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      rfind(const basic_string& __str, size_type __pos = npos) const
      noexcept
      { return this->rfind(__str.data(), __pos, __str.size()); }
# 2721 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      rfind(const _CharT* __s, size_type __pos, size_type __n) const
      noexcept;
# 2736 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      rfind(const _CharT* __s, size_type __pos = npos) const
      {
                               ;
 return this->rfind(__s, __pos, traits_type::length(__s));
      }
# 2754 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      rfind(_CharT __c, size_type __pos = npos) const noexcept;
# 2769 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_of(const basic_string& __str, size_type __pos = 0) const
      noexcept
      { return this->find_first_of(__str.data(), __pos, __str.size()); }
# 2806 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_of(const _CharT* __s, size_type __pos, size_type __n) const
      noexcept;
# 2821 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_of(const _CharT* __s, size_type __pos = 0) const
      noexcept
      {
                               ;
 return this->find_first_of(__s, __pos, traits_type::length(__s));
      }
# 2842 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_of(_CharT __c, size_type __pos = 0) const noexcept
      { return this->find(__c, __pos); }
# 2858 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_of(const basic_string& __str, size_type __pos = npos) const
      noexcept
      { return this->find_last_of(__str.data(), __pos, __str.size()); }
# 2895 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_of(const _CharT* __s, size_type __pos, size_type __n) const
      noexcept;
# 2910 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_of(const _CharT* __s, size_type __pos = npos) const
      noexcept
      {
                               ;
 return this->find_last_of(__s, __pos, traits_type::length(__s));
      }
# 2931 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_of(_CharT __c, size_type __pos = npos) const noexcept
      { return this->rfind(__c, __pos); }
# 2946 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_not_of(const basic_string& __str, size_type __pos = 0) const
      noexcept
      { return this->find_first_not_of(__str.data(), __pos, __str.size()); }
# 2983 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_not_of(const _CharT* __s, size_type __pos,
   size_type __n) const noexcept;
# 2998 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_not_of(const _CharT* __s, size_type __pos = 0) const
      noexcept
      {
                               ;
 return this->find_first_not_of(__s, __pos, traits_type::length(__s));
      }
# 3017 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_first_not_of(_CharT __c, size_type __pos = 0) const
      noexcept;
# 3033 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_not_of(const basic_string& __str, size_type __pos = npos) const
      noexcept
      { return this->find_last_not_of(__str.data(), __pos, __str.size()); }
# 3070 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_not_of(const _CharT* __s, size_type __pos,
         size_type __n) const noexcept;
# 3085 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_not_of(const _CharT* __s, size_type __pos = npos) const
      noexcept
      {
                               ;
 return this->find_last_not_of(__s, __pos, traits_type::length(__s));
      }
# 3104 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      size_type
      find_last_not_of(_CharT __c, size_type __pos = npos) const
      noexcept;
# 3121 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      basic_string
      substr(size_type __pos = 0, size_type __n = npos) const
      { return basic_string(*this,
       _M_check(__pos, "basic_string::substr"), __n); }
# 3141 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(const basic_string& __str) const
      {
 const size_type __size = this->size();
 const size_type __osize = __str.size();
 const size_type __len = std::min(__size, __osize);

 int __r = traits_type::compare(_M_data(), __str.data(), __len);
 if (!__r)
   __r = _S_compare(__size, __osize);
 return __r;
      }
# 3238 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(size_type __pos, size_type __n, const basic_string& __str) const;
# 3265 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(size_type __pos1, size_type __n1, const basic_string& __str,
       size_type __pos2, size_type __n2 = npos) const;
# 3284 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(const _CharT* __s) const noexcept;
# 3309 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(size_type __pos, size_type __n1, const _CharT* __s) const;
# 3337 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      int
      compare(size_type __pos, size_type __n1, const _CharT* __s,
       size_type __n2) const;
# 3382 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
      template<typename, typename, typename> friend class basic_stringbuf;
    };
}

}


namespace std __attribute__ ((__visibility__ ("default")))
{
# 3429 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>
    operator+(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    {
      basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
      __str.append(__rhs);
      return __str;
    }







  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT,_Traits,_Alloc>
    operator+(const _CharT* __lhs,
       const basic_string<_CharT,_Traits,_Alloc>& __rhs);







  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT,_Traits,_Alloc>
    operator+(_CharT __lhs, const basic_string<_CharT,_Traits,_Alloc>& __rhs);







  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const _CharT* __rhs)
    {
      basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
      __str.append(__rhs);
      return __str;
    }







  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(const basic_string<_CharT, _Traits, _Alloc>& __lhs, _CharT __rhs)
    {
      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef typename __string_type::size_type __size_type;
      __string_type __str(__lhs);
      __str.append(__size_type(1), __rhs);
      return __str;
    }


  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(basic_string<_CharT, _Traits, _Alloc>&& __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return std::move(__lhs.append(__rhs)); }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       basic_string<_CharT, _Traits, _Alloc>&& __rhs)
    { return std::move(__rhs.insert(0, __lhs)); }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(basic_string<_CharT, _Traits, _Alloc>&& __lhs,
       basic_string<_CharT, _Traits, _Alloc>&& __rhs)
    {

      using _Alloc_traits = allocator_traits<_Alloc>;
      bool __use_rhs = false;
      if (typename _Alloc_traits::is_always_equal{})
 __use_rhs = true;
      else if (__lhs.get_allocator() == __rhs.get_allocator())
 __use_rhs = true;
      if (__use_rhs)

 {
   const auto __size = __lhs.size() + __rhs.size();
   if (__size > __lhs.capacity() && __size <= __rhs.capacity())
     return std::move(__rhs.insert(0, __lhs));
 }
      return std::move(__lhs.append(__rhs));
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(const _CharT* __lhs,
       basic_string<_CharT, _Traits, _Alloc>&& __rhs)
    { return std::move(__rhs.insert(0, __lhs)); }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(_CharT __lhs,
       basic_string<_CharT, _Traits, _Alloc>&& __rhs)
    { return std::move(__rhs.insert(0, 1, __lhs)); }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(basic_string<_CharT, _Traits, _Alloc>&& __lhs,
       const _CharT* __rhs)
    { return std::move(__lhs.append(__rhs)); }

  template<typename _CharT, typename _Traits, typename _Alloc>

    inline basic_string<_CharT, _Traits, _Alloc>
    operator+(basic_string<_CharT, _Traits, _Alloc>&& __lhs,
       _CharT __rhs)
    { return std::move(__lhs.append(1, __rhs)); }
# 3572 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>

    inline bool
    operator==(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return __lhs.compare(__rhs) == 0; }

  template<typename _CharT>

    inline
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value, bool>::__type
    operator==(const basic_string<_CharT>& __lhs,
        const basic_string<_CharT>& __rhs) noexcept
    { return (__lhs.size() == __rhs.size()
       && !std::char_traits<_CharT>::compare(__lhs.data(), __rhs.data(),
          __lhs.size())); }







  template<typename _CharT, typename _Traits, typename _Alloc>

    inline bool
    operator==(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const _CharT* __rhs)
    { return __lhs.compare(__rhs) == 0; }
# 3638 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator==(const _CharT* __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return __rhs.compare(__lhs) == 0; }
# 3651 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator!=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return !(__lhs == __rhs); }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator!=(const _CharT* __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return !(__lhs == __rhs); }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator!=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const _CharT* __rhs)
    { return !(__lhs == __rhs); }
# 3689 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return __lhs.compare(__rhs) < 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const _CharT* __rhs)
    { return __lhs.compare(__rhs) < 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<(const _CharT* __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return __rhs.compare(__lhs) > 0; }
# 3727 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return __lhs.compare(__rhs) > 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
       const _CharT* __rhs)
    { return __lhs.compare(__rhs) > 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>(const _CharT* __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return __rhs.compare(__lhs) < 0; }
# 3765 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return __lhs.compare(__rhs) <= 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const _CharT* __rhs)
    { return __lhs.compare(__rhs) <= 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator<=(const _CharT* __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return __rhs.compare(__lhs) >= 0; }
# 3803 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept
    { return __lhs.compare(__rhs) >= 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>=(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
        const _CharT* __rhs)
    { return __lhs.compare(__rhs) >= 0; }







  template<typename _CharT, typename _Traits, typename _Alloc>
    inline bool
    operator>=(const _CharT* __lhs,
      const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    { return __rhs.compare(__lhs) <= 0; }
# 3842 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>

    inline void
    swap(basic_string<_CharT, _Traits, _Alloc>& __lhs,
  basic_string<_CharT, _Traits, _Alloc>& __rhs)
    noexcept(noexcept(__lhs.swap(__rhs)))
    { __lhs.swap(__rhs); }
# 3863 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __is,
        basic_string<_CharT, _Traits, _Alloc>& __str);

  template<>
    basic_istream<char>&
    operator>>(basic_istream<char>& __is, basic_string<char>& __str);
# 3881 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __os,
        const basic_string<_CharT, _Traits, _Alloc>& __str)
    {


      return __ostream_insert(__os, __str.data(), __str.size());
    }
# 3904 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    basic_istream<_CharT, _Traits>&
    getline(basic_istream<_CharT, _Traits>& __is,
     basic_string<_CharT, _Traits, _Alloc>& __str, _CharT __delim);
# 3921 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    inline basic_istream<_CharT, _Traits>&
    getline(basic_istream<_CharT, _Traits>& __is,
     basic_string<_CharT, _Traits, _Alloc>& __str)
    { return std::getline(__is, __str, __is.widen('\n')); }



  template<typename _CharT, typename _Traits, typename _Alloc>
    inline basic_istream<_CharT, _Traits>&
    getline(basic_istream<_CharT, _Traits>&& __is,
     basic_string<_CharT, _Traits, _Alloc>& __str, _CharT __delim)
    { return std::getline(__is, __str, __delim); }


  template<typename _CharT, typename _Traits, typename _Alloc>
    inline basic_istream<_CharT, _Traits>&
    getline(basic_istream<_CharT, _Traits>&& __is,
     basic_string<_CharT, _Traits, _Alloc>& __str)
    { return std::getline(__is, __str); }


  template<>
    basic_istream<char>&
    getline(basic_istream<char>& __in, basic_string<char>& __str,
     char __delim);


  template<>
    basic_istream<wchar_t>&
    getline(basic_istream<wchar_t>& __in, basic_string<wchar_t>& __str,
     wchar_t __delim);



}



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 3








# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdlib" 3
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwchar" 3
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 3


# 1 "/usr/include/stdio.h" 1 3 4
# 27 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/libc-header-start.h" 1 3 4
# 28 "/usr/include/stdio.h" 2 3 4

extern "C" {



# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 34 "/usr/include/stdio.h" 2 3 4





# 1 "/usr/include/x86_64-linux-gnu/bits/types/__fpos_t.h" 1 3 4
# 10 "/usr/include/x86_64-linux-gnu/bits/types/__fpos_t.h" 3 4
typedef struct _G_fpos_t
{
  __off_t __pos;
  __mbstate_t __state;
} __fpos_t;
# 40 "/usr/include/stdio.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/__fpos64_t.h" 1 3 4
# 10 "/usr/include/x86_64-linux-gnu/bits/types/__fpos64_t.h" 3 4
typedef struct _G_fpos64_t
{
  __off64_t __pos;
  __mbstate_t __state;
} __fpos64_t;
# 41 "/usr/include/stdio.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_FILE.h" 1 3 4
# 35 "/usr/include/x86_64-linux-gnu/bits/types/struct_FILE.h" 3 4
struct _IO_FILE;
struct _IO_marker;
struct _IO_codecvt;
struct _IO_wide_data;




typedef void _IO_lock_t;





struct _IO_FILE
{
  int _flags;


  char *_IO_read_ptr;
  char *_IO_read_end;
  char *_IO_read_base;
  char *_IO_write_base;
  char *_IO_write_ptr;
  char *_IO_write_end;
  char *_IO_buf_base;
  char *_IO_buf_end;


  char *_IO_save_base;
  char *_IO_backup_base;
  char *_IO_save_end;

  struct _IO_marker *_markers;

  struct _IO_FILE *_chain;

  int _fileno;
  int _flags2;
  __off_t _old_offset;


  unsigned short _cur_column;
  signed char _vtable_offset;
  char _shortbuf[1];

  _IO_lock_t *_lock;







  __off64_t _offset;

  struct _IO_codecvt *_codecvt;
  struct _IO_wide_data *_wide_data;
  struct _IO_FILE *_freeres_list;
  void *_freeres_buf;
  size_t __pad5;
  int _mode;

  char _unused2[15 * sizeof (int) - 4 * sizeof (void *) - sizeof (size_t)];
};
# 44 "/usr/include/stdio.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/cookie_io_functions_t.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/types/cookie_io_functions_t.h" 3 4
typedef __ssize_t cookie_read_function_t (void *__cookie, char *__buf,
                                          size_t __nbytes);







typedef __ssize_t cookie_write_function_t (void *__cookie, const char *__buf,
                                           size_t __nbytes);







typedef int cookie_seek_function_t (void *__cookie, __off64_t *__pos, int __w);


typedef int cookie_close_function_t (void *__cookie);






typedef struct _IO_cookie_io_functions_t
{
  cookie_read_function_t *read;
  cookie_write_function_t *write;
  cookie_seek_function_t *seek;
  cookie_close_function_t *close;
} cookie_io_functions_t;
# 47 "/usr/include/stdio.h" 2 3 4





typedef __gnuc_va_list va_list;
# 84 "/usr/include/stdio.h" 3 4
typedef __fpos_t fpos_t;




typedef __fpos64_t fpos64_t;
# 133 "/usr/include/stdio.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/stdio_lim.h" 1 3 4
# 134 "/usr/include/stdio.h" 2 3 4
# 143 "/usr/include/stdio.h" 3 4
extern FILE *stdin;
extern FILE *stdout;
extern FILE *stderr;






extern int remove (const char *__filename) noexcept (true);

extern int rename (const char *__old, const char *__new) noexcept (true);



extern int renameat (int __oldfd, const char *__old, int __newfd,
       const char *__new) noexcept (true);
# 170 "/usr/include/stdio.h" 3 4
extern int renameat2 (int __oldfd, const char *__old, int __newfd,
        const char *__new, unsigned int __flags) noexcept (true);






extern int fclose (FILE *__stream);
# 188 "/usr/include/stdio.h" 3 4
extern FILE *tmpfile (void)
  __attribute__ ((__malloc__)) ;
# 200 "/usr/include/stdio.h" 3 4
extern FILE *tmpfile64 (void)
   __attribute__ ((__malloc__)) ;



extern char *tmpnam (char[20]) noexcept (true) ;




extern char *tmpnam_r (char __s[20]) noexcept (true) ;
# 222 "/usr/include/stdio.h" 3 4
extern char *tempnam (const char *__dir, const char *__pfx)
   noexcept (true) __attribute__ ((__malloc__)) ;






extern int fflush (FILE *__stream);
# 239 "/usr/include/stdio.h" 3 4
extern int fflush_unlocked (FILE *__stream);
# 249 "/usr/include/stdio.h" 3 4
extern int fcloseall (void);
# 258 "/usr/include/stdio.h" 3 4
extern FILE *fopen (const char *__restrict __filename,
      const char *__restrict __modes)
  __attribute__ ((__malloc__)) ;




extern FILE *freopen (const char *__restrict __filename,
        const char *__restrict __modes,
        FILE *__restrict __stream) ;
# 283 "/usr/include/stdio.h" 3 4
extern FILE *fopen64 (const char *__restrict __filename,
        const char *__restrict __modes)
  __attribute__ ((__malloc__)) ;
extern FILE *freopen64 (const char *__restrict __filename,
   const char *__restrict __modes,
   FILE *__restrict __stream) ;




extern FILE *fdopen (int __fd, const char *__modes) noexcept (true)
  __attribute__ ((__malloc__)) ;





extern FILE *fopencookie (void *__restrict __magic_cookie,
     const char *__restrict __modes,
     cookie_io_functions_t __io_funcs) noexcept (true)
  __attribute__ ((__malloc__)) ;




extern FILE *fmemopen (void *__s, size_t __len, const char *__modes)
  noexcept (true) __attribute__ ((__malloc__)) ;




extern FILE *open_memstream (char **__bufloc, size_t *__sizeloc) noexcept (true)
  __attribute__ ((__malloc__)) ;





extern __FILE *open_wmemstream (wchar_t **__bufloc, size_t *__sizeloc) noexcept (true)
  __attribute__ ((__malloc__)) ;





extern void setbuf (FILE *__restrict __stream, char *__restrict __buf) noexcept (true);



extern int setvbuf (FILE *__restrict __stream, char *__restrict __buf,
      int __modes, size_t __n) noexcept (true);




extern void setbuffer (FILE *__restrict __stream, char *__restrict __buf,
         size_t __size) noexcept (true);


extern void setlinebuf (FILE *__stream) noexcept (true);







extern int fprintf (FILE *__restrict __stream,
      const char *__restrict __format, ...);




extern int printf (const char *__restrict __format, ...);

extern int sprintf (char *__restrict __s,
      const char *__restrict __format, ...) noexcept (true);





extern int vfprintf (FILE *__restrict __s, const char *__restrict __format,
       __gnuc_va_list __arg);




extern int vprintf (const char *__restrict __format, __gnuc_va_list __arg);

extern int vsprintf (char *__restrict __s, const char *__restrict __format,
       __gnuc_va_list __arg) noexcept (true);



extern int snprintf (char *__restrict __s, size_t __maxlen,
       const char *__restrict __format, ...)
     noexcept (true) __attribute__ ((__format__ (__printf__, 3, 4)));

extern int vsnprintf (char *__restrict __s, size_t __maxlen,
        const char *__restrict __format, __gnuc_va_list __arg)
     noexcept (true) __attribute__ ((__format__ (__printf__, 3, 0)));





extern int vasprintf (char **__restrict __ptr, const char *__restrict __f,
        __gnuc_va_list __arg)
     noexcept (true) __attribute__ ((__format__ (__printf__, 2, 0))) ;
extern int __asprintf (char **__restrict __ptr,
         const char *__restrict __fmt, ...)
     noexcept (true) __attribute__ ((__format__ (__printf__, 2, 3))) ;
extern int asprintf (char **__restrict __ptr,
       const char *__restrict __fmt, ...)
     noexcept (true) __attribute__ ((__format__ (__printf__, 2, 3))) ;




extern int vdprintf (int __fd, const char *__restrict __fmt,
       __gnuc_va_list __arg)
     __attribute__ ((__format__ (__printf__, 2, 0)));
extern int dprintf (int __fd, const char *__restrict __fmt, ...)
     __attribute__ ((__format__ (__printf__, 2, 3)));







extern int fscanf (FILE *__restrict __stream,
     const char *__restrict __format, ...) ;




extern int scanf (const char *__restrict __format, ...) ;

extern int sscanf (const char *__restrict __s,
     const char *__restrict __format, ...) noexcept (true);
# 434 "/usr/include/stdio.h" 3 4
extern int fscanf (FILE *__restrict __stream, const char *__restrict __format, ...) __asm__ ("" "__isoc99_fscanf") ;


extern int scanf (const char *__restrict __format, ...) __asm__ ("" "__isoc99_scanf") ;

extern int sscanf (const char *__restrict __s, const char *__restrict __format, ...) noexcept (true) __asm__ ("" "__isoc99_sscanf");
# 459 "/usr/include/stdio.h" 3 4
extern int vfscanf (FILE *__restrict __s, const char *__restrict __format,
      __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 2, 0))) ;





extern int vscanf (const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 1, 0))) ;


extern int vsscanf (const char *__restrict __s,
      const char *__restrict __format, __gnuc_va_list __arg)
     noexcept (true) __attribute__ ((__format__ (__scanf__, 2, 0)));





extern int vfscanf (FILE *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vfscanf")



     __attribute__ ((__format__ (__scanf__, 2, 0))) ;
extern int vscanf (const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vscanf")

     __attribute__ ((__format__ (__scanf__, 1, 0))) ;
extern int vsscanf (const char *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) noexcept (true) __asm__ ("" "__isoc99_vsscanf")



     __attribute__ ((__format__ (__scanf__, 2, 0)));
# 513 "/usr/include/stdio.h" 3 4
extern int fgetc (FILE *__stream);
extern int getc (FILE *__stream);





extern int getchar (void);






extern int getc_unlocked (FILE *__stream);
extern int getchar_unlocked (void);
# 538 "/usr/include/stdio.h" 3 4
extern int fgetc_unlocked (FILE *__stream);
# 549 "/usr/include/stdio.h" 3 4
extern int fputc (int __c, FILE *__stream);
extern int putc (int __c, FILE *__stream);





extern int putchar (int __c);
# 565 "/usr/include/stdio.h" 3 4
extern int fputc_unlocked (int __c, FILE *__stream);







extern int putc_unlocked (int __c, FILE *__stream);
extern int putchar_unlocked (int __c);






extern int getw (FILE *__stream);


extern int putw (int __w, FILE *__stream);







extern char *fgets (char *__restrict __s, int __n, FILE *__restrict __stream)
                                                         ;
# 605 "/usr/include/stdio.h" 3 4
extern char *gets (char *__s) __attribute__ ((__deprecated__));
# 615 "/usr/include/stdio.h" 3 4
extern char *fgets_unlocked (char *__restrict __s, int __n,
        FILE *__restrict __stream)
                                                  ;
# 632 "/usr/include/stdio.h" 3 4
extern __ssize_t __getdelim (char **__restrict __lineptr,
                             size_t *__restrict __n, int __delimiter,
                             FILE *__restrict __stream) ;
extern __ssize_t getdelim (char **__restrict __lineptr,
                           size_t *__restrict __n, int __delimiter,
                           FILE *__restrict __stream) ;







extern __ssize_t getline (char **__restrict __lineptr,
                          size_t *__restrict __n,
                          FILE *__restrict __stream) ;







extern int fputs (const char *__restrict __s, FILE *__restrict __stream);





extern int puts (const char *__s);






extern int ungetc (int __c, FILE *__stream);






extern size_t fread (void *__restrict __ptr, size_t __size,
       size_t __n, FILE *__restrict __stream) ;




extern size_t fwrite (const void *__restrict __ptr, size_t __size,
        size_t __n, FILE *__restrict __s);
# 691 "/usr/include/stdio.h" 3 4
extern int fputs_unlocked (const char *__restrict __s,
      FILE *__restrict __stream);
# 702 "/usr/include/stdio.h" 3 4
extern size_t fread_unlocked (void *__restrict __ptr, size_t __size,
         size_t __n, FILE *__restrict __stream) ;
extern size_t fwrite_unlocked (const void *__restrict __ptr, size_t __size,
          size_t __n, FILE *__restrict __stream);







extern int fseek (FILE *__stream, long int __off, int __whence);




extern long int ftell (FILE *__stream) ;




extern void rewind (FILE *__stream);
# 736 "/usr/include/stdio.h" 3 4
extern int fseeko (FILE *__stream, __off_t __off, int __whence);




extern __off_t ftello (FILE *__stream) ;
# 760 "/usr/include/stdio.h" 3 4
extern int fgetpos (FILE *__restrict __stream, fpos_t *__restrict __pos);




extern int fsetpos (FILE *__stream, const fpos_t *__pos);
# 779 "/usr/include/stdio.h" 3 4
extern int fseeko64 (FILE *__stream, __off64_t __off, int __whence);
extern __off64_t ftello64 (FILE *__stream) ;
extern int fgetpos64 (FILE *__restrict __stream, fpos64_t *__restrict __pos);
extern int fsetpos64 (FILE *__stream, const fpos64_t *__pos);



extern void clearerr (FILE *__stream) noexcept (true);

extern int feof (FILE *__stream) noexcept (true) ;

extern int ferror (FILE *__stream) noexcept (true) ;



extern void clearerr_unlocked (FILE *__stream) noexcept (true);
extern int feof_unlocked (FILE *__stream) noexcept (true) ;
extern int ferror_unlocked (FILE *__stream) noexcept (true) ;







extern void perror (const char *__s);




extern int fileno (FILE *__stream) noexcept (true) ;




extern int fileno_unlocked (FILE *__stream) noexcept (true) ;
# 823 "/usr/include/stdio.h" 3 4
extern int pclose (FILE *__stream);





extern FILE *popen (const char *__command, const char *__modes)
  __attribute__ ((__malloc__)) ;






extern char *ctermid (char *__s) noexcept (true)
                                     ;





extern char *cuserid (char *__s)
                                     ;




struct obstack;


extern int obstack_printf (struct obstack *__restrict __obstack,
      const char *__restrict __format, ...)
     noexcept (true) __attribute__ ((__format__ (__printf__, 2, 3)));
extern int obstack_vprintf (struct obstack *__restrict __obstack,
       const char *__restrict __format,
       __gnuc_va_list __args)
     noexcept (true) __attribute__ ((__format__ (__printf__, 2, 0)));







extern void flockfile (FILE *__stream) noexcept (true);



extern int ftrylockfile (FILE *__stream) noexcept (true) ;


extern void funlockfile (FILE *__stream) noexcept (true);
# 885 "/usr/include/stdio.h" 3 4
extern int __uflow (FILE *);
extern int __overflow (FILE *, int);
# 909 "/usr/include/stdio.h" 3 4
}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 2 3
# 96 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 3
namespace std
{
  using ::FILE;
  using ::fpos_t;

  using ::clearerr;
  using ::fclose;
  using ::feof;
  using ::ferror;
  using ::fflush;
  using ::fgetc;
  using ::fgetpos;
  using ::fgets;
  using ::fopen;
  using ::fprintf;
  using ::fputc;
  using ::fputs;
  using ::fread;
  using ::freopen;
  using ::fscanf;
  using ::fseek;
  using ::fsetpos;
  using ::ftell;
  using ::fwrite;
  using ::getc;
  using ::getchar;


  using ::gets;

  using ::perror;
  using ::printf;
  using ::putc;
  using ::putchar;
  using ::puts;
  using ::remove;
  using ::rename;
  using ::rewind;
  using ::scanf;
  using ::setbuf;
  using ::setvbuf;
  using ::sprintf;
  using ::sscanf;
  using ::tmpfile;

  using ::tmpnam;

  using ::ungetc;
  using ::vfprintf;
  using ::vprintf;
  using ::vsprintf;
}
# 157 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 3
namespace __gnu_cxx
{
# 175 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cstdio" 3
  using ::snprintf;
  using ::vfscanf;
  using ::vscanf;
  using ::vsnprintf;
  using ::vsscanf;

}

namespace std
{
  using ::__gnu_cxx::snprintf;
  using ::__gnu_cxx::vfscanf;
  using ::__gnu_cxx::vscanf;
  using ::__gnu_cxx::vsnprintf;
  using ::__gnu_cxx::vsscanf;
}
# 44 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cerrno" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cerrno" 3


# 1 "/usr/include/errno.h" 1 3 4
# 28 "/usr/include/errno.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/errno.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/errno.h" 3 4
# 1 "/usr/include/linux/errno.h" 1 3 4
# 1 "/usr/include/x86_64-linux-gnu/asm/errno.h" 1 3 4
# 1 "/usr/include/asm-generic/errno.h" 1 3 4




# 1 "/usr/include/asm-generic/errno-base.h" 1 3 4
# 6 "/usr/include/asm-generic/errno.h" 2 3 4
# 2 "/usr/include/x86_64-linux-gnu/asm/errno.h" 2 3 4
# 2 "/usr/include/linux/errno.h" 2 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/errno.h" 2 3 4
# 29 "/usr/include/errno.h" 2 3 4





extern "C" {


extern int *__errno_location (void) noexcept (true) __attribute__ ((__const__));







extern char *program_invocation_name;
extern char *program_invocation_short_name;

# 1 "/usr/include/x86_64-linux-gnu/bits/types/error_t.h" 1 3 4
# 22 "/usr/include/x86_64-linux-gnu/bits/types/error_t.h" 3 4
typedef int error_t;
# 49 "/usr/include/errno.h" 2 3 4



}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cerrno" 2 3
# 45 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/string_conversions.h" 2 3

namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{



  template<typename _TRet, typename _Ret = _TRet, typename _CharT,
    typename... _Base>
    _Ret
    __stoa(_TRet (*__convf) (const _CharT*, _CharT**, _Base...),
    const char* __name, const _CharT* __str, std::size_t* __idx,
    _Base... __base)
    {
      _Ret __ret;

      _CharT* __endptr;

      struct _Save_errno {
 _Save_errno() : _M_errno((*__errno_location ())) { (*__errno_location ()) = 0; }
 ~_Save_errno() { if ((*__errno_location ()) == 0) (*__errno_location ()) = _M_errno; }
 int _M_errno;
      } const __save_errno;

      struct _Range_chk {
   static bool
   _S_chk(_TRet, std::false_type) { return false; }

   static bool
   _S_chk(_TRet __val, std::true_type)
   {
     return __val < _TRet(__numeric_traits<int>::__min)
       || __val > _TRet(__numeric_traits<int>::__max);
   }
      };

      const _TRet __tmp = __convf(__str, &__endptr, __base...);

      if (__endptr == __str)
 std::__throw_invalid_argument(__name);
      else if ((*__errno_location ()) == 34
   || _Range_chk::_S_chk(__tmp, std::is_same<_Ret, int>{}))
 std::__throw_out_of_range(__name);
      else
 __ret = __tmp;

      if (__idx)
 *__idx = __endptr - __str;

      return __ret;
    }


  template<typename _String, typename _CharT = typename _String::value_type>
    _String
    __to_xstring(int (*__convf) (_CharT*, std::size_t, const _CharT*,
     __builtin_va_list), std::size_t __n,
   const _CharT* __fmt, ...)
    {


      _CharT* __s = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
         * __n));

      __builtin_va_list __args;
      __builtin_va_start(__args, __fmt);

      const int __len = __convf(__s, __n, __fmt, __args);

      __builtin_va_end(__args);

      return _String(__s, __s + __len);
    }


}
# 3961 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/charconv.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/charconv.h" 3





namespace std __attribute__ ((__visibility__ ("default")))
{

namespace __detail
{

  template<typename _Tp>
                         unsigned
    __to_chars_len(_Tp __value, int __base = 10) noexcept
    {
      static_assert(is_integral<_Tp>::value, "implementation bug");
      static_assert(is_unsigned<_Tp>::value, "implementation bug");

      unsigned __n = 1;
      const unsigned __b2 = __base * __base;
      const unsigned __b3 = __b2 * __base;
      const unsigned long __b4 = __b3 * __base;
      for (;;)
 {
   if (__value < (unsigned)__base) return __n;
   if (__value < __b2) return __n + 1;
   if (__value < __b3) return __n + 2;
   if (__value < __b4) return __n + 3;
   __value /= __b4;
   __n += 4;
 }
    }




  template<typename _Tp>
    void
    __to_chars_10_impl(char* __first, unsigned __len, _Tp __val) noexcept
    {
      static_assert(is_integral<_Tp>::value, "implementation bug");
      static_assert(is_unsigned<_Tp>::value, "implementation bug");

      static constexpr char __digits[201] =
 "0001020304050607080910111213141516171819"
 "2021222324252627282930313233343536373839"
 "4041424344454647484950515253545556575859"
 "6061626364656667686970717273747576777879"
 "8081828384858687888990919293949596979899";
      unsigned __pos = __len - 1;
      while (__val >= 100)
 {
   auto const __num = (__val % 100) * 2;
   __val /= 100;
   __first[__pos] = __digits[__num + 1];
   __first[__pos - 1] = __digits[__num];
   __pos -= 2;
 }
      if (__val >= 10)
 {
   auto const __num = __val * 2;
   __first[1] = __digits[__num + 1];
   __first[0] = __digits[__num];
 }
      else
 __first[0] = '0' + __val;
    }

}

}
# 3962 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{

namespace __cxx11 {



  inline int
  stoi(const string& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa<long, int>(&std::strtol, "stoi", __str.c_str(),
     __idx, __base); }

  inline long
  stol(const string& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::strtol, "stol", __str.c_str(),
        __idx, __base); }

  inline unsigned long
  stoul(const string& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::strtoul, "stoul", __str.c_str(),
        __idx, __base); }

  inline long long
  stoll(const string& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::strtoll, "stoll", __str.c_str(),
        __idx, __base); }

  inline unsigned long long
  stoull(const string& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::strtoull, "stoull", __str.c_str(),
        __idx, __base); }


  inline float
  stof(const string& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::strtof, "stof", __str.c_str(), __idx); }

  inline double
  stod(const string& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::strtod, "stod", __str.c_str(), __idx); }

  inline long double
  stold(const string& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::strtold, "stold", __str.c_str(), __idx); }




  inline string
  to_string(int __val)

  noexcept

  {
    const bool __neg = __val < 0;
    const unsigned __uval = __neg ? (unsigned)~__val + 1u : __val;
    const auto __len = __detail::__to_chars_len(__uval);
    string __str(__neg + __len, '-');
    __detail::__to_chars_10_impl(&__str[__neg], __len, __uval);
    return __str;
  }

  inline string
  to_string(unsigned __val)

  noexcept

  {
    string __str(__detail::__to_chars_len(__val), '\0');
    __detail::__to_chars_10_impl(&__str[0], __str.size(), __val);
    return __str;
  }

  inline string
  to_string(long __val)



  {
    const bool __neg = __val < 0;
    const unsigned long __uval = __neg ? (unsigned long)~__val + 1ul : __val;
    const auto __len = __detail::__to_chars_len(__uval);
    string __str(__neg + __len, '-');
    __detail::__to_chars_10_impl(&__str[__neg], __len, __uval);
    return __str;
  }

  inline string
  to_string(unsigned long __val)



  {
    string __str(__detail::__to_chars_len(__val), '\0');
    __detail::__to_chars_10_impl(&__str[0], __str.size(), __val);
    return __str;
  }

  inline string
  to_string(long long __val)
  {
    const bool __neg = __val < 0;
    const unsigned long long __uval
      = __neg ? (unsigned long long)~__val + 1ull : __val;
    const auto __len = __detail::__to_chars_len(__uval);
    string __str(__neg + __len, '-');
    __detail::__to_chars_10_impl(&__str[__neg], __len, __uval);
    return __str;
  }

  inline string
  to_string(unsigned long long __val)
  {
    string __str(__detail::__to_chars_len(__val), '\0');
    __detail::__to_chars_10_impl(&__str[0], __str.size(), __val);
    return __str;
  }




  inline string
  to_string(float __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<float>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<string>(&std::vsnprintf, __n,
        "%f", __val);
  }

  inline string
  to_string(double __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<double>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<string>(&std::vsnprintf, __n,
        "%f", __val);
  }

  inline string
  to_string(long double __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<long double>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<string>(&std::vsnprintf, __n,
        "%Lf", __val);
  }



  inline int
  stoi(const wstring& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa<long, int>(&std::wcstol, "stoi", __str.c_str(),
     __idx, __base); }

  inline long
  stol(const wstring& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::wcstol, "stol", __str.c_str(),
        __idx, __base); }

  inline unsigned long
  stoul(const wstring& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::wcstoul, "stoul", __str.c_str(),
        __idx, __base); }

  inline long long
  stoll(const wstring& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::wcstoll, "stoll", __str.c_str(),
        __idx, __base); }

  inline unsigned long long
  stoull(const wstring& __str, size_t* __idx = 0, int __base = 10)
  { return __gnu_cxx::__stoa(&std::wcstoull, "stoull", __str.c_str(),
        __idx, __base); }


  inline float
  stof(const wstring& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::wcstof, "stof", __str.c_str(), __idx); }

  inline double
  stod(const wstring& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::wcstod, "stod", __str.c_str(), __idx); }

  inline long double
  stold(const wstring& __str, size_t* __idx = 0)
  { return __gnu_cxx::__stoa(&std::wcstold, "stold", __str.c_str(), __idx); }



  inline wstring
  to_wstring(int __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf, 4 * sizeof(int),
         L"%d", __val); }

  inline wstring
  to_wstring(unsigned __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf,
         4 * sizeof(unsigned),
         L"%u", __val); }

  inline wstring
  to_wstring(long __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf, 4 * sizeof(long),
         L"%ld", __val); }

  inline wstring
  to_wstring(unsigned long __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf,
         4 * sizeof(unsigned long),
         L"%lu", __val); }

  inline wstring
  to_wstring(long long __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf,
         4 * sizeof(long long),
         L"%lld", __val); }

  inline wstring
  to_wstring(unsigned long long __val)
  { return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf,
         4 * sizeof(unsigned long long),
         L"%llu", __val); }

  inline wstring
  to_wstring(float __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<float>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf, __n,
         L"%f", __val);
  }

  inline wstring
  to_wstring(double __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<double>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf, __n,
         L"%f", __val);
  }

  inline wstring
  to_wstring(long double __val)
  {
    const int __n =
      __gnu_cxx::__numeric_traits<long double>::__max_exponent10 + 20;
    return __gnu_cxx::__to_xstring<wstring>(&std::vswprintf, __n,
         L"%Lf", __val);
  }



}

}





# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 3




namespace std __attribute__ ((__visibility__ ("default")))
{
# 50 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 3
  template<typename _Result, typename _Arg>
    struct __hash_base
    {
      typedef _Result result_type ;
      typedef _Arg argument_type ;
    };


  template<typename _Tp>
    struct hash;

  template<typename _Tp, typename = void>
    struct __poison_hash
    {
      static constexpr bool __enable_hash_call = false;
    private:

      __poison_hash(__poison_hash&&);
      ~__poison_hash();
    };

  template<typename _Tp>
    struct __poison_hash<_Tp, __void_t<decltype(hash<_Tp>()(declval<_Tp>()))>>
    {
      static constexpr bool __enable_hash_call = true;
    };


  template<typename _Tp, bool = is_enum<_Tp>::value>
    struct __hash_enum
    {
    private:

      __hash_enum(__hash_enum&&);
      ~__hash_enum();
    };


  template<typename _Tp>
    struct __hash_enum<_Tp, true> : public __hash_base<size_t, _Tp>
    {
      size_t
      operator()(_Tp __val) const noexcept
      {
       using __type = typename underlying_type<_Tp>::type;
       return hash<__type>{}(static_cast<__type>(__val));
      }
    };



  template<typename _Tp>
    struct hash : __hash_enum<_Tp>
    { };


  template<typename _Tp>
    struct hash<_Tp*> : public __hash_base<size_t, _Tp*>
    {
      size_t
      operator()(_Tp* __p) const noexcept
      { return reinterpret_cast<size_t>(__p); }
    };
# 125 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 3
  template<> struct hash<bool> : public __hash_base<size_t, bool> { size_t operator()(bool __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<char> : public __hash_base<size_t, char> { size_t operator()(char __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<signed char> : public __hash_base<size_t, signed char> { size_t operator()(signed char __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<unsigned char> : public __hash_base<size_t, unsigned char> { size_t operator()(unsigned char __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<wchar_t> : public __hash_base<size_t, wchar_t> { size_t operator()(wchar_t __val) const noexcept { return static_cast<size_t>(__val); } };







  template<> struct hash<char16_t> : public __hash_base<size_t, char16_t> { size_t operator()(char16_t __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<char32_t> : public __hash_base<size_t, char32_t> { size_t operator()(char32_t __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<short> : public __hash_base<size_t, short> { size_t operator()(short __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<int> : public __hash_base<size_t, int> { size_t operator()(int __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<long> : public __hash_base<size_t, long> { size_t operator()(long __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<long long> : public __hash_base<size_t, long long> { size_t operator()(long long __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<unsigned short> : public __hash_base<size_t, unsigned short> { size_t operator()(unsigned short __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<unsigned int> : public __hash_base<size_t, unsigned int> { size_t operator()(unsigned int __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<unsigned long> : public __hash_base<size_t, unsigned long> { size_t operator()(unsigned long __val) const noexcept { return static_cast<size_t>(__val); } };


  template<> struct hash<unsigned long long> : public __hash_base<size_t, unsigned long long> { size_t operator()(unsigned long long __val) const noexcept { return static_cast<size_t>(__val); } };
# 201 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 3
  struct _Hash_impl
  {
    static size_t
    hash(const void* __ptr, size_t __clength,
  size_t __seed = static_cast<size_t>(0xc70f6907UL))
    { return _Hash_bytes(__ptr, __clength, __seed); }

    template<typename _Tp>
      static size_t
      hash(const _Tp& __val)
      { return hash(&__val, sizeof(__val)); }

    template<typename _Tp>
      static size_t
      __hash_combine(const _Tp& __val, size_t __hash)
      { return hash(&__val, sizeof(__val), __hash); }
  };


  struct _Fnv_hash_impl
  {
    static size_t
    hash(const void* __ptr, size_t __clength,
  size_t __seed = static_cast<size_t>(2166136261UL))
    { return _Fnv_hash_bytes(__ptr, __clength, __seed); }

    template<typename _Tp>
      static size_t
      hash(const _Tp& __val)
      { return hash(&__val, sizeof(__val)); }

    template<typename _Tp>
      static size_t
      __hash_combine(const _Tp& __val, size_t __hash)
      { return hash(&__val, sizeof(__val), __hash); }
  };


  template<>
    struct hash<float> : public __hash_base<size_t, float>
    {
      size_t
      operator()(float __val) const noexcept
      {

 return __val != 0.0f ? std::_Hash_impl::hash(__val) : 0;
      }
    };


  template<>
    struct hash<double> : public __hash_base<size_t, double>
    {
      size_t
      operator()(double __val) const noexcept
      {

 return __val != 0.0 ? std::_Hash_impl::hash(__val) : 0;
      }
    };


  template<>
    struct hash<long double>
    : public __hash_base<size_t, long double>
    {
      __attribute__ ((__pure__)) size_t
      operator()(long double __val) const noexcept;
    };
# 287 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/functional_hash.h" 3
  template<typename _Hash>
    struct __is_fast_hash : public std::true_type
    { };

  template<>
    struct __is_fast_hash<hash<long double>> : public std::false_type
    { };


}
# 4225 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{






  template<>
    struct hash<string>
    : public __hash_base<size_t, string>
    {
      size_t
      operator()(const string& __s) const noexcept
      { return std::_Hash_impl::hash(__s.data(), __s.length()); }
    };

  template<>
    struct __is_fast_hash<hash<string>> : std::false_type
    { };


  template<>
    struct hash<wstring>
    : public __hash_base<size_t, wstring>
    {
      size_t
      operator()(const wstring& __s) const noexcept
      { return std::_Hash_impl::hash(__s.data(),
                                     __s.length() * sizeof(wchar_t)); }
    };

  template<>
    struct __is_fast_hash<hash<wstring>> : std::false_type
    { };
# 4281 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
  template<>
    struct hash<u16string>
    : public __hash_base<size_t, u16string>
    {
      size_t
      operator()(const u16string& __s) const noexcept
      { return std::_Hash_impl::hash(__s.data(),
                                     __s.length() * sizeof(char16_t)); }
    };

  template<>
    struct __is_fast_hash<hash<u16string>> : std::false_type
    { };


  template<>
    struct hash<u32string>
    : public __hash_base<size_t, u32string>
    {
      size_t
      operator()(const u32string& __s) const noexcept
      { return std::_Hash_impl::hash(__s.data(),
                                     __s.length() * sizeof(char32_t)); }
    };

  template<>
    struct __is_fast_hash<hash<u32string>> : std::false_type
    { };
# 4378 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.h" 3
}
# 54 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.tcc" 1 3
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.tcc" 3



namespace std __attribute__ ((__visibility__ ("default")))
{




  template<typename _CharT, typename _Traits, typename _Alloc>
    const typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::npos;

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    swap(basic_string& __s) noexcept
    {
      if (this == std::__addressof(__s))
 return;

      _Alloc_traits::_S_on_swap(_M_get_allocator(), __s._M_get_allocator());

      if (_M_is_local())
 if (__s._M_is_local())
   {
     if (length() && __s.length())
       {
  _CharT __tmp_data[_S_local_capacity + 1];
  traits_type::copy(__tmp_data, __s._M_local_buf,
      __s.length() + 1);
  traits_type::copy(__s._M_local_buf, _M_local_buf,
      length() + 1);
  traits_type::copy(_M_local_buf, __tmp_data,
      __s.length() + 1);
       }
     else if (__s.length())
       {
  traits_type::copy(_M_local_buf, __s._M_local_buf,
      __s.length() + 1);
  _M_length(__s.length());
  __s._M_set_length(0);
  return;
       }
     else if (length())
       {
  traits_type::copy(__s._M_local_buf, _M_local_buf,
      length() + 1);
  __s._M_length(length());
  _M_set_length(0);
  return;
       }
   }
 else
   {
     const size_type __tmp_capacity = __s._M_allocated_capacity;
     traits_type::copy(__s._M_local_buf, _M_local_buf,
         length() + 1);
     _M_data(__s._M_data());
     __s._M_data(__s._M_local_buf);
     _M_capacity(__tmp_capacity);
   }
      else
 {
   const size_type __tmp_capacity = _M_allocated_capacity;
   if (__s._M_is_local())
     {
       traits_type::copy(_M_local_buf, __s._M_local_buf,
    __s.length() + 1);
       __s._M_data(_M_data());
       _M_data(_M_local_buf);
     }
   else
     {
       pointer __tmp_ptr = _M_data();
       _M_data(__s._M_data());
       __s._M_data(__tmp_ptr);
       _M_capacity(__s._M_allocated_capacity);
     }
   __s._M_capacity(__tmp_capacity);
 }

      const size_type __tmp_length = length();
      _M_length(__s.length());
      __s._M_length(__tmp_length);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::pointer
    basic_string<_CharT, _Traits, _Alloc>::
    _M_create(size_type& __capacity, size_type __old_capacity)
    {


      if (__capacity > max_size())
 std::__throw_length_error(("basic_string::_M_create"));




      if (__capacity > __old_capacity && __capacity < 2 * __old_capacity)
 {
   __capacity = 2 * __old_capacity;

   if (__capacity > max_size())
     __capacity = max_size();
 }



      return _Alloc_traits::allocate(_M_get_allocator(), __capacity + 1);
    }





  template<typename _CharT, typename _Traits, typename _Alloc>
    template<typename _InIterator>

      void
      basic_string<_CharT, _Traits, _Alloc>::
      _M_construct(_InIterator __beg, _InIterator __end,
     std::input_iterator_tag)
      {
 size_type __len = 0;
 size_type __capacity = size_type(_S_local_capacity);

 pointer __p = _M_use_local_data();

 while (__beg != __end && __len < __capacity)
   {
     __p[__len++] = *__beg;
     ++__beg;
   }

 struct _Guard
 {

   explicit _Guard(basic_string* __s) : _M_guarded(__s) { }


   ~_Guard() { if (_M_guarded) _M_guarded->_M_dispose(); }

   basic_string* _M_guarded;
 } __guard(this);

 while (__beg != __end)
   {
     if (__len == __capacity)
       {

  __capacity = __len + 1;
  pointer __another = _M_create(__capacity, __len);
  this->_S_copy(__another, _M_data(), __len);
  _M_dispose();
  _M_data(__another);
  _M_capacity(__capacity);
       }
     traits_type::assign(_M_data()[__len++], *__beg);
     ++__beg;
   }

 __guard._M_guarded = 0;

 _M_set_length(__len);
      }

  template<typename _CharT, typename _Traits, typename _Alloc>
    template<typename _InIterator>

      void
      basic_string<_CharT, _Traits, _Alloc>::
      _M_construct(_InIterator __beg, _InIterator __end,
     std::forward_iterator_tag)
      {
 size_type __dnew = static_cast<size_type>(std::distance(__beg, __end));

 if (__dnew > size_type(_S_local_capacity))
   {
     _M_data(_M_create(__dnew, size_type(0)));
     _M_capacity(__dnew);
   }
 else
   _M_use_local_data();


 struct _Guard
 {

   explicit _Guard(basic_string* __s) : _M_guarded(__s) { }


   ~_Guard() { if (_M_guarded) _M_guarded->_M_dispose(); }

   basic_string* _M_guarded;
 } __guard(this);

 this->_S_copy_chars(_M_data(), __beg, __end);

 __guard._M_guarded = 0;

 _M_set_length(__dnew);
      }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    _M_construct(size_type __n, _CharT __c)
    {
      if (__n > size_type(_S_local_capacity))
 {
   _M_data(_M_create(__n, size_type(0)));
   _M_capacity(__n);
 }
      else
 _M_use_local_data();

      if (__n)
 this->_S_assign(_M_data(), __n, __c);

      _M_set_length(__n);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    _M_assign(const basic_string& __str)
    {
      if (this != std::__addressof(__str))
 {
   const size_type __rsize = __str.length();
   const size_type __capacity = capacity();

   if (__rsize > __capacity)
     {
       size_type __new_capacity = __rsize;
       pointer __tmp = _M_create(__new_capacity, __capacity);
       _M_dispose();
       _M_data(__tmp);
       _M_capacity(__new_capacity);
     }

   if (__rsize)
     this->_S_copy(_M_data(), __str._M_data(), __rsize);

   _M_set_length(__rsize);
 }
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    reserve(size_type __res)
    {
      const size_type __capacity = capacity();




      if (__res <= __capacity)
 return;

      pointer __tmp = _M_create(__res, __capacity);
      this->_S_copy(__tmp, _M_data(), length() + 1);
      _M_dispose();
      _M_data(__tmp);
      _M_capacity(__res);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    _M_mutate(size_type __pos, size_type __len1, const _CharT* __s,
       size_type __len2)
    {
      const size_type __how_much = length() - __pos - __len1;

      size_type __new_capacity = length() + __len2 - __len1;
      pointer __r = _M_create(__new_capacity, capacity());

      if (__pos)
 this->_S_copy(__r, _M_data(), __pos);
      if (__s && __len2)
 this->_S_copy(__r + __pos, __s, __len2);
      if (__how_much)
 this->_S_copy(__r + __pos + __len2,
        _M_data() + __pos + __len1, __how_much);

      _M_dispose();
      _M_data(__r);
      _M_capacity(__new_capacity);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    _M_erase(size_type __pos, size_type __n)
    {
      const size_type __how_much = length() - __pos - __n;

      if (__how_much && __n)
 this->_S_move(_M_data() + __pos, _M_data() + __pos + __n, __how_much);

      _M_set_length(length() - __n);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    reserve()
    {
      if (_M_is_local())
 return;

      const size_type __length = length();
      const size_type __capacity = _M_allocated_capacity;

      if (__length <= size_type(_S_local_capacity))
 {
   this->_S_copy(_M_use_local_data(), _M_data(), __length + 1);
   _M_destroy(__capacity);
   _M_data(_M_local_data());
 }

      else if (__length < __capacity)
 try
   {
     pointer __tmp
       = _Alloc_traits::allocate(_M_get_allocator(), __length + 1);
     this->_S_copy(__tmp, _M_data(), __length + 1);
     _M_dispose();
     _M_data(__tmp);
     _M_capacity(__length);
   }
 catch (const __cxxabiv1::__forced_unwind&)
   { throw; }
 catch (...)
   { }

    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    void
    basic_string<_CharT, _Traits, _Alloc>::
    resize(size_type __n, _CharT __c)
    {
      const size_type __size = this->size();
      if (__size < __n)
 this->append(__n - __size, __c);
      else if (__n < __size)
 this->_M_set_length(__n);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>&
    basic_string<_CharT, _Traits, _Alloc>::
    _M_append(const _CharT* __s, size_type __n)
    {
      const size_type __len = __n + this->size();

      if (__len <= this->capacity())
 {
   if (__n)
     this->_S_copy(this->_M_data() + this->size(), __s, __n);
 }
      else
 this->_M_mutate(this->size(), size_type(0), __s, __n);

      this->_M_set_length(__len);
      return *this;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>
    template<typename _InputIterator>

      basic_string<_CharT, _Traits, _Alloc>&
      basic_string<_CharT, _Traits, _Alloc>::
      _M_replace_dispatch(const_iterator __i1, const_iterator __i2,
     _InputIterator __k1, _InputIterator __k2,
     std::__false_type)
      {


 const basic_string __s(__k1, __k2, this->get_allocator());
 const size_type __n1 = __i2 - __i1;
 return _M_replace(__i1 - begin(), __n1, __s._M_data(),
     __s.size());
      }

  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>&
    basic_string<_CharT, _Traits, _Alloc>::
    _M_replace_aux(size_type __pos1, size_type __n1, size_type __n2,
     _CharT __c)
    {
      _M_check_length(__n1, __n2, "basic_string::_M_replace_aux");

      const size_type __old_size = this->size();
      const size_type __new_size = __old_size + __n2 - __n1;

      if (__new_size <= this->capacity())
 {
   pointer __p = this->_M_data() + __pos1;

   const size_type __how_much = __old_size - __pos1 - __n1;
   if (__how_much && __n1 != __n2)
     this->_S_move(__p + __n2, __p + __n1, __how_much);
 }
      else
 this->_M_mutate(__pos1, __n1, 0, __n2);

      if (__n2)
 this->_S_assign(this->_M_data() + __pos1, __n2, __c);

      this->_M_set_length(__new_size);
      return *this;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>&
    basic_string<_CharT, _Traits, _Alloc>::
    _M_replace(size_type __pos, size_type __len1, const _CharT* __s,
        const size_type __len2)
    {
      _M_check_length(__len1, __len2, "basic_string::_M_replace");

      const size_type __old_size = this->size();
      const size_type __new_size = __old_size + __len2 - __len1;

      if (__new_size <= this->capacity())
 {
   pointer __p = this->_M_data() + __pos;

   const size_type __how_much = __old_size - __pos - __len1;
# 503 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.tcc" 3
   if (_M_disjunct(__s))
     {
       if (__how_much && __len1 != __len2)
  this->_S_move(__p + __len2, __p + __len1, __how_much);
       if (__len2)
  this->_S_copy(__p, __s, __len2);
     }
   else
     {

       if (__len2 && __len2 <= __len1)
  this->_S_move(__p, __s, __len2);
       if (__how_much && __len1 != __len2)
  this->_S_move(__p + __len2, __p + __len1, __how_much);
       if (__len2 > __len1)
  {
    if (__s + __len2 <= __p + __len1)
      this->_S_move(__p, __s, __len2);
    else if (__s >= __p + __len1)
      {


        const size_type __poff = (__s - __p) + (__len2 - __len1);
        this->_S_copy(__p, __p + __poff, __len2);
      }
    else
      {
        const size_type __nleft = (__p + __len1) - __s;
        this->_S_move(__p, __s, __nleft);
        this->_S_copy(__p + __nleft, __p + __len2,
        __len2 - __nleft);
      }
  }
     }
 }
      else
 this->_M_mutate(__pos, __len1, __s, __len2);

      this->_M_set_length(__new_size);
      return *this;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    copy(_CharT* __s, size_type __n, size_type __pos) const
    {
      _M_check(__pos, "basic_string::copy");
      __n = _M_limit(__pos, __n);
                                             ;
      if (__n)
 _S_copy(__s, _M_data() + __pos, __n);

      return __n;
    }
# 603 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.tcc" 3
  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>
    operator+(const _CharT* __lhs,
       const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    {
                                      ;
      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef typename __string_type::size_type __size_type;
      typedef typename __gnu_cxx::__alloc_traits<_Alloc>::template
 rebind<_CharT>::other _Char_alloc_type;
      typedef __gnu_cxx::__alloc_traits<_Char_alloc_type> _Alloc_traits;
      const __size_type __len = _Traits::length(__lhs);
      __string_type __str(_Alloc_traits::_S_select_on_copy(
          __rhs.get_allocator()));
      __str.reserve(__len + __rhs.size());
      __str.append(__lhs, __len);
      __str.append(__rhs);
      return __str;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    basic_string<_CharT, _Traits, _Alloc>
    operator+(_CharT __lhs, const basic_string<_CharT, _Traits, _Alloc>& __rhs)
    {
      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef typename __string_type::size_type __size_type;
      typedef typename __gnu_cxx::__alloc_traits<_Alloc>::template
 rebind<_CharT>::other _Char_alloc_type;
      typedef __gnu_cxx::__alloc_traits<_Char_alloc_type> _Alloc_traits;
      __string_type __str(_Alloc_traits::_S_select_on_copy(
          __rhs.get_allocator()));
      const __size_type __len = __rhs.size();
      __str.reserve(__len + 1);
      __str.append(__size_type(1), __lhs);
      __str.append(__rhs);
      return __str;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      const size_type __size = this->size();

      if (__n == 0)
 return __pos <= __size ? __pos : npos;
      if (__pos >= __size)
 return npos;

      const _CharT __elem0 = __s[0];
      const _CharT* const __data = data();
      const _CharT* __first = __data + __pos;
      const _CharT* const __last = __data + __size;
      size_type __len = __size - __pos;

      while (__len >= __n)
 {

   __first = traits_type::find(__first, __len - __n + 1, __elem0);
   if (!__first)
     return npos;



   if (traits_type::compare(__first, __s, __n) == 0)
     return __first - __data;
   __len = __last - ++__first;
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find(_CharT __c, size_type __pos) const noexcept
    {
      size_type __ret = npos;
      const size_type __size = this->size();
      if (__pos < __size)
 {
   const _CharT* __data = _M_data();
   const size_type __n = __size - __pos;
   const _CharT* __p = traits_type::find(__data + __pos, __n, __c);
   if (__p)
     __ret = __p - __data;
 }
      return __ret;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    rfind(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      const size_type __size = this->size();
      if (__n <= __size)
 {
   __pos = std::min(size_type(__size - __n), __pos);
   const _CharT* __data = _M_data();
   do
     {
       if (traits_type::compare(__data + __pos, __s, __n) == 0)
  return __pos;
     }
   while (__pos-- > 0);
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    rfind(_CharT __c, size_type __pos) const noexcept
    {
      size_type __size = this->size();
      if (__size)
 {
   if (--__size > __pos)
     __size = __pos;
   for (++__size; __size-- > 0; )
     if (traits_type::eq(_M_data()[__size], __c))
       return __size;
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_first_of(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      for (; __n && __pos < this->size(); ++__pos)
 {
   const _CharT* __p = traits_type::find(__s, __n, _M_data()[__pos]);
   if (__p)
     return __pos;
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_last_of(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      size_type __size = this->size();
      if (__size && __n)
 {
   if (--__size > __pos)
     __size = __pos;
   do
     {
       if (traits_type::find(__s, __n, _M_data()[__size]))
  return __size;
     }
   while (__size-- != 0);
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_first_not_of(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      for (; __pos < this->size(); ++__pos)
 if (!traits_type::find(__s, __n, _M_data()[__pos]))
   return __pos;
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_first_not_of(_CharT __c, size_type __pos) const noexcept
    {
      for (; __pos < this->size(); ++__pos)
 if (!traits_type::eq(_M_data()[__pos], __c))
   return __pos;
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_last_not_of(const _CharT* __s, size_type __pos, size_type __n) const
    noexcept
    {
                                             ;
      size_type __size = this->size();
      if (__size)
 {
   if (--__size > __pos)
     __size = __pos;
   do
     {
       if (!traits_type::find(__s, __n, _M_data()[__size]))
  return __size;
     }
   while (__size--);
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    typename basic_string<_CharT, _Traits, _Alloc>::size_type
    basic_string<_CharT, _Traits, _Alloc>::
    find_last_not_of(_CharT __c, size_type __pos) const noexcept
    {
      size_type __size = this->size();
      if (__size)
 {
   if (--__size > __pos)
     __size = __pos;
   do
     {
       if (!traits_type::eq(_M_data()[__size], __c))
  return __size;
     }
   while (__size--);
 }
      return npos;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    int
    basic_string<_CharT, _Traits, _Alloc>::
    compare(size_type __pos, size_type __n, const basic_string& __str) const
    {
      _M_check(__pos, "basic_string::compare");
      __n = _M_limit(__pos, __n);
      const size_type __osize = __str.size();
      const size_type __len = std::min(__n, __osize);
      int __r = traits_type::compare(_M_data() + __pos, __str.data(), __len);
      if (!__r)
 __r = _S_compare(__n, __osize);
      return __r;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    int
    basic_string<_CharT, _Traits, _Alloc>::
    compare(size_type __pos1, size_type __n1, const basic_string& __str,
     size_type __pos2, size_type __n2) const
    {
      _M_check(__pos1, "basic_string::compare");
      __str._M_check(__pos2, "basic_string::compare");
      __n1 = _M_limit(__pos1, __n1);
      __n2 = __str._M_limit(__pos2, __n2);
      const size_type __len = std::min(__n1, __n2);
      int __r = traits_type::compare(_M_data() + __pos1,
         __str.data() + __pos2, __len);
      if (!__r)
 __r = _S_compare(__n1, __n2);
      return __r;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    int
    basic_string<_CharT, _Traits, _Alloc>::
    compare(const _CharT* __s) const noexcept
    {
                                    ;
      const size_type __size = this->size();
      const size_type __osize = traits_type::length(__s);
      const size_type __len = std::min(__size, __osize);
      int __r = traits_type::compare(_M_data(), __s, __len);
      if (!__r)
 __r = _S_compare(__size, __osize);
      return __r;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    int
    basic_string <_CharT, _Traits, _Alloc>::
    compare(size_type __pos, size_type __n1, const _CharT* __s) const
    {
                                    ;
      _M_check(__pos, "basic_string::compare");
      __n1 = _M_limit(__pos, __n1);
      const size_type __osize = traits_type::length(__s);
      const size_type __len = std::min(__n1, __osize);
      int __r = traits_type::compare(_M_data() + __pos, __s, __len);
      if (!__r)
 __r = _S_compare(__n1, __osize);
      return __r;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>

    int
    basic_string <_CharT, _Traits, _Alloc>::
    compare(size_type __pos, size_type __n1, const _CharT* __s,
     size_type __n2) const
    {
                                              ;
      _M_check(__pos, "basic_string::compare");
      __n1 = _M_limit(__pos, __n1);
      const size_type __len = std::min(__n1, __n2);
      int __r = traits_type::compare(_M_data() + __pos, __s, __len);
      if (!__r)
 __r = _S_compare(__n1, __n2);
      return __r;
    }




  template<typename _CharT, typename _Traits, typename _Alloc>
    basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __in,
        basic_string<_CharT, _Traits, _Alloc>& __str)
    {
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef typename __istream_type::ios_base __ios_base;
      typedef typename __istream_type::int_type __int_type;
      typedef typename __string_type::size_type __size_type;
      typedef ctype<_CharT> __ctype_type;
      typedef typename __ctype_type::ctype_base __ctype_base;

      __size_type __extracted = 0;
      typename __ios_base::iostate __err = __ios_base::goodbit;
      typename __istream_type::sentry __cerb(__in, false);
      if (__cerb)
 {
   try
     {

       __str.erase();
       _CharT __buf[128];
       __size_type __len = 0;
       const streamsize __w = __in.width();
       const __size_type __n = __w > 0 ? static_cast<__size_type>(__w)
                                : __str.max_size();
       const __ctype_type& __ct = use_facet<__ctype_type>(__in.getloc());
       const __int_type __eof = _Traits::eof();
       __int_type __c = __in.rdbuf()->sgetc();

       while (__extracted < __n
       && !_Traits::eq_int_type(__c, __eof)
       && !__ct.is(__ctype_base::space,
     _Traits::to_char_type(__c)))
  {
    if (__len == sizeof(__buf) / sizeof(_CharT))
      {
        __str.append(__buf, sizeof(__buf) / sizeof(_CharT));
        __len = 0;
      }
    __buf[__len++] = _Traits::to_char_type(__c);
    ++__extracted;
    __c = __in.rdbuf()->snextc();
  }
       __str.append(__buf, __len);

       if (__extracted < __n && _Traits::eq_int_type(__c, __eof))
  __err |= __ios_base::eofbit;
       __in.width(0);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(__ios_base::badbit);
       throw;
     }
   catch(...)
     {



       __in._M_setstate(__ios_base::badbit);
     }
 }

      if (!__extracted)
 __err |= __ios_base::failbit;
      if (__err)
 __in.setstate(__err);
      return __in;
    }

  template<typename _CharT, typename _Traits, typename _Alloc>
    basic_istream<_CharT, _Traits>&
    getline(basic_istream<_CharT, _Traits>& __in,
     basic_string<_CharT, _Traits, _Alloc>& __str, _CharT __delim)
    {
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef typename __istream_type::ios_base __ios_base;
      typedef typename __istream_type::int_type __int_type;
      typedef typename __string_type::size_type __size_type;

      __size_type __extracted = 0;
      const __size_type __n = __str.max_size();
      typename __ios_base::iostate __err = __ios_base::goodbit;
      typename __istream_type::sentry __cerb(__in, true);
      if (__cerb)
 {
   try
     {
       __str.erase();
       const __int_type __idelim = _Traits::to_int_type(__delim);
       const __int_type __eof = _Traits::eof();
       __int_type __c = __in.rdbuf()->sgetc();

       while (__extracted < __n
       && !_Traits::eq_int_type(__c, __eof)
       && !_Traits::eq_int_type(__c, __idelim))
  {
    __str += _Traits::to_char_type(__c);
    ++__extracted;
    __c = __in.rdbuf()->snextc();
  }

       if (_Traits::eq_int_type(__c, __eof))
  __err |= __ios_base::eofbit;
       else if (_Traits::eq_int_type(__c, __idelim))
  {
    ++__extracted;
    __in.rdbuf()->sbumpc();
  }
       else
  __err |= __ios_base::failbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(__ios_base::badbit);
       throw;
     }
   catch(...)
     {



       __in._M_setstate(__ios_base::badbit);
     }
 }
      if (!__extracted)
 __err |= __ios_base::failbit;
      if (__err)
 __in.setstate(__err);
      return __in;
    }
# 1082 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_string.tcc" 3
  extern template class basic_string<char>;







  extern template
    basic_istream<char>&
    operator>>(basic_istream<char>&, string&);
  extern template
    basic_ostream<char>&
    operator<<(basic_ostream<char>&, const string&);
  extern template
    basic_istream<char>&
    getline(basic_istream<char>&, string&, char);
  extern template
    basic_istream<char>&
    getline(basic_istream<char>&, string&);



  extern template class basic_string<wchar_t>;





  extern template
    basic_istream<wchar_t>&
    operator>>(basic_istream<wchar_t>&, wstring&);
  extern template
    basic_ostream<wchar_t>&
    operator<<(basic_ostream<wchar_t>&, const wstring&);
  extern template
    basic_istream<wchar_t>&
    getline(basic_istream<wchar_t>&, wstring&, wchar_t);
  extern template
    basic_istream<wchar_t>&
    getline(basic_istream<wchar_t>&, wstring&);




}
# 55 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/string" 2 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdexcept" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{





  struct __cow_string
  {
    union {
      const char* _M_p;
      char _M_bytes[sizeof(const char*)];
    };

    __cow_string();
    __cow_string(const std::string&);
    __cow_string(const char*, size_t);
    __cow_string(const __cow_string&) noexcept;
    __cow_string& operator=(const __cow_string&) noexcept;
    ~__cow_string();

    __cow_string(__cow_string&&) noexcept;
    __cow_string& operator=(__cow_string&&) noexcept;

  };

  typedef basic_string<char> __sso_string;
# 113 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/stdexcept" 3
  class logic_error : public exception
  {
    __cow_string _M_msg;

  public:

    explicit
    logic_error(const string& __arg) ;


    explicit
    logic_error(const char*) ;

    logic_error(logic_error&&) noexcept;
    logic_error& operator=(logic_error&&) noexcept;



    logic_error(const logic_error&) noexcept;
    logic_error& operator=(const logic_error&) noexcept;





    virtual ~logic_error() noexcept;



    virtual const char*
    what() const noexcept;





  };



  class domain_error : public logic_error
  {
  public:
    explicit domain_error(const string& __arg) ;

    explicit domain_error(const char*) ;
    domain_error(const domain_error&) = default;
    domain_error& operator=(const domain_error&) = default;
    domain_error(domain_error&&) = default;
    domain_error& operator=(domain_error&&) = default;

    virtual ~domain_error() noexcept;
  };


  class invalid_argument : public logic_error
  {
  public:
    explicit invalid_argument(const string& __arg) ;

    explicit invalid_argument(const char*) ;
    invalid_argument(const invalid_argument&) = default;
    invalid_argument& operator=(const invalid_argument&) = default;
    invalid_argument(invalid_argument&&) = default;
    invalid_argument& operator=(invalid_argument&&) = default;

    virtual ~invalid_argument() noexcept;
  };



  class length_error : public logic_error
  {
  public:
    explicit length_error(const string& __arg) ;

    explicit length_error(const char*) ;
    length_error(const length_error&) = default;
    length_error& operator=(const length_error&) = default;
    length_error(length_error&&) = default;
    length_error& operator=(length_error&&) = default;

    virtual ~length_error() noexcept;
  };



  class out_of_range : public logic_error
  {
  public:
    explicit out_of_range(const string& __arg) ;

    explicit out_of_range(const char*) ;
    out_of_range(const out_of_range&) = default;
    out_of_range& operator=(const out_of_range&) = default;
    out_of_range(out_of_range&&) = default;
    out_of_range& operator=(out_of_range&&) = default;

    virtual ~out_of_range() noexcept;
  };






  class runtime_error : public exception
  {
    __cow_string _M_msg;

  public:

    explicit
    runtime_error(const string& __arg) ;


    explicit
    runtime_error(const char*) ;

    runtime_error(runtime_error&&) noexcept;
    runtime_error& operator=(runtime_error&&) noexcept;



    runtime_error(const runtime_error&) noexcept;
    runtime_error& operator=(const runtime_error&) noexcept;





    virtual ~runtime_error() noexcept;



    virtual const char*
    what() const noexcept;





  };


  class range_error : public runtime_error
  {
  public:
    explicit range_error(const string& __arg) ;

    explicit range_error(const char*) ;
    range_error(const range_error&) = default;
    range_error& operator=(const range_error&) = default;
    range_error(range_error&&) = default;
    range_error& operator=(range_error&&) = default;

    virtual ~range_error() noexcept;
  };


  class overflow_error : public runtime_error
  {
  public:
    explicit overflow_error(const string& __arg) ;

    explicit overflow_error(const char*) ;
    overflow_error(const overflow_error&) = default;
    overflow_error& operator=(const overflow_error&) = default;
    overflow_error(overflow_error&&) = default;
    overflow_error& operator=(overflow_error&&) = default;

    virtual ~overflow_error() noexcept;
  };


  class underflow_error : public runtime_error
  {
  public:
    explicit underflow_error(const string& __arg) ;

    explicit underflow_error(const char*) ;
    underflow_error(const underflow_error&) = default;
    underflow_error& operator=(const underflow_error&) = default;
    underflow_error(underflow_error&&) = default;
    underflow_error& operator=(underflow_error&&) = default;

    virtual ~underflow_error() noexcept;
  };




}
# 36 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
# 37 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ios" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ios" 3





# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 3


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr.h" 1 3
# 30 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr.h" 3
#pragma GCC visibility push(default)
# 148 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 1 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
# 1 "/usr/include/pthread.h" 1 3 4
# 22 "/usr/include/pthread.h" 3 4
# 1 "/usr/include/sched.h" 1 3 4
# 29 "/usr/include/sched.h" 3 4
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 30 "/usr/include/sched.h" 2 3 4
# 43 "/usr/include/sched.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/sched.h" 1 3 4
# 80 "/usr/include/x86_64-linux-gnu/bits/sched.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_sched_param.h" 1 3 4
# 23 "/usr/include/x86_64-linux-gnu/bits/types/struct_sched_param.h" 3 4
struct sched_param
{
  int sched_priority;
};
# 81 "/usr/include/x86_64-linux-gnu/bits/sched.h" 2 3 4

extern "C" {



extern int clone (int (*__fn) (void *__arg), void *__child_stack,
    int __flags, void *__arg, ...) noexcept (true);


extern int unshare (int __flags) noexcept (true);


extern int sched_getcpu (void) noexcept (true);


extern int getcpu (unsigned int *, unsigned int *) noexcept (true);


extern int setns (int __fd, int __nstype) noexcept (true);


}
# 44 "/usr/include/sched.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/cpu-set.h" 1 3 4
# 32 "/usr/include/x86_64-linux-gnu/bits/cpu-set.h" 3 4
typedef unsigned long int __cpu_mask;






typedef struct
{
  __cpu_mask __bits[1024 / (8 * sizeof (__cpu_mask))];
} cpu_set_t;
# 115 "/usr/include/x86_64-linux-gnu/bits/cpu-set.h" 3 4
extern "C" {

extern int __sched_cpucount (size_t __setsize, const cpu_set_t *__setp)
     noexcept (true);
extern cpu_set_t *__sched_cpualloc (size_t __count) noexcept (true) ;
extern void __sched_cpufree (cpu_set_t *__set) noexcept (true);

}
# 45 "/usr/include/sched.h" 2 3 4






extern "C" {


extern int sched_setparam (__pid_t __pid, const struct sched_param *__param)
     noexcept (true);


extern int sched_getparam (__pid_t __pid, struct sched_param *__param) noexcept (true);


extern int sched_setscheduler (__pid_t __pid, int __policy,
          const struct sched_param *__param) noexcept (true);


extern int sched_getscheduler (__pid_t __pid) noexcept (true);


extern int sched_yield (void) noexcept (true);


extern int sched_get_priority_max (int __algorithm) noexcept (true);


extern int sched_get_priority_min (int __algorithm) noexcept (true);



extern int sched_rr_get_interval (__pid_t __pid, struct timespec *__t) noexcept (true);
# 130 "/usr/include/sched.h" 3 4
extern int sched_setaffinity (__pid_t __pid, size_t __cpusetsize,
         const cpu_set_t *__cpuset) noexcept (true);


extern int sched_getaffinity (__pid_t __pid, size_t __cpusetsize,
         cpu_set_t *__cpuset) noexcept (true);


}
# 23 "/usr/include/pthread.h" 2 3 4
# 1 "/usr/include/time.h" 1 3 4
# 29 "/usr/include/time.h" 3 4
# 1 "/usr/lib/llvm-15/lib/clang/15.0.6/include/stddef.h" 1 3 4
# 30 "/usr/include/time.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/time.h" 1 3 4
# 73 "/usr/include/x86_64-linux-gnu/bits/time.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/timex.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/timex.h" 3 4
struct timex
{
# 58 "/usr/include/x86_64-linux-gnu/bits/timex.h" 3 4
  unsigned int modes;
  __syscall_slong_t offset;
  __syscall_slong_t freq;
  __syscall_slong_t maxerror;
  __syscall_slong_t esterror;
  int status;
  __syscall_slong_t constant;
  __syscall_slong_t precision;
  __syscall_slong_t tolerance;
  struct timeval time;
  __syscall_slong_t tick;
  __syscall_slong_t ppsfreq;
  __syscall_slong_t jitter;
  int shift;
  __syscall_slong_t stabil;
  __syscall_slong_t jitcnt;
  __syscall_slong_t calcnt;
  __syscall_slong_t errcnt;
  __syscall_slong_t stbcnt;

  int tai;


  int :32; int :32; int :32; int :32;
  int :32; int :32; int :32; int :32;
  int :32; int :32; int :32;

};
# 74 "/usr/include/x86_64-linux-gnu/bits/time.h" 2 3 4

extern "C" {


extern int clock_adjtime (__clockid_t __clock_id, struct timex *__utx) noexcept (true) __attribute__ ((__nonnull__ (2)));
# 90 "/usr/include/x86_64-linux-gnu/bits/time.h" 3 4
}
# 34 "/usr/include/time.h" 2 3 4





# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_tm.h" 1 3 4






struct tm
{
  int tm_sec;
  int tm_min;
  int tm_hour;
  int tm_mday;
  int tm_mon;
  int tm_year;
  int tm_wday;
  int tm_yday;
  int tm_isdst;


  long int tm_gmtoff;
  const char *tm_zone;




};
# 40 "/usr/include/time.h" 2 3 4








# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct_itimerspec.h" 1 3 4







struct itimerspec
  {
    struct timespec it_interval;
    struct timespec it_value;
  };
# 49 "/usr/include/time.h" 2 3 4
struct sigevent;
# 68 "/usr/include/time.h" 3 4
extern "C" {



extern clock_t clock (void) noexcept (true);



extern time_t time (time_t *__timer) noexcept (true);


extern double difftime (time_t __time1, time_t __time0)
     noexcept (true) __attribute__ ((__const__));


extern time_t mktime (struct tm *__tp) noexcept (true);
# 100 "/usr/include/time.h" 3 4
extern size_t strftime (char *__restrict __s, size_t __maxsize,
   const char *__restrict __format,
   const struct tm *__restrict __tp) noexcept (true);




extern char *strptime (const char *__restrict __s,
         const char *__restrict __fmt, struct tm *__tp)
     noexcept (true);






extern size_t strftime_l (char *__restrict __s, size_t __maxsize,
     const char *__restrict __format,
     const struct tm *__restrict __tp,
     locale_t __loc) noexcept (true);



extern char *strptime_l (const char *__restrict __s,
    const char *__restrict __fmt, struct tm *__tp,
    locale_t __loc) noexcept (true);






extern struct tm *gmtime (const time_t *__timer) noexcept (true);



extern struct tm *localtime (const time_t *__timer) noexcept (true);
# 154 "/usr/include/time.h" 3 4
extern struct tm *gmtime_r (const time_t *__restrict __timer,
       struct tm *__restrict __tp) noexcept (true);



extern struct tm *localtime_r (const time_t *__restrict __timer,
          struct tm *__restrict __tp) noexcept (true);
# 179 "/usr/include/time.h" 3 4
extern char *asctime (const struct tm *__tp) noexcept (true);



extern char *ctime (const time_t *__timer) noexcept (true);
# 197 "/usr/include/time.h" 3 4
extern char *asctime_r (const struct tm *__restrict __tp,
   char *__restrict __buf) noexcept (true);



extern char *ctime_r (const time_t *__restrict __timer,
        char *__restrict __buf) noexcept (true);
# 217 "/usr/include/time.h" 3 4
extern char *__tzname[2];
extern int __daylight;
extern long int __timezone;




extern char *tzname[2];



extern void tzset (void) noexcept (true);



extern int daylight;
extern long int timezone;
# 246 "/usr/include/time.h" 3 4
extern time_t timegm (struct tm *__tp) noexcept (true);
# 263 "/usr/include/time.h" 3 4
extern time_t timelocal (struct tm *__tp) noexcept (true);







extern int dysize (int __year) noexcept (true) __attribute__ ((__const__));
# 281 "/usr/include/time.h" 3 4
extern int nanosleep (const struct timespec *__requested_time,
        struct timespec *__remaining);


extern int clock_getres (clockid_t __clock_id, struct timespec *__res) noexcept (true);


extern int clock_gettime (clockid_t __clock_id, struct timespec *__tp)
     noexcept (true) __attribute__ ((__nonnull__ (2)));


extern int clock_settime (clockid_t __clock_id, const struct timespec *__tp)
     noexcept (true) __attribute__ ((__nonnull__ (2)));
# 323 "/usr/include/time.h" 3 4
extern int clock_nanosleep (clockid_t __clock_id, int __flags,
       const struct timespec *__req,
       struct timespec *__rem);
# 338 "/usr/include/time.h" 3 4
extern int clock_getcpuclockid (pid_t __pid, clockid_t *__clock_id) noexcept (true);




extern int timer_create (clockid_t __clock_id,
    struct sigevent *__restrict __evp,
    timer_t *__restrict __timerid) noexcept (true);


extern int timer_delete (timer_t __timerid) noexcept (true);



extern int timer_settime (timer_t __timerid, int __flags,
     const struct itimerspec *__restrict __value,
     struct itimerspec *__restrict __ovalue) noexcept (true);


extern int timer_gettime (timer_t __timerid, struct itimerspec *__value)
     noexcept (true);
# 376 "/usr/include/time.h" 3 4
extern int timer_getoverrun (timer_t __timerid) noexcept (true);






extern int timespec_get (struct timespec *__ts, int __base)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 399 "/usr/include/time.h" 3 4
extern int timespec_getres (struct timespec *__ts, int __base)
     noexcept (true);
# 425 "/usr/include/time.h" 3 4
extern int getdate_err;
# 434 "/usr/include/time.h" 3 4
extern struct tm *getdate (const char *__string);
# 448 "/usr/include/time.h" 3 4
extern int getdate_r (const char *__restrict __string,
        struct tm *__restrict __resbufp);


}
# 24 "/usr/include/pthread.h" 2 3 4



# 1 "/usr/include/x86_64-linux-gnu/bits/setjmp.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/setjmp.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 27 "/usr/include/x86_64-linux-gnu/bits/setjmp.h" 2 3 4




typedef long int __jmp_buf[8];
# 28 "/usr/include/pthread.h" 2 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wordsize.h" 1 3 4
# 29 "/usr/include/pthread.h" 2 3 4


# 1 "/usr/include/x86_64-linux-gnu/bits/types/struct___jmp_buf_tag.h" 1 3 4
# 26 "/usr/include/x86_64-linux-gnu/bits/types/struct___jmp_buf_tag.h" 3 4
struct __jmp_buf_tag
  {




    __jmp_buf __jmpbuf;
    int __mask_was_saved;
    __sigset_t __saved_mask;
  };
# 32 "/usr/include/pthread.h" 2 3 4





enum
{
  PTHREAD_CREATE_JOINABLE,

  PTHREAD_CREATE_DETACHED

};



enum
{
  PTHREAD_MUTEX_TIMED_NP,
  PTHREAD_MUTEX_RECURSIVE_NP,
  PTHREAD_MUTEX_ERRORCHECK_NP,
  PTHREAD_MUTEX_ADAPTIVE_NP

  ,
  PTHREAD_MUTEX_NORMAL = PTHREAD_MUTEX_TIMED_NP,
  PTHREAD_MUTEX_RECURSIVE = PTHREAD_MUTEX_RECURSIVE_NP,
  PTHREAD_MUTEX_ERRORCHECK = PTHREAD_MUTEX_ERRORCHECK_NP,
  PTHREAD_MUTEX_DEFAULT = PTHREAD_MUTEX_NORMAL



  , PTHREAD_MUTEX_FAST_NP = PTHREAD_MUTEX_TIMED_NP

};




enum
{
  PTHREAD_MUTEX_STALLED,
  PTHREAD_MUTEX_STALLED_NP = PTHREAD_MUTEX_STALLED,
  PTHREAD_MUTEX_ROBUST,
  PTHREAD_MUTEX_ROBUST_NP = PTHREAD_MUTEX_ROBUST
};





enum
{
  PTHREAD_PRIO_NONE,
  PTHREAD_PRIO_INHERIT,
  PTHREAD_PRIO_PROTECT
};
# 104 "/usr/include/pthread.h" 3 4
enum
{
  PTHREAD_RWLOCK_PREFER_READER_NP,
  PTHREAD_RWLOCK_PREFER_WRITER_NP,
  PTHREAD_RWLOCK_PREFER_WRITER_NONRECURSIVE_NP,
  PTHREAD_RWLOCK_DEFAULT_NP = PTHREAD_RWLOCK_PREFER_READER_NP
};
# 124 "/usr/include/pthread.h" 3 4
enum
{
  PTHREAD_INHERIT_SCHED,

  PTHREAD_EXPLICIT_SCHED

};



enum
{
  PTHREAD_SCOPE_SYSTEM,

  PTHREAD_SCOPE_PROCESS

};



enum
{
  PTHREAD_PROCESS_PRIVATE,

  PTHREAD_PROCESS_SHARED

};
# 159 "/usr/include/pthread.h" 3 4
struct _pthread_cleanup_buffer
{
  void (*__routine) (void *);
  void *__arg;
  int __canceltype;
  struct _pthread_cleanup_buffer *__prev;
};


enum
{
  PTHREAD_CANCEL_ENABLE,

  PTHREAD_CANCEL_DISABLE

};
enum
{
  PTHREAD_CANCEL_DEFERRED,

  PTHREAD_CANCEL_ASYNCHRONOUS

};
# 197 "/usr/include/pthread.h" 3 4
extern "C" {




extern int pthread_create (pthread_t *__restrict __newthread,
      const pthread_attr_t *__restrict __attr,
      void *(*__start_routine) (void *),
      void *__restrict __arg) noexcept (true) __attribute__ ((__nonnull__ (1, 3)));





extern void pthread_exit (void *__retval) __attribute__ ((__noreturn__));







extern int pthread_join (pthread_t __th, void **__thread_return);




extern int pthread_tryjoin_np (pthread_t __th, void **__thread_return) noexcept (true);
# 233 "/usr/include/pthread.h" 3 4
extern int pthread_timedjoin_np (pthread_t __th, void **__thread_return,
     const struct timespec *__abstime);
# 243 "/usr/include/pthread.h" 3 4
extern int pthread_clockjoin_np (pthread_t __th, void **__thread_return,
                                 clockid_t __clockid,
     const struct timespec *__abstime);
# 269 "/usr/include/pthread.h" 3 4
extern int pthread_detach (pthread_t __th) noexcept (true);



extern pthread_t pthread_self (void) noexcept (true) __attribute__ ((__const__));


extern int pthread_equal (pthread_t __thread1, pthread_t __thread2)
  noexcept (true) __attribute__ ((__const__));







extern int pthread_attr_init (pthread_attr_t *__attr) noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_attr_destroy (pthread_attr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_attr_getdetachstate (const pthread_attr_t *__attr,
     int *__detachstate)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setdetachstate (pthread_attr_t *__attr,
     int __detachstate)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_attr_getguardsize (const pthread_attr_t *__attr,
          size_t *__guardsize)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setguardsize (pthread_attr_t *__attr,
          size_t __guardsize)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_attr_getschedparam (const pthread_attr_t *__restrict __attr,
           struct sched_param *__restrict __param)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setschedparam (pthread_attr_t *__restrict __attr,
           const struct sched_param *__restrict
           __param) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_getschedpolicy (const pthread_attr_t *__restrict
     __attr, int *__restrict __policy)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setschedpolicy (pthread_attr_t *__attr, int __policy)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_attr_getinheritsched (const pthread_attr_t *__restrict
      __attr, int *__restrict __inherit)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setinheritsched (pthread_attr_t *__attr,
      int __inherit)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_attr_getscope (const pthread_attr_t *__restrict __attr,
      int *__restrict __scope)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_attr_setscope (pthread_attr_t *__attr, int __scope)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_attr_getstackaddr (const pthread_attr_t *__restrict
          __attr, void **__restrict __stackaddr)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2))) __attribute__ ((__deprecated__));





extern int pthread_attr_setstackaddr (pthread_attr_t *__attr,
          void *__stackaddr)
     noexcept (true) __attribute__ ((__nonnull__ (1))) __attribute__ ((__deprecated__));


extern int pthread_attr_getstacksize (const pthread_attr_t *__restrict
          __attr, size_t *__restrict __stacksize)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));




extern int pthread_attr_setstacksize (pthread_attr_t *__attr,
          size_t __stacksize)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_attr_getstack (const pthread_attr_t *__restrict __attr,
      void **__restrict __stackaddr,
      size_t *__restrict __stacksize)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2, 3)));




extern int pthread_attr_setstack (pthread_attr_t *__attr, void *__stackaddr,
      size_t __stacksize) noexcept (true) __attribute__ ((__nonnull__ (1)));





extern int pthread_attr_setaffinity_np (pthread_attr_t *__attr,
     size_t __cpusetsize,
     const cpu_set_t *__cpuset)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));



extern int pthread_attr_getaffinity_np (const pthread_attr_t *__attr,
     size_t __cpusetsize,
     cpu_set_t *__cpuset)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));


extern int pthread_getattr_default_np (pthread_attr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_attr_setsigmask_np (pthread_attr_t *__attr,
           const __sigset_t *sigmask);




extern int pthread_attr_getsigmask_np (const pthread_attr_t *__attr,
           __sigset_t *sigmask);







extern int pthread_setattr_default_np (const pthread_attr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));




extern int pthread_getattr_np (pthread_t __th, pthread_attr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (2)));







extern int pthread_setschedparam (pthread_t __target_thread, int __policy,
      const struct sched_param *__param)
     noexcept (true) __attribute__ ((__nonnull__ (3)));


extern int pthread_getschedparam (pthread_t __target_thread,
      int *__restrict __policy,
      struct sched_param *__restrict __param)
     noexcept (true) __attribute__ ((__nonnull__ (2, 3)));


extern int pthread_setschedprio (pthread_t __target_thread, int __prio)
     noexcept (true);




extern int pthread_getname_np (pthread_t __target_thread, char *__buf,
          size_t __buflen)
     noexcept (true) __attribute__ ((__nonnull__ (2)));


extern int pthread_setname_np (pthread_t __target_thread, const char *__name)
     noexcept (true) __attribute__ ((__nonnull__ (2)));





extern int pthread_getconcurrency (void) noexcept (true);


extern int pthread_setconcurrency (int __level) noexcept (true);



extern int pthread_yield (void) noexcept (true);

extern int pthread_yield (void) noexcept (true) __asm__ ("" "sched_yield")
  __attribute__ ((__deprecated__ ("pthread_yield is deprecated, use sched_yield instead")));
# 489 "/usr/include/pthread.h" 3 4
extern int pthread_setaffinity_np (pthread_t __th, size_t __cpusetsize,
       const cpu_set_t *__cpuset)
     noexcept (true) __attribute__ ((__nonnull__ (3)));


extern int pthread_getaffinity_np (pthread_t __th, size_t __cpusetsize,
       cpu_set_t *__cpuset)
     noexcept (true) __attribute__ ((__nonnull__ (3)));
# 509 "/usr/include/pthread.h" 3 4
extern int pthread_once (pthread_once_t *__once_control,
    void (*__init_routine) (void)) __attribute__ ((__nonnull__ (1, 2)));
# 521 "/usr/include/pthread.h" 3 4
extern int pthread_setcancelstate (int __state, int *__oldstate);



extern int pthread_setcanceltype (int __type, int *__oldtype);


extern int pthread_cancel (pthread_t __th);




extern void pthread_testcancel (void);




struct __cancel_jmp_buf_tag
{
  __jmp_buf __cancel_jmp_buf;
  int __mask_was_saved;
};

typedef struct
{
  struct __cancel_jmp_buf_tag __cancel_jmp_buf[1];
  void *__pad[4];
} __pthread_unwind_buf_t __attribute__ ((__aligned__));
# 557 "/usr/include/pthread.h" 3 4
struct __pthread_cleanup_frame
{
  void (*__cancel_routine) (void *);
  void *__cancel_arg;
  int __do_it;
  int __cancel_type;
};




class __pthread_cleanup_class
{
  void (*__cancel_routine) (void *);
  void *__cancel_arg;
  int __do_it;
  int __cancel_type;

 public:
  __pthread_cleanup_class (void (*__fct) (void *), void *__arg)
    : __cancel_routine (__fct), __cancel_arg (__arg), __do_it (1) { }
  ~__pthread_cleanup_class () { if (__do_it) __cancel_routine (__cancel_arg); }
  void __setdoit (int __newval) { __do_it = __newval; }
  void __defer () { pthread_setcanceltype (PTHREAD_CANCEL_DEFERRED,
        &__cancel_type); }
  void __restore () const { pthread_setcanceltype (__cancel_type, 0); }
};
# 773 "/usr/include/pthread.h" 3 4
extern int __sigsetjmp (struct __jmp_buf_tag __env[1],
   int __savemask) noexcept (true);






extern int pthread_mutex_init (pthread_mutex_t *__mutex,
          const pthread_mutexattr_t *__mutexattr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutex_destroy (pthread_mutex_t *__mutex)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutex_trylock (pthread_mutex_t *__mutex)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutex_lock (pthread_mutex_t *__mutex)
     noexcept (true) __attribute__ ((__nonnull__ (1)));




extern int pthread_mutex_timedlock (pthread_mutex_t *__restrict __mutex,
        const struct timespec *__restrict
        __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
# 817 "/usr/include/pthread.h" 3 4
extern int pthread_mutex_clocklock (pthread_mutex_t *__restrict __mutex,
        clockid_t __clockid,
        const struct timespec *__restrict
        __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 835 "/usr/include/pthread.h" 3 4
extern int pthread_mutex_unlock (pthread_mutex_t *__mutex)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_mutex_getprioceiling (const pthread_mutex_t *
      __restrict __mutex,
      int *__restrict __prioceiling)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));



extern int pthread_mutex_setprioceiling (pthread_mutex_t *__restrict __mutex,
      int __prioceiling,
      int *__restrict __old_ceiling)
     noexcept (true) __attribute__ ((__nonnull__ (1, 3)));




extern int pthread_mutex_consistent (pthread_mutex_t *__mutex)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutex_consistent_np (pthread_mutex_t *) noexcept (true) __asm__ ("" "pthread_mutex_consistent") __attribute__ ((__nonnull__ (1)))

  __attribute__ ((__deprecated__ ("pthread_mutex_consistent_np is deprecated, use pthread_mutex_consistent")));
# 874 "/usr/include/pthread.h" 3 4
extern int pthread_mutexattr_init (pthread_mutexattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutexattr_destroy (pthread_mutexattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutexattr_getpshared (const pthread_mutexattr_t *
      __restrict __attr,
      int *__restrict __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_mutexattr_setpshared (pthread_mutexattr_t *__attr,
      int __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_mutexattr_gettype (const pthread_mutexattr_t *__restrict
          __attr, int *__restrict __kind)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));




extern int pthread_mutexattr_settype (pthread_mutexattr_t *__attr, int __kind)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_mutexattr_getprotocol (const pthread_mutexattr_t *
       __restrict __attr,
       int *__restrict __protocol)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));



extern int pthread_mutexattr_setprotocol (pthread_mutexattr_t *__attr,
       int __protocol)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutexattr_getprioceiling (const pthread_mutexattr_t *
          __restrict __attr,
          int *__restrict __prioceiling)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_mutexattr_setprioceiling (pthread_mutexattr_t *__attr,
          int __prioceiling)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_mutexattr_getrobust (const pthread_mutexattr_t *__attr,
     int *__robustness)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_mutexattr_getrobust_np (pthread_mutexattr_t *, int *) noexcept (true) __asm__ ("" "pthread_mutexattr_getrobust") __attribute__ ((__nonnull__ (1)))


  __attribute__ ((__deprecated__ ("pthread_mutexattr_getrobust_np is deprecated, use pthread_mutexattr_getrobust")));







extern int pthread_mutexattr_setrobust (pthread_mutexattr_t *__attr,
     int __robustness)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_mutexattr_setrobust_np (pthread_mutexattr_t *, int) noexcept (true) __asm__ ("" "pthread_mutexattr_setrobust") __attribute__ ((__nonnull__ (1)))


  __attribute__ ((__deprecated__ ("pthread_mutexattr_setrobust_np is deprecated, use pthread_mutexattr_setrobust")));
# 967 "/usr/include/pthread.h" 3 4
extern int pthread_rwlock_init (pthread_rwlock_t *__restrict __rwlock,
    const pthread_rwlockattr_t *__restrict
    __attr) noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlock_destroy (pthread_rwlock_t *__rwlock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlock_rdlock (pthread_rwlock_t *__rwlock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlock_tryrdlock (pthread_rwlock_t *__rwlock)
  noexcept (true) __attribute__ ((__nonnull__ (1)));




extern int pthread_rwlock_timedrdlock (pthread_rwlock_t *__restrict __rwlock,
           const struct timespec *__restrict
           __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
# 1004 "/usr/include/pthread.h" 3 4
extern int pthread_rwlock_clockrdlock (pthread_rwlock_t *__restrict __rwlock,
           clockid_t __clockid,
           const struct timespec *__restrict
           __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 1023 "/usr/include/pthread.h" 3 4
extern int pthread_rwlock_wrlock (pthread_rwlock_t *__rwlock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlock_trywrlock (pthread_rwlock_t *__rwlock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));




extern int pthread_rwlock_timedwrlock (pthread_rwlock_t *__restrict __rwlock,
           const struct timespec *__restrict
           __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 2)));
# 1051 "/usr/include/pthread.h" 3 4
extern int pthread_rwlock_clockwrlock (pthread_rwlock_t *__restrict __rwlock,
           clockid_t __clockid,
           const struct timespec *__restrict
           __abstime) noexcept (true) __attribute__ ((__nonnull__ (1, 3)));
# 1071 "/usr/include/pthread.h" 3 4
extern int pthread_rwlock_unlock (pthread_rwlock_t *__rwlock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));





extern int pthread_rwlockattr_init (pthread_rwlockattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlockattr_destroy (pthread_rwlockattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlockattr_getpshared (const pthread_rwlockattr_t *
       __restrict __attr,
       int *__restrict __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_rwlockattr_setpshared (pthread_rwlockattr_t *__attr,
       int __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_rwlockattr_getkind_np (const pthread_rwlockattr_t *
       __restrict __attr,
       int *__restrict __pref)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_rwlockattr_setkind_np (pthread_rwlockattr_t *__attr,
       int __pref) noexcept (true) __attribute__ ((__nonnull__ (1)));







extern int pthread_cond_init (pthread_cond_t *__restrict __cond,
         const pthread_condattr_t *__restrict __cond_attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_cond_destroy (pthread_cond_t *__cond)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_cond_signal (pthread_cond_t *__cond)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_cond_broadcast (pthread_cond_t *__cond)
     noexcept (true) __attribute__ ((__nonnull__ (1)));






extern int pthread_cond_wait (pthread_cond_t *__restrict __cond,
         pthread_mutex_t *__restrict __mutex)
     __attribute__ ((__nonnull__ (1, 2)));
# 1145 "/usr/include/pthread.h" 3 4
extern int pthread_cond_timedwait (pthread_cond_t *__restrict __cond,
       pthread_mutex_t *__restrict __mutex,
       const struct timespec *__restrict __abstime)
     __attribute__ ((__nonnull__ (1, 2, 3)));
# 1171 "/usr/include/pthread.h" 3 4
extern int pthread_cond_clockwait (pthread_cond_t *__restrict __cond,
       pthread_mutex_t *__restrict __mutex,
       __clockid_t __clock_id,
       const struct timespec *__restrict __abstime)
     __attribute__ ((__nonnull__ (1, 2, 4)));
# 1194 "/usr/include/pthread.h" 3 4
extern int pthread_condattr_init (pthread_condattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_condattr_destroy (pthread_condattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_condattr_getpshared (const pthread_condattr_t *
     __restrict __attr,
     int *__restrict __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_condattr_setpshared (pthread_condattr_t *__attr,
     int __pshared) noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_condattr_getclock (const pthread_condattr_t *
          __restrict __attr,
          __clockid_t *__restrict __clock_id)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_condattr_setclock (pthread_condattr_t *__attr,
          __clockid_t __clock_id)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 1230 "/usr/include/pthread.h" 3 4
extern int pthread_spin_init (pthread_spinlock_t *__lock, int __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_spin_destroy (pthread_spinlock_t *__lock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_spin_lock (pthread_spinlock_t *__lock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_spin_trylock (pthread_spinlock_t *__lock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_spin_unlock (pthread_spinlock_t *__lock)
     noexcept (true) __attribute__ ((__nonnull__ (1)));






extern int pthread_barrier_init (pthread_barrier_t *__restrict __barrier,
     const pthread_barrierattr_t *__restrict
     __attr, unsigned int __count)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_barrier_destroy (pthread_barrier_t *__barrier)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_barrier_wait (pthread_barrier_t *__barrier)
     noexcept (true) __attribute__ ((__nonnull__ (1)));



extern int pthread_barrierattr_init (pthread_barrierattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_barrierattr_destroy (pthread_barrierattr_t *__attr)
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_barrierattr_getpshared (const pthread_barrierattr_t *
        __restrict __attr,
        int *__restrict __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1, 2)));


extern int pthread_barrierattr_setpshared (pthread_barrierattr_t *__attr,
        int __pshared)
     noexcept (true) __attribute__ ((__nonnull__ (1)));
# 1297 "/usr/include/pthread.h" 3 4
extern int pthread_key_create (pthread_key_t *__key,
          void (*__destr_function) (void *))
     noexcept (true) __attribute__ ((__nonnull__ (1)));


extern int pthread_key_delete (pthread_key_t __key) noexcept (true);


extern void *pthread_getspecific (pthread_key_t __key) noexcept (true);


extern int pthread_setspecific (pthread_key_t __key,
    const void *__pointer)
  noexcept (true) ;




extern int pthread_getcpuclockid (pthread_t __thread_id,
      __clockid_t *__clock_id)
     noexcept (true) __attribute__ ((__nonnull__ (2)));
# 1332 "/usr/include/pthread.h" 3 4
extern int pthread_atfork (void (*__prepare) (void),
      void (*__parent) (void),
      void (*__child) (void)) noexcept (true);
# 1346 "/usr/include/pthread.h" 3 4
}
# 36 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 2 3
# 47 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
typedef pthread_t __gthread_t;
typedef pthread_key_t __gthread_key_t;
typedef pthread_once_t __gthread_once_t;
typedef pthread_mutex_t __gthread_mutex_t;
typedef pthread_mutex_t __gthread_recursive_mutex_t;
typedef pthread_cond_t __gthread_cond_t;
typedef struct timespec __gthread_time_t;
# 299 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
static inline int
__gthread_active_p (void)
{
  return 1;
}
# 659 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
static inline int
__gthread_create (__gthread_t *__threadid, void *(*__func) (void*),
    void *__args)
{
  return pthread_create (__threadid, __null, __func, __args);
}

static inline int
__gthread_join (__gthread_t __threadid, void **__value_ptr)
{
  return pthread_join (__threadid, __value_ptr);
}

static inline int
__gthread_detach (__gthread_t __threadid)
{
  return pthread_detach (__threadid);
}

static inline int
__gthread_equal (__gthread_t __t1, __gthread_t __t2)
{
  return pthread_equal (__t1, __t2);
}

static inline __gthread_t
__gthread_self (void)
{
  return pthread_self ();
}

static inline int
__gthread_yield (void)
{
  return sched_yield ();
}

static inline int
__gthread_once (__gthread_once_t *__once, void (*__func) (void))
{
  if (__gthread_active_p ())
    return pthread_once (__once, __func);
  else
    return -1;
}

static inline int
__gthread_key_create (__gthread_key_t *__key, void (*__dtor) (void *))
{
  return pthread_key_create (__key, __dtor);
}

static inline int
__gthread_key_delete (__gthread_key_t __key)
{
  return pthread_key_delete (__key);
}

static inline void *
__gthread_getspecific (__gthread_key_t __key)
{
  return pthread_getspecific (__key);
}

static inline int
__gthread_setspecific (__gthread_key_t __key, const void *__ptr)
{
  return pthread_setspecific (__key, __ptr);
}

static inline void
__gthread_mutex_init_function (__gthread_mutex_t *__mutex)
{
  if (__gthread_active_p ())
    pthread_mutex_init (__mutex, __null);
}

static inline int
__gthread_mutex_destroy (__gthread_mutex_t *__mutex)
{
  if (__gthread_active_p ())
    return pthread_mutex_destroy (__mutex);
  else
    return 0;
}

static inline int
__gthread_mutex_lock (__gthread_mutex_t *__mutex)
{
  if (__gthread_active_p ())
    return pthread_mutex_lock (__mutex);
  else
    return 0;
}

static inline int
__gthread_mutex_trylock (__gthread_mutex_t *__mutex)
{
  if (__gthread_active_p ())
    return pthread_mutex_trylock (__mutex);
  else
    return 0;
}


static inline int
__gthread_mutex_timedlock (__gthread_mutex_t *__mutex,
      const __gthread_time_t *__abs_timeout)
{
  if (__gthread_active_p ())
    return pthread_mutex_timedlock (__mutex, __abs_timeout);
  else
    return 0;
}


static inline int
__gthread_mutex_unlock (__gthread_mutex_t *__mutex)
{
  if (__gthread_active_p ())
    return pthread_mutex_unlock (__mutex);
  else
    return 0;
}
# 808 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
static inline int
__gthread_recursive_mutex_lock (__gthread_recursive_mutex_t *__mutex)
{
  return __gthread_mutex_lock (__mutex);
}

static inline int
__gthread_recursive_mutex_trylock (__gthread_recursive_mutex_t *__mutex)
{
  return __gthread_mutex_trylock (__mutex);
}


static inline int
__gthread_recursive_mutex_timedlock (__gthread_recursive_mutex_t *__mutex,
         const __gthread_time_t *__abs_timeout)
{
  return __gthread_mutex_timedlock (__mutex, __abs_timeout);
}


static inline int
__gthread_recursive_mutex_unlock (__gthread_recursive_mutex_t *__mutex)
{
  return __gthread_mutex_unlock (__mutex);
}

static inline int
__gthread_recursive_mutex_destroy (__gthread_recursive_mutex_t *__mutex)
{
  return __gthread_mutex_destroy (__mutex);
}
# 850 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr-default.h" 3
static inline int
__gthread_cond_broadcast (__gthread_cond_t *__cond)
{
  return pthread_cond_broadcast (__cond);
}

static inline int
__gthread_cond_signal (__gthread_cond_t *__cond)
{
  return pthread_cond_signal (__cond);
}

static inline int
__gthread_cond_wait (__gthread_cond_t *__cond, __gthread_mutex_t *__mutex)
{
  return pthread_cond_wait (__cond, __mutex);
}

static inline int
__gthread_cond_timedwait (__gthread_cond_t *__cond, __gthread_mutex_t *__mutex,
     const __gthread_time_t *__abs_timeout)
{
  return pthread_cond_timedwait (__cond, __mutex, __abs_timeout);
}

static inline int
__gthread_cond_wait_recursive (__gthread_cond_t *__cond,
          __gthread_recursive_mutex_t *__mutex)
{
  return __gthread_cond_wait (__cond, __mutex);
}

static inline int
__gthread_cond_destroy (__gthread_cond_t* __cond)
{
  return pthread_cond_destroy (__cond);
}
# 149 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/gthr.h" 2 3


#pragma GCC visibility pop
# 36 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/atomic_word.h" 1 3
# 32 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/atomic_word.h" 3
typedef int _Atomic_word;
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 2 3

# 1 "/usr/include/x86_64-linux-gnu/sys/single_threaded.h" 1 3 4
# 24 "/usr/include/x86_64-linux-gnu/sys/single_threaded.h" 3 4
extern "C" {




extern char __libc_single_threaded;

}
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 2 3


namespace __gnu_cxx __attribute__ ((__visibility__ ("default")))
{


  __attribute__((__always_inline__))
  inline bool
  __is_single_threaded() noexcept
  {



    return ::__libc_single_threaded;



  }






  inline _Atomic_word
  __attribute__((__always_inline__))
  __exchange_and_add(volatile _Atomic_word* __mem, int __val)
  { return __atomic_fetch_add(__mem, __val, 4); }

  inline void
  __attribute__((__always_inline__))
  __atomic_add(volatile _Atomic_word* __mem, int __val)
  { __atomic_fetch_add(__mem, __val, 4); }
# 80 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ext/atomicity.h" 3
  inline _Atomic_word
  __attribute__((__always_inline__))
  __exchange_and_add_single(_Atomic_word* __mem, int __val)
  {
    _Atomic_word __result = *__mem;
    *__mem += __val;
    return __result;
  }

  inline void
  __attribute__((__always_inline__))
  __atomic_add_single(_Atomic_word* __mem, int __val)
  { *__mem += __val; }

  inline _Atomic_word
  __attribute__ ((__always_inline__))
  __exchange_and_add_dispatch(_Atomic_word* __mem, int __val)
  {
    if (__is_single_threaded())
      return __exchange_and_add_single(__mem, __val);
    else
      return __exchange_and_add(__mem, __val);
  }

  inline void
  __attribute__ ((__always_inline__))
  __atomic_add_dispatch(_Atomic_word* __mem, int __val)
  {
    if (__is_single_threaded())
      __atomic_add_single(__mem, __val);
    else
      __atomic_add(__mem, __val);
  }


}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 2 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3





namespace std __attribute__ ((__visibility__ ("default")))
{
# 62 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
  class locale
  {
  public:


    typedef int category;


    class facet;
    class id;
    class _Impl;

    friend class facet;
    friend class _Impl;

    template<typename _Facet>
      friend bool
      has_facet(const locale&) throw();

    template<typename _Facet>
      friend const _Facet&
      use_facet(const locale&);

    template<typename _Cache>
      friend struct __use_cache;
# 98 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    static const category none = 0;
    static const category ctype = 1L << 0;
    static const category numeric = 1L << 1;
    static const category collate = 1L << 2;
    static const category time = 1L << 3;
    static const category monetary = 1L << 4;
    static const category messages = 1L << 5;
    static const category all = (ctype | numeric | collate |
        time | monetary | messages);
# 117 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    locale() throw();
# 126 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    locale(const locale& __other) throw();
# 136 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    explicit
    locale(const char* __s);
# 151 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    locale(const locale& __base, const char* __s, category __cat);
# 162 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    explicit
    locale(const std::string& __s) : locale(__s.c_str()) { }
# 177 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    locale(const locale& __base, const std::string& __s, category __cat)
    : locale(__base, __s.c_str(), __cat) { }
# 192 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    locale(const locale& __base, const locale& __add, category __cat);
# 205 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    template<typename _Facet>
      locale(const locale& __other, _Facet* __f);


    ~locale() throw();
# 219 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    const locale&
    operator=(const locale& __other) throw();
# 234 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    template<typename _Facet>
      locale
      combine(const locale& __other) const;






    __attribute ((__abi_tag__ ("cxx11")))
    string
    name() const;
# 254 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    bool
    operator==(const locale& __other) const throw();
# 264 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    bool
    operator!=(const locale& __other) const throw()
    { return !(this->operator==(__other)); }
# 284 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    template<typename _Char, typename _Traits, typename _Alloc>
      bool
      operator()(const basic_string<_Char, _Traits, _Alloc>& __s1,
   const basic_string<_Char, _Traits, _Alloc>& __s2) const;
# 300 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    static locale
    global(const locale& __loc);




    static const locale&
    classic();

  private:

    _Impl* _M_impl;


    static _Impl* _S_classic;


    static _Impl* _S_global;





    static const char* const* const _S_categories;
# 335 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    enum { _S_categories_size = 6 + 6 };


    static __gthread_once_t _S_once;


    explicit
    locale(_Impl*) throw();

    static void
    _S_initialize();

    static void
    _S_initialize_once() throw();

    static category
    _S_normalize_category(category);

    void
    _M_coalesce(const locale& __base, const locale& __add, category __cat);


    static const id* const _S_twinned_facets[];

  };
# 373 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
  class locale::facet
  {
  private:
    friend class locale;
    friend class locale::_Impl;

    mutable _Atomic_word _M_refcount;


    static __c_locale _S_c_locale;


    static const char _S_c_name[2];


    static __gthread_once_t _S_once;


    static void
    _S_initialize_once();

  protected:
# 404 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    explicit
    facet(size_t __refs = 0) throw() : _M_refcount(__refs ? 1 : 0)
    { }


    virtual
    ~facet();

    static void
    _S_create_c_locale(__c_locale& __cloc, const char* __s,
         __c_locale __old = 0);

    static __c_locale
    _S_clone_c_locale(__c_locale& __cloc) throw();

    static void
    _S_destroy_c_locale(__c_locale& __cloc);

    static __c_locale
    _S_lc_ctype_c_locale(__c_locale __cloc, const char* __s);



    static __c_locale
    _S_get_c_locale();

    __attribute__ ((__const__)) static const char*
    _S_get_c_name() throw();
# 440 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
    facet(const facet&) = delete;

    facet&
    operator=(const facet&) = delete;


  private:
    void
    _M_add_reference() const throw()
    { __gnu_cxx::__atomic_add_dispatch(&_M_refcount, 1); }

    void
    _M_remove_reference() const throw()
    {

                                                           ;
      if (__gnu_cxx::__exchange_and_add_dispatch(&_M_refcount, -1) == 1)
 {
                                                              ;
   try
     { delete this; }
   catch(...)
     { }
 }
    }

    const facet* _M_sso_shim(const id*) const;
    const facet* _M_cow_shim(const id*) const;

  protected:
    class __shim;
  };
# 485 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
  class locale::id
  {
  private:
    friend class locale;
    friend class locale::_Impl;

    template<typename _Facet>
      friend const _Facet&
      use_facet(const locale&);

    template<typename _Facet>
      friend bool
      has_facet(const locale&) throw();




    mutable size_t _M_index;


    static _Atomic_word _S_refcount;

    void
    operator=(const id&);

    id(const id&);

  public:



    id() { }

    size_t
    _M_id() const throw();
  };



  class locale::_Impl
  {
  public:

    friend class locale;
    friend class locale::facet;

    template<typename _Facet>
      friend bool
      has_facet(const locale&) throw();

    template<typename _Facet>
      friend const _Facet&
      use_facet(const locale&);

    template<typename _Cache>
      friend struct __use_cache;

  private:

    _Atomic_word _M_refcount;
    const facet** _M_facets;
    size_t _M_facets_size;
    const facet** _M_caches;
    char** _M_names;
    static const locale::id* const _S_id_ctype[];
    static const locale::id* const _S_id_numeric[];
    static const locale::id* const _S_id_collate[];
    static const locale::id* const _S_id_time[];
    static const locale::id* const _S_id_monetary[];
    static const locale::id* const _S_id_messages[];
    static const locale::id* const* const _S_facet_categories[];

    void
    _M_add_reference() throw()
    { __gnu_cxx::__atomic_add_dispatch(&_M_refcount, 1); }

    void
    _M_remove_reference() throw()
    {

                                                           ;
      if (__gnu_cxx::__exchange_and_add_dispatch(&_M_refcount, -1) == 1)
 {
                                                              ;
   try
     { delete this; }
   catch(...)
     { }
 }
    }

    _Impl(const _Impl&, size_t);
    _Impl(const char*, size_t);
    _Impl(size_t) throw();

   ~_Impl() throw();

    _Impl(const _Impl&);

    void
    operator=(const _Impl&);

    bool
    _M_check_same_name()
    {
      bool __ret = true;
      if (_M_names[1])

 for (size_t __i = 0; __ret && __i < _S_categories_size - 1; ++__i)
   __ret = __builtin_strcmp(_M_names[__i], _M_names[__i + 1]) == 0;
      return __ret;
    }

    void
    _M_replace_categories(const _Impl*, category);

    void
    _M_replace_category(const _Impl*, const locale::id* const*);

    void
    _M_replace_facet(const _Impl*, const locale::id*);

    void
    _M_install_facet(const locale::id*, const facet*);

    template<typename _Facet>
      void
      _M_init_facet(_Facet* __facet)
      { _M_install_facet(&_Facet::id, __facet); }

    template<typename _Facet>
      void
      _M_init_facet_unchecked(_Facet* __facet)
      {
 __facet->_M_add_reference();
 _M_facets[_Facet::id._M_id()] = __facet;
      }

    void
    _M_install_cache(const facet*, size_t);

    void _M_init_extra(facet**);
    void _M_init_extra(void*, void*, const char*, const char*);




  };
# 647 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
  template<typename _CharT>
    class __cxx11:: collate : public locale::facet
    {
    public:



      typedef _CharT char_type;
      typedef basic_string<_CharT> string_type;


    protected:


      __c_locale _M_c_locale_collate;

    public:

      static locale::id id;
# 674 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      explicit
      collate(size_t __refs = 0)
      : facet(__refs), _M_c_locale_collate(_S_get_c_locale())
      { }
# 688 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      explicit
      collate(__c_locale __cloc, size_t __refs = 0)
      : facet(__refs), _M_c_locale_collate(_S_clone_c_locale(__cloc))
      { }
# 705 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      int
      compare(const _CharT* __lo1, const _CharT* __hi1,
       const _CharT* __lo2, const _CharT* __hi2) const
      { return this->do_compare(__lo1, __hi1, __lo2, __hi2); }
# 724 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      string_type
      transform(const _CharT* __lo, const _CharT* __hi) const
      { return this->do_transform(__lo, __hi); }
# 738 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      long
      hash(const _CharT* __lo, const _CharT* __hi) const
      { return this->do_hash(__lo, __hi); }


      int
      _M_compare(const _CharT*, const _CharT*) const throw();

      size_t
      _M_transform(_CharT*, const _CharT*, size_t) const throw();

  protected:

      virtual
      ~collate()
      { _S_destroy_c_locale(_M_c_locale_collate); }
# 767 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      virtual int
      do_compare(const _CharT* __lo1, const _CharT* __hi1,
   const _CharT* __lo2, const _CharT* __hi2) const;
# 781 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      virtual string_type
      do_transform(const _CharT* __lo, const _CharT* __hi) const;
# 794 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 3
      virtual long
      do_hash(const _CharT* __lo, const _CharT* __hi) const;
    };

  template<typename _CharT>
    locale::id collate<_CharT>::id;


  template<>
    int
    collate<char>::_M_compare(const char*, const char*) const throw();

  template<>
    size_t
    collate<char>::_M_transform(char*, const char*, size_t) const throw();


  template<>
    int
    collate<wchar_t>::_M_compare(const wchar_t*, const wchar_t*) const throw();

  template<>
    size_t
    collate<wchar_t>::_M_transform(wchar_t*, const wchar_t*, size_t) const throw();



  template<typename _CharT>
    class __cxx11:: collate_byname : public collate<_CharT>
    {
    public:


      typedef _CharT char_type;
      typedef basic_string<_CharT> string_type;


      explicit
      collate_byname(const char* __s, size_t __refs = 0)
      : collate<_CharT>(__refs)
      {
 if (__builtin_strcmp(__s, "C") != 0
     && __builtin_strcmp(__s, "POSIX") != 0)
   {
     this->_S_destroy_c_locale(this->_M_c_locale_collate);
     this->_S_create_c_locale(this->_M_c_locale_collate, __s);
   }
      }


      explicit
      collate_byname(const string& __s, size_t __refs = 0)
      : collate_byname(__s.c_str(), __refs) { }


    protected:
      virtual
      ~collate_byname() { }
    };


}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.tcc" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.tcc" 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _Facet>
    locale::
    locale(const locale& __other, _Facet* __f)
    {
      _M_impl = new _Impl(*__other._M_impl, 1);

      try
 { _M_impl->_M_install_facet(&_Facet::id, __f); }
      catch(...)
 {
   _M_impl->_M_remove_reference();
   throw;
 }
      delete [] _M_impl->_M_names[0];
      _M_impl->_M_names[0] = 0;
    }

  template<typename _Facet>
    locale
    locale::
    combine(const locale& __other) const
    {
      _Impl* __tmp = new _Impl(*_M_impl, 1);
      try
 {
   __tmp->_M_replace_facet(__other._M_impl, &_Facet::id);
 }
      catch(...)
 {
   __tmp->_M_remove_reference();
   throw;
 }
      return locale(__tmp);
    }

  template<typename _CharT, typename _Traits, typename _Alloc>
    bool
    locale::
    operator()(const basic_string<_CharT, _Traits, _Alloc>& __s1,
        const basic_string<_CharT, _Traits, _Alloc>& __s2) const
    {
      typedef std::collate<_CharT> __collate_type;
      const __collate_type& __collate = use_facet<__collate_type>(*this);
      return (__collate.compare(__s1.data(), __s1.data() + __s1.length(),
    __s2.data(), __s2.data() + __s2.length()) < 0);
    }
# 102 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.tcc" 3
  template<typename _Facet>
    bool
    has_facet(const locale& __loc) throw()
    {
      const size_t __i = _Facet::id._M_id();
      const locale::facet** __facets = __loc._M_impl->_M_facets;
      return (__i < __loc._M_impl->_M_facets_size

       && dynamic_cast<const _Facet*>(__facets[__i]));



    }
# 130 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.tcc" 3
  template<typename _Facet>
    const _Facet&
    use_facet(const locale& __loc)
    {
      const size_t __i = _Facet::id._M_id();
      const locale::facet** __facets = __loc._M_impl->_M_facets;
      if (__i >= __loc._M_impl->_M_facets_size || !__facets[__i])
        __throw_bad_cast();

      return dynamic_cast<const _Facet&>(*__facets[__i]);



    }



  template<typename _CharT>
    int
    collate<_CharT>::_M_compare(const _CharT*, const _CharT*) const throw ()
    { return 0; }


  template<typename _CharT>
    size_t
    collate<_CharT>::_M_transform(_CharT*, const _CharT*, size_t) const throw ()
    { return 0; }

  template<typename _CharT>
    int
    collate<_CharT>::
    do_compare(const _CharT* __lo1, const _CharT* __hi1,
        const _CharT* __lo2, const _CharT* __hi2) const
    {


      const string_type __one(__lo1, __hi1);
      const string_type __two(__lo2, __hi2);

      const _CharT* __p = __one.c_str();
      const _CharT* __pend = __one.data() + __one.length();
      const _CharT* __q = __two.c_str();
      const _CharT* __qend = __two.data() + __two.length();




      for (;;)
 {
   const int __res = _M_compare(__p, __q);
   if (__res)
     return __res;

   __p += char_traits<_CharT>::length(__p);
   __q += char_traits<_CharT>::length(__q);
   if (__p == __pend && __q == __qend)
     return 0;
   else if (__p == __pend)
     return -1;
   else if (__q == __qend)
     return 1;

   __p++;
   __q++;
 }
    }

  template<typename _CharT>
    typename collate<_CharT>::string_type
    collate<_CharT>::
    do_transform(const _CharT* __lo, const _CharT* __hi) const
    {
      string_type __ret;


      const string_type __str(__lo, __hi);

      const _CharT* __p = __str.c_str();
      const _CharT* __pend = __str.data() + __str.length();

      size_t __len = (__hi - __lo) * 2;

      _CharT* __c = new _CharT[__len];

      try
 {



   for (;;)
     {

       size_t __res = _M_transform(__c, __p, __len);


       if (__res >= __len)
  {
    __len = __res + 1;
    delete [] __c, __c = 0;
    __c = new _CharT[__len];
    __res = _M_transform(__c, __p, __len);
  }

       __ret.append(__c, __res);
       __p += char_traits<_CharT>::length(__p);
       if (__p == __pend)
  break;

       __p++;
       __ret.push_back(_CharT());
     }
 }
      catch(...)
 {
   delete [] __c;
   throw;
 }

      delete [] __c;

      return __ret;
    }

  template<typename _CharT>
    long
    collate<_CharT>::
    do_hash(const _CharT* __lo, const _CharT* __hi) const
    {
      unsigned long __val = 0;
      for (; __lo < __hi; ++__lo)
 __val =
   *__lo + ((__val << 7)
     | (__val >> (__gnu_cxx::__numeric_traits<unsigned long>::
    __digits - 7)));
      return static_cast<long>(__val);
    }




  extern template class collate<char>;
  extern template class collate_byname<char>;

  extern template
    const collate<char>&
    use_facet<collate<char> >(const locale&);

  extern template
    bool
    has_facet<collate<char> >(const locale&);


  extern template class collate<wchar_t>;
  extern template class collate_byname<wchar_t>;

  extern template
    const collate<wchar_t>&
    use_facet<collate<wchar_t> >(const locale&);

  extern template
    bool
    has_facet<collate<wchar_t> >(const locale&);




}
# 858 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_classes.h" 2 3
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 2 3




# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 1 3
# 33 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3






# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/error_constants.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/error_constants.h" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cerrno" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cerrno" 3
# 35 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/error_constants.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  enum class errc
    {
      address_family_not_supported = 97,
      address_in_use = 98,
      address_not_available = 99,
      already_connected = 106,
      argument_list_too_long = 7,
      argument_out_of_domain = 33,
      bad_address = 14,
      bad_file_descriptor = 9,


      bad_message = 74,


      broken_pipe = 32,
      connection_aborted = 103,
      connection_already_in_progress = 114,
      connection_refused = 111,
      connection_reset = 104,
      cross_device_link = 18,
      destination_address_required = 89,
      device_or_resource_busy = 16,
      directory_not_empty = 39,
      executable_format_error = 8,
      file_exists = 17,
      file_too_large = 27,
      filename_too_long = 36,
      function_not_supported = 38,
      host_unreachable = 113,


      identifier_removed = 43,


      illegal_byte_sequence = 84,
      inappropriate_io_control_operation = 25,
      interrupted = 4,
      invalid_argument = 22,
      invalid_seek = 29,
      io_error = 5,
      is_a_directory = 21,
      message_size = 90,
      network_down = 100,
      network_reset = 102,
      network_unreachable = 101,
      no_buffer_space = 105,
      no_child_process = 10,


      no_link = 67,


      no_lock_available = 37,


      no_message_available = 61,


      no_message = 42,
      no_protocol_option = 92,
      no_space_on_device = 28,


      no_stream_resources = 63,


      no_such_device_or_address = 6,
      no_such_device = 19,
      no_such_file_or_directory = 2,
      no_such_process = 3,
      not_a_directory = 20,
      not_a_socket = 88,


      not_a_stream = 60,


      not_connected = 107,
      not_enough_memory = 12,


      not_supported = 95,



      operation_canceled = 125,


      operation_in_progress = 115,
      operation_not_permitted = 1,
      operation_not_supported = 95,
      operation_would_block = 11,


      owner_dead = 130,


      permission_denied = 13,


      protocol_error = 71,


      protocol_not_supported = 93,
      read_only_file_system = 30,
      resource_deadlock_would_occur = 35,
      resource_unavailable_try_again = 11,
      result_out_of_range = 34,


      state_not_recoverable = 131,



      stream_timeout = 62,



      text_file_busy = 26,


      timed_out = 110,
      too_many_files_open_in_system = 23,
      too_many_files_open = 24,
      too_many_links = 31,
      too_many_symbolic_link_levels = 40,


      value_too_large = 75,


      wrong_protocol_type = 91
    };


}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 2 3






namespace std __attribute__ ((__visibility__ ("default")))
{






  class error_code;
  class error_condition;
  class system_error;


  template<typename _Tp>
    struct is_error_code_enum : public false_type { };


  template<typename _Tp>
    struct is_error_condition_enum : public false_type { };

  template<>
    struct is_error_condition_enum<errc>
    : public true_type { };
# 80 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  inline namespace _V2 {
# 97 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  class error_category
  {
  public:
    constexpr error_category() noexcept = default;

    virtual ~error_category();

    error_category(const error_category&) = delete;
    error_category& operator=(const error_category&) = delete;

    virtual const char*
    name() const noexcept = 0;






  private:
    __attribute ((__abi_tag__ ("cxx11")))
    virtual __cow_string
    _M_message(int) const;

  public:
    __attribute ((__abi_tag__ ("cxx11")))
    virtual string
    message(int) const = 0;
# 133 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  public:
    virtual error_condition
    default_error_condition(int __i) const noexcept;

    virtual bool
    equivalent(int __i, const error_condition& __cond) const noexcept;

    virtual bool
    equivalent(const error_code& __code, int __i) const noexcept;

    bool
    operator==(const error_category& __other) const noexcept
    { return this == &__other; }






    bool
    operator!=(const error_category& __other) const noexcept
    { return this != &__other; }

    bool
    operator<(const error_category& __other) const noexcept
    { return less<const error_category*>()(this, &__other); }

  };




  __attribute__ ((__const__)) const error_category& generic_category() noexcept;


  __attribute__ ((__const__)) const error_category& system_category() noexcept;


  }





  error_code make_error_code(errc) noexcept;
# 196 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  class error_code
  {
  public:
    error_code() noexcept
    : _M_value(0), _M_cat(&system_category()) { }

    error_code(int __v, const error_category& __cat) noexcept
    : _M_value(__v), _M_cat(&__cat) { }

    template<typename _ErrorCodeEnum, typename = typename
      enable_if<is_error_code_enum<_ErrorCodeEnum>::value>::type>
      error_code(_ErrorCodeEnum __e) noexcept
      { *this = make_error_code(__e); }

    void
    assign(int __v, const error_category& __cat) noexcept
    {
      _M_value = __v;
      _M_cat = &__cat;
    }

    void
    clear() noexcept
    { assign(0, system_category()); }


    template<typename _ErrorCodeEnum>
      typename enable_if<is_error_code_enum<_ErrorCodeEnum>::value,
    error_code&>::type
      operator=(_ErrorCodeEnum __e) noexcept
      { return *this = make_error_code(__e); }

    int
    value() const noexcept { return _M_value; }

    const error_category&
    category() const noexcept { return *_M_cat; }

    error_condition
    default_error_condition() const noexcept;

    __attribute ((__abi_tag__ ("cxx11")))
    string
    message() const
    { return category().message(value()); }

    explicit operator bool() const noexcept
    { return _M_value != 0; }


  private:
    int _M_value;
    const error_category* _M_cat;
  };





  inline error_code
  make_error_code(errc __e) noexcept
  { return error_code(static_cast<int>(__e), generic_category()); }
# 268 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  inline bool
  operator<(const error_code& __lhs, const error_code& __rhs) noexcept
  {
    return (__lhs.category() < __rhs.category()
     || (__lhs.category() == __rhs.category()
  && __lhs.value() < __rhs.value()));
  }


  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __os, const error_code& __e)
    { return (__os << __e.category().name() << ':' << __e.value()); }



  error_condition make_error_condition(errc) noexcept;
# 297 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  class error_condition
  {
  public:
    error_condition() noexcept
    : _M_value(0), _M_cat(&generic_category()) { }

    error_condition(int __v, const error_category& __cat) noexcept
    : _M_value(__v), _M_cat(&__cat) { }

    template<typename _ErrorConditionEnum, typename = typename
  enable_if<is_error_condition_enum<_ErrorConditionEnum>::value>::type>
      error_condition(_ErrorConditionEnum __e) noexcept
      { *this = make_error_condition(__e); }

    void
    assign(int __v, const error_category& __cat) noexcept
    {
      _M_value = __v;
      _M_cat = &__cat;
    }


    template<typename _ErrorConditionEnum>
      typename enable_if<is_error_condition_enum
    <_ErrorConditionEnum>::value, error_condition&>::type
      operator=(_ErrorConditionEnum __e) noexcept
      { return *this = make_error_condition(__e); }

    void
    clear() noexcept
    { assign(0, generic_category()); }


    int
    value() const noexcept { return _M_value; }

    const error_category&
    category() const noexcept { return *_M_cat; }

    __attribute ((__abi_tag__ ("cxx11")))
    string
    message() const
    { return category().message(value()); }

    explicit operator bool() const noexcept
    { return _M_value != 0; }


  private:
    int _M_value;
    const error_category* _M_cat;
  };





  inline error_condition
  make_error_condition(errc __e) noexcept
  { return error_condition(static_cast<int>(__e), generic_category()); }




  inline bool
  operator==(const error_code& __lhs, const error_code& __rhs) noexcept
  { return (__lhs.category() == __rhs.category()
     && __lhs.value() == __rhs.value()); }


  inline bool
  operator==(const error_code& __lhs, const error_condition& __rhs) noexcept
  {
    return (__lhs.category().equivalent(__lhs.value(), __rhs)
     || __rhs.category().equivalent(__lhs, __rhs.value()));
  }


  inline bool
  operator==(const error_condition& __lhs,
      const error_condition& __rhs) noexcept
  {
    return (__lhs.category() == __rhs.category()
     && __lhs.value() == __rhs.value());
  }
# 397 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  inline bool
  operator<(const error_condition& __lhs,
     const error_condition& __rhs) noexcept
  {
    return (__lhs.category() < __rhs.category()
     || (__lhs.category() == __rhs.category()
  && __lhs.value() < __rhs.value()));
  }


  inline bool
  operator==(const error_condition& __lhs, const error_code& __rhs) noexcept
  {
    return (__rhs.category().equivalent(__rhs.value(), __lhs)
     || __lhs.category().equivalent(__rhs, __lhs.value()));
  }


  inline bool
  operator!=(const error_code& __lhs, const error_code& __rhs) noexcept
  { return !(__lhs == __rhs); }


  inline bool
  operator!=(const error_code& __lhs, const error_condition& __rhs) noexcept
  { return !(__lhs == __rhs); }


  inline bool
  operator!=(const error_condition& __lhs, const error_code& __rhs) noexcept
  { return !(__lhs == __rhs); }


  inline bool
  operator!=(const error_condition& __lhs,
      const error_condition& __rhs) noexcept
  { return !(__lhs == __rhs); }
# 446 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
  class system_error : public std::runtime_error
  {
  private:
    error_code _M_code;

  public:
    system_error(error_code __ec = error_code())
    : runtime_error(__ec.message()), _M_code(__ec) { }

    system_error(error_code __ec, const string& __what)
    : runtime_error(__what + ": " + __ec.message()), _M_code(__ec) { }

    system_error(error_code __ec, const char* __what)
    : runtime_error(__what + (": " + __ec.message())), _M_code(__ec) { }

    system_error(int __v, const error_category& __ecat, const char* __what)
    : system_error(error_code(__v, __ecat), __what) { }

    system_error(int __v, const error_category& __ecat)
    : runtime_error(error_code(__v, __ecat).message()),
      _M_code(__v, __ecat) { }

    system_error(int __v, const error_category& __ecat, const string& __what)
    : runtime_error(__what + ": " + error_code(__v, __ecat).message()),
      _M_code(__v, __ecat) { }


    system_error (const system_error &) = default;
    system_error &operator= (const system_error &) = default;


    virtual ~system_error() noexcept;

    const error_code&
    code() const noexcept { return _M_code; }
  };


}



namespace std __attribute__ ((__visibility__ ("default")))
{






  template<>
    struct hash<error_code>
    : public __hash_base<size_t, error_code>
    {
      size_t
      operator()(const error_code& __e) const noexcept
      {
 const size_t __tmp = std::_Hash_impl::hash(__e.value());
 return std::_Hash_impl::__hash_combine(&__e.category(), __tmp);
      }
    };
# 527 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/system_error" 3
}
# 47 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 2 3


namespace std __attribute__ ((__visibility__ ("default")))
{






  enum _Ios_Fmtflags
    {
      _S_boolalpha = 1L << 0,
      _S_dec = 1L << 1,
      _S_fixed = 1L << 2,
      _S_hex = 1L << 3,
      _S_internal = 1L << 4,
      _S_left = 1L << 5,
      _S_oct = 1L << 6,
      _S_right = 1L << 7,
      _S_scientific = 1L << 8,
      _S_showbase = 1L << 9,
      _S_showpoint = 1L << 10,
      _S_showpos = 1L << 11,
      _S_skipws = 1L << 12,
      _S_unitbuf = 1L << 13,
      _S_uppercase = 1L << 14,
      _S_adjustfield = _S_left | _S_right | _S_internal,
      _S_basefield = _S_dec | _S_oct | _S_hex,
      _S_floatfield = _S_scientific | _S_fixed,
      _S_ios_fmtflags_end = 1L << 16,
      _S_ios_fmtflags_max = 2147483647,
      _S_ios_fmtflags_min = ~2147483647
    };

  inline constexpr _Ios_Fmtflags
  operator&(_Ios_Fmtflags __a, _Ios_Fmtflags __b)
  { return _Ios_Fmtflags(static_cast<int>(__a) & static_cast<int>(__b)); }

  inline constexpr _Ios_Fmtflags
  operator|(_Ios_Fmtflags __a, _Ios_Fmtflags __b)
  { return _Ios_Fmtflags(static_cast<int>(__a) | static_cast<int>(__b)); }

  inline constexpr _Ios_Fmtflags
  operator^(_Ios_Fmtflags __a, _Ios_Fmtflags __b)
  { return _Ios_Fmtflags(static_cast<int>(__a) ^ static_cast<int>(__b)); }

  inline constexpr _Ios_Fmtflags
  operator~(_Ios_Fmtflags __a)
  { return _Ios_Fmtflags(~static_cast<int>(__a)); }

  inline const _Ios_Fmtflags&
  operator|=(_Ios_Fmtflags& __a, _Ios_Fmtflags __b)
  { return __a = __a | __b; }

  inline const _Ios_Fmtflags&
  operator&=(_Ios_Fmtflags& __a, _Ios_Fmtflags __b)
  { return __a = __a & __b; }

  inline const _Ios_Fmtflags&
  operator^=(_Ios_Fmtflags& __a, _Ios_Fmtflags __b)
  { return __a = __a ^ __b; }


  enum _Ios_Openmode
    {
      _S_app = 1L << 0,
      _S_ate = 1L << 1,
      _S_bin = 1L << 2,
      _S_in = 1L << 3,
      _S_out = 1L << 4,
      _S_trunc = 1L << 5,
      _S_noreplace = 1L << 6,
      _S_ios_openmode_end = 1L << 16,
      _S_ios_openmode_max = 2147483647,
      _S_ios_openmode_min = ~2147483647
    };

  inline constexpr _Ios_Openmode
  operator&(_Ios_Openmode __a, _Ios_Openmode __b)
  { return _Ios_Openmode(static_cast<int>(__a) & static_cast<int>(__b)); }

  inline constexpr _Ios_Openmode
  operator|(_Ios_Openmode __a, _Ios_Openmode __b)
  { return _Ios_Openmode(static_cast<int>(__a) | static_cast<int>(__b)); }

  inline constexpr _Ios_Openmode
  operator^(_Ios_Openmode __a, _Ios_Openmode __b)
  { return _Ios_Openmode(static_cast<int>(__a) ^ static_cast<int>(__b)); }

  inline constexpr _Ios_Openmode
  operator~(_Ios_Openmode __a)
  { return _Ios_Openmode(~static_cast<int>(__a)); }

  inline const _Ios_Openmode&
  operator|=(_Ios_Openmode& __a, _Ios_Openmode __b)
  { return __a = __a | __b; }

  inline const _Ios_Openmode&
  operator&=(_Ios_Openmode& __a, _Ios_Openmode __b)
  { return __a = __a & __b; }

  inline const _Ios_Openmode&
  operator^=(_Ios_Openmode& __a, _Ios_Openmode __b)
  { return __a = __a ^ __b; }


  enum _Ios_Iostate
    {
      _S_goodbit = 0,
      _S_badbit = 1L << 0,
      _S_eofbit = 1L << 1,
      _S_failbit = 1L << 2,
      _S_ios_iostate_end = 1L << 16,
      _S_ios_iostate_max = 2147483647,
      _S_ios_iostate_min = ~2147483647
    };

  inline constexpr _Ios_Iostate
  operator&(_Ios_Iostate __a, _Ios_Iostate __b)
  { return _Ios_Iostate(static_cast<int>(__a) & static_cast<int>(__b)); }

  inline constexpr _Ios_Iostate
  operator|(_Ios_Iostate __a, _Ios_Iostate __b)
  { return _Ios_Iostate(static_cast<int>(__a) | static_cast<int>(__b)); }

  inline constexpr _Ios_Iostate
  operator^(_Ios_Iostate __a, _Ios_Iostate __b)
  { return _Ios_Iostate(static_cast<int>(__a) ^ static_cast<int>(__b)); }

  inline constexpr _Ios_Iostate
  operator~(_Ios_Iostate __a)
  { return _Ios_Iostate(~static_cast<int>(__a)); }

  inline const _Ios_Iostate&
  operator|=(_Ios_Iostate& __a, _Ios_Iostate __b)
  { return __a = __a | __b; }

  inline const _Ios_Iostate&
  operator&=(_Ios_Iostate& __a, _Ios_Iostate __b)
  { return __a = __a & __b; }

  inline const _Ios_Iostate&
  operator^=(_Ios_Iostate& __a, _Ios_Iostate __b)
  { return __a = __a ^ __b; }


  enum _Ios_Seekdir
    {
      _S_beg = 0,
      _S_cur = 1,
      _S_end = 2,
      _S_ios_seekdir_end = 1L << 16
    };



  enum class io_errc { stream = 1 };

  template <> struct is_error_code_enum<io_errc> : public true_type { };

  const error_category& iostream_category() noexcept;

  inline error_code
  make_error_code(io_errc __e) noexcept
  { return error_code(static_cast<int>(__e), iostream_category()); }

  inline error_condition
  make_error_condition(io_errc __e) noexcept
  { return error_condition(static_cast<int>(__e), iostream_category()); }
# 229 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
  class ios_base
  {
# 247 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
  public:
# 256 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    class __attribute ((__abi_tag__ ("cxx11"))) failure : public system_error
    {
    public:
      explicit
      failure(const string& __str);


      explicit
      failure(const string&, const error_code&);

      explicit
      failure(const char*, const error_code& = io_errc::stream);


      virtual
      ~failure() throw();

      virtual const char*
      what() const throw();
    };
# 342 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    typedef _Ios_Fmtflags fmtflags;


    static const fmtflags boolalpha = _S_boolalpha;


    static const fmtflags dec = _S_dec;


    static const fmtflags fixed = _S_fixed;


    static const fmtflags hex = _S_hex;




    static const fmtflags internal = _S_internal;



    static const fmtflags left = _S_left;


    static const fmtflags oct = _S_oct;



    static const fmtflags right = _S_right;


    static const fmtflags scientific = _S_scientific;



    static const fmtflags showbase = _S_showbase;



    static const fmtflags showpoint = _S_showpoint;


    static const fmtflags showpos = _S_showpos;


    static const fmtflags skipws = _S_skipws;


    static const fmtflags unitbuf = _S_unitbuf;



    static const fmtflags uppercase = _S_uppercase;


    static const fmtflags adjustfield = _S_adjustfield;


    static const fmtflags basefield = _S_basefield;


    static const fmtflags floatfield = _S_floatfield;
# 417 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    typedef _Ios_Iostate iostate;



    static const iostate badbit = _S_badbit;


    static const iostate eofbit = _S_eofbit;




    static const iostate failbit = _S_failbit;


    static const iostate goodbit = _S_goodbit;
# 448 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    typedef _Ios_Openmode openmode;


    static const openmode app = _S_app;


    static const openmode ate = _S_ate;




    static const openmode binary = _S_bin;


    static const openmode in = _S_in;


    static const openmode out = _S_out;


    static const openmode trunc = _S_trunc;

    static const openmode __noreplace = _S_noreplace;
# 488 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    typedef _Ios_Seekdir seekdir;


    static const seekdir beg = _S_beg;


    static const seekdir cur = _S_cur;


    static const seekdir end = _S_end;



    typedef int io_state
      __attribute__ ((__deprecated__ ("use '" "std::iostate" "' instead")));
    typedef int open_mode
      __attribute__ ((__deprecated__ ("use '" "std::openmode" "' instead")));
    typedef int seek_dir
      __attribute__ ((__deprecated__ ("use '" "std::seekdir" "' instead")));

    typedef std::streampos streampos
      __attribute__ ((__deprecated__ ("use '" "std::streampos" "' instead")));
    typedef std::streamoff streamoff
      __attribute__ ((__deprecated__ ("use '" "std::streamoff" "' instead")));
# 521 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    enum event
    {
      erase_event,
      imbue_event,
      copyfmt_event
    };
# 538 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    typedef void (*event_callback) (event __e, ios_base& __b, int __i);
# 550 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    void
    register_callback(event_callback __fn, int __index);

  protected:
    streamsize _M_precision;
    streamsize _M_width;
    fmtflags _M_flags;
    iostate _M_exception;
    iostate _M_streambuf_state;



    struct _Callback_list
    {

      _Callback_list* _M_next;
      ios_base::event_callback _M_fn;
      int _M_index;
      _Atomic_word _M_refcount;

      _Callback_list(ios_base::event_callback __fn, int __index,
       _Callback_list* __cb)
      : _M_next(__cb), _M_fn(__fn), _M_index(__index), _M_refcount(0) { }

      void
      _M_add_reference() { __gnu_cxx::__atomic_add_dispatch(&_M_refcount, 1); }


      int
      _M_remove_reference()
      {

                                                             ;
        int __res = __gnu_cxx::__exchange_and_add_dispatch(&_M_refcount, -1);
        if (__res == 0)
          {
                                                                ;
          }
        return __res;
      }
    };

     _Callback_list* _M_callbacks;

    void
    _M_call_callbacks(event __ev) throw();

    void
    _M_dispose_callbacks(void) throw();


    struct _Words
    {
      void* _M_pword;
      long _M_iword;
      _Words() : _M_pword(0), _M_iword(0) { }
    };


    _Words _M_word_zero;



    enum { _S_local_word_size = 8 };
    _Words _M_local_word[_S_local_word_size];


    int _M_word_size;
    _Words* _M_word;

    _Words&
    _M_grow_words(int __index, bool __iword);


    locale _M_ios_locale;

    void
    _M_init() throw();

  public:





    class Init
    {
      friend class ios_base;
    public:
      Init();
      ~Init();


      Init(const Init&) = default;
      Init& operator=(const Init&) = default;


    private:
      static _Atomic_word _S_refcount;
      static bool _S_synced_with_stdio;
    };






    fmtflags
    flags() const
    { return _M_flags; }
# 668 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    fmtflags
    flags(fmtflags __fmtfl)
    {
      fmtflags __old = _M_flags;
      _M_flags = __fmtfl;
      return __old;
    }
# 684 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    fmtflags
    setf(fmtflags __fmtfl)
    {
      fmtflags __old = _M_flags;
      _M_flags |= __fmtfl;
      return __old;
    }
# 701 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    fmtflags
    setf(fmtflags __fmtfl, fmtflags __mask)
    {
      fmtflags __old = _M_flags;
      _M_flags &= ~__mask;
      _M_flags |= (__fmtfl & __mask);
      return __old;
    }







    void
    unsetf(fmtflags __mask)
    { _M_flags &= ~__mask; }
# 727 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    streamsize
    precision() const
    { return _M_precision; }






    streamsize
    precision(streamsize __prec)
    {
      streamsize __old = _M_precision;
      _M_precision = __prec;
      return __old;
    }







    streamsize
    width() const
    { return _M_width; }






    streamsize
    width(streamsize __wide)
    {
      streamsize __old = _M_width;
      _M_width = __wide;
      return __old;
    }
# 778 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    static bool
    sync_with_stdio(bool __sync = true);
# 790 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    locale
    imbue(const locale& __loc) throw();
# 801 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    locale
    getloc() const
    { return _M_ios_locale; }
# 812 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    const locale&
    _M_getloc() const
    { return _M_ios_locale; }
# 831 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    static int
    xalloc() throw();
# 847 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    long&
    iword(int __ix)
    {
      _Words& __word = ((unsigned)__ix < (unsigned)_M_word_size)
   ? _M_word[__ix] : _M_grow_words(__ix, true);
      return __word._M_iword;
    }
# 868 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    void*&
    pword(int __ix)
    {
      _Words& __word = ((unsigned)__ix < (unsigned)_M_word_size)
   ? _M_word[__ix] : _M_grow_words(__ix, false);
      return __word._M_pword;
    }
# 885 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
    virtual ~ios_base();

  protected:
    ios_base() throw ();
# 899 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ios_base.h" 3
  public:
    ios_base(const ios_base&) = delete;

    ios_base&
    operator=(const ios_base&) = delete;

  protected:
    void
    _M_move(ios_base&) noexcept;

    void
    _M_swap(ios_base& __rhs) noexcept;

  };



  inline ios_base&
  boolalpha(ios_base& __base)
  {
    __base.setf(ios_base::boolalpha);
    return __base;
  }


  inline ios_base&
  noboolalpha(ios_base& __base)
  {
    __base.unsetf(ios_base::boolalpha);
    return __base;
  }


  inline ios_base&
  showbase(ios_base& __base)
  {
    __base.setf(ios_base::showbase);
    return __base;
  }


  inline ios_base&
  noshowbase(ios_base& __base)
  {
    __base.unsetf(ios_base::showbase);
    return __base;
  }


  inline ios_base&
  showpoint(ios_base& __base)
  {
    __base.setf(ios_base::showpoint);
    return __base;
  }


  inline ios_base&
  noshowpoint(ios_base& __base)
  {
    __base.unsetf(ios_base::showpoint);
    return __base;
  }


  inline ios_base&
  showpos(ios_base& __base)
  {
    __base.setf(ios_base::showpos);
    return __base;
  }


  inline ios_base&
  noshowpos(ios_base& __base)
  {
    __base.unsetf(ios_base::showpos);
    return __base;
  }


  inline ios_base&
  skipws(ios_base& __base)
  {
    __base.setf(ios_base::skipws);
    return __base;
  }


  inline ios_base&
  noskipws(ios_base& __base)
  {
    __base.unsetf(ios_base::skipws);
    return __base;
  }


  inline ios_base&
  uppercase(ios_base& __base)
  {
    __base.setf(ios_base::uppercase);
    return __base;
  }


  inline ios_base&
  nouppercase(ios_base& __base)
  {
    __base.unsetf(ios_base::uppercase);
    return __base;
  }


  inline ios_base&
  unitbuf(ios_base& __base)
  {
     __base.setf(ios_base::unitbuf);
     return __base;
  }


  inline ios_base&
  nounitbuf(ios_base& __base)
  {
     __base.unsetf(ios_base::unitbuf);
     return __base;
  }



  inline ios_base&
  internal(ios_base& __base)
  {
     __base.setf(ios_base::internal, ios_base::adjustfield);
     return __base;
  }


  inline ios_base&
  left(ios_base& __base)
  {
    __base.setf(ios_base::left, ios_base::adjustfield);
    return __base;
  }


  inline ios_base&
  right(ios_base& __base)
  {
    __base.setf(ios_base::right, ios_base::adjustfield);
    return __base;
  }



  inline ios_base&
  dec(ios_base& __base)
  {
    __base.setf(ios_base::dec, ios_base::basefield);
    return __base;
  }


  inline ios_base&
  hex(ios_base& __base)
  {
    __base.setf(ios_base::hex, ios_base::basefield);
    return __base;
  }


  inline ios_base&
  oct(ios_base& __base)
  {
    __base.setf(ios_base::oct, ios_base::basefield);
    return __base;
  }



  inline ios_base&
  fixed(ios_base& __base)
  {
    __base.setf(ios_base::fixed, ios_base::floatfield);
    return __base;
  }


  inline ios_base&
  scientific(ios_base& __base)
  {
    __base.setf(ios_base::scientific, ios_base::floatfield);
    return __base;
  }






  inline ios_base&
  hexfloat(ios_base& __base)
  {
    __base.setf(ios_base::fixed | ios_base::scientific, ios_base::floatfield);
    return __base;
  }


  inline ios_base&
  defaultfloat(ios_base& __base)
  {
    __base.unsetf(ios_base::floatfield);
    return __base;
  }



}
# 43 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ios" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3








namespace std __attribute__ ((__visibility__ ("default")))
{




  template<typename _CharT, typename _Traits>
    streamsize
    __copy_streambufs_eof(basic_streambuf<_CharT, _Traits>*,
     basic_streambuf<_CharT, _Traits>*, bool&);
# 121 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
  template<typename _CharT, typename _Traits>
    class basic_streambuf
    {
    public:






      typedef _CharT char_type;
      typedef _Traits traits_type;
      typedef typename traits_type::int_type int_type;
      typedef typename traits_type::pos_type pos_type;
      typedef typename traits_type::off_type off_type;




      typedef basic_streambuf<char_type, traits_type> __streambuf_type;


      friend class basic_ios<char_type, traits_type>;
      friend class basic_istream<char_type, traits_type>;
      friend class basic_ostream<char_type, traits_type>;
      friend class istreambuf_iterator<char_type, traits_type>;
      friend class ostreambuf_iterator<char_type, traits_type>;

      friend streamsize
      __copy_streambufs_eof<>(basic_streambuf*, basic_streambuf*, bool&);

      template<bool _IsMove, typename _CharT2>
        friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
            _CharT2*>::__type
        __copy_move_a2(istreambuf_iterator<_CharT2>,
         istreambuf_iterator<_CharT2>, _CharT2*);

      template<typename _CharT2>
        friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
      istreambuf_iterator<_CharT2> >::__type
        find(istreambuf_iterator<_CharT2>, istreambuf_iterator<_CharT2>,
      const _CharT2&);

      template<typename _CharT2, typename _Distance>
        friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
            void>::__type
        advance(istreambuf_iterator<_CharT2>&, _Distance);

      friend void __istream_extract(istream&, char*, streamsize);

      template<typename _CharT2, typename _Traits2, typename _Alloc>
        friend basic_istream<_CharT2, _Traits2>&
        operator>>(basic_istream<_CharT2, _Traits2>&,
     basic_string<_CharT2, _Traits2, _Alloc>&);

      template<typename _CharT2, typename _Traits2, typename _Alloc>
        friend basic_istream<_CharT2, _Traits2>&
        getline(basic_istream<_CharT2, _Traits2>&,
  basic_string<_CharT2, _Traits2, _Alloc>&, _CharT2);

    protected:







      char_type* _M_in_beg;
      char_type* _M_in_cur;
      char_type* _M_in_end;
      char_type* _M_out_beg;
      char_type* _M_out_cur;
      char_type* _M_out_end;


      locale _M_buf_locale;

  public:

      virtual
      ~basic_streambuf()
      { }
# 213 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      locale
      pubimbue(const locale& __loc)
      {
 locale __tmp(this->getloc());
 this->imbue(__loc);
 _M_buf_locale = __loc;
 return __tmp;
      }
# 230 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      locale
      getloc() const
      { return _M_buf_locale; }
# 243 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      basic_streambuf*
      pubsetbuf(char_type* __s, streamsize __n)
      { return this->setbuf(__s, __n); }
# 255 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      pos_type
      pubseekoff(off_type __off, ios_base::seekdir __way,
   ios_base::openmode __mode = ios_base::in | ios_base::out)
      { return this->seekoff(__off, __way, __mode); }
# 267 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      pos_type
      pubseekpos(pos_type __sp,
   ios_base::openmode __mode = ios_base::in | ios_base::out)
      { return this->seekpos(__sp, __mode); }




      int
      pubsync() { return this->sync(); }
# 288 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      streamsize
      in_avail()
      {
 const streamsize __ret = this->egptr() - this->gptr();
 return __ret ? __ret : this->showmanyc();
      }
# 302 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      snextc()
      {
 int_type __ret = traits_type::eof();
 if (__builtin_expect(!traits_type::eq_int_type(this->sbumpc(),
             __ret), true))
   __ret = this->sgetc();
 return __ret;
      }
# 320 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      sbumpc()
      {
 int_type __ret;
 if (__builtin_expect(this->gptr() < this->egptr(), true))
   {
     __ret = traits_type::to_int_type(*this->gptr());
     this->gbump(1);
   }
 else
   __ret = this->uflow();
 return __ret;
      }
# 342 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      sgetc()
      {
 int_type __ret;
 if (__builtin_expect(this->gptr() < this->egptr(), true))
   __ret = traits_type::to_int_type(*this->gptr());
 else
   __ret = this->underflow();
 return __ret;
      }
# 361 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      streamsize
      sgetn(char_type* __s, streamsize __n)
      { return this->xsgetn(__s, __n); }
# 376 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      sputbackc(char_type __c)
      {
 int_type __ret;
 const bool __testpos = this->eback() < this->gptr();
 if (__builtin_expect(!__testpos ||
        !traits_type::eq(__c, this->gptr()[-1]), false))
   __ret = this->pbackfail(traits_type::to_int_type(__c));
 else
   {
     this->gbump(-1);
     __ret = traits_type::to_int_type(*this->gptr());
   }
 return __ret;
      }
# 401 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      sungetc()
      {
 int_type __ret;
 if (__builtin_expect(this->eback() < this->gptr(), true))
   {
     this->gbump(-1);
     __ret = traits_type::to_int_type(*this->gptr());
   }
 else
   __ret = this->pbackfail();
 return __ret;
      }
# 428 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      int_type
      sputc(char_type __c)
      {
 int_type __ret;
 if (__builtin_expect(this->pptr() < this->epptr(), true))
   {
     *this->pptr() = __c;
     this->pbump(1);
     __ret = traits_type::to_int_type(__c);
   }
 else
   __ret = this->overflow(traits_type::to_int_type(__c));
 return __ret;
      }
# 454 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      streamsize
      sputn(const char_type* __s, streamsize __n)
      { return this->xsputn(__s, __n); }

    protected:
# 468 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      basic_streambuf()
      : _M_in_beg(0), _M_in_cur(0), _M_in_end(0),
      _M_out_beg(0), _M_out_cur(0), _M_out_end(0),
      _M_buf_locale(locale())
      { }
# 486 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      char_type*
      eback() const { return _M_in_beg; }

      char_type*
      gptr() const { return _M_in_cur; }

      char_type*
      egptr() const { return _M_in_end; }
# 502 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      void
      gbump(int __n) { _M_in_cur += __n; }
# 513 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      void
      setg(char_type* __gbeg, char_type* __gnext, char_type* __gend)
      {
 _M_in_beg = __gbeg;
 _M_in_cur = __gnext;
 _M_in_end = __gend;
      }
# 533 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      char_type*
      pbase() const { return _M_out_beg; }

      char_type*
      pptr() const { return _M_out_cur; }

      char_type*
      epptr() const { return _M_out_end; }
# 549 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      void
      pbump(int __n) { _M_out_cur += __n; }
# 559 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      void
      setp(char_type* __pbeg, char_type* __pend)
      {
 _M_out_beg = _M_out_cur = __pbeg;
 _M_out_end = __pend;
      }
# 580 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual void
      imbue(const locale& __loc __attribute__ ((__unused__)))
      { }
# 595 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual basic_streambuf<char_type,_Traits>*
      setbuf(char_type*, streamsize)
      { return this; }
# 606 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual pos_type
      seekoff(off_type, ios_base::seekdir,
       ios_base::openmode = ios_base::in | ios_base::out)
      { return pos_type(off_type(-1)); }
# 618 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual pos_type
      seekpos(pos_type,
       ios_base::openmode = ios_base::in | ios_base::out)
      { return pos_type(off_type(-1)); }
# 631 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual int
      sync() { return 0; }
# 653 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual streamsize
      showmanyc() { return 0; }
# 669 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual streamsize
      xsgetn(char_type* __s, streamsize __n);
# 691 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual int_type
      underflow()
      { return traits_type::eof(); }
# 704 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual int_type
      uflow()
      {
 int_type __ret = traits_type::eof();
 const bool __testeof = traits_type::eq_int_type(this->underflow(),
       __ret);
 if (!__testeof)
   {
     __ret = traits_type::to_int_type(*this->gptr());
     this->gbump(1);
   }
 return __ret;
      }
# 728 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual int_type
      pbackfail(int_type __c __attribute__ ((__unused__)) = traits_type::eof())
      { return traits_type::eof(); }
# 746 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual streamsize
      xsputn(const char_type* __s, streamsize __n);
# 772 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      virtual int_type
      overflow(int_type __c __attribute__ ((__unused__)) = traits_type::eof())
      { return traits_type::eof(); }



    public:
# 787 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 3
      __attribute__ ((__deprecated__ ("use '" "std::basic_streambuf::sbumpc" "' instead")))
      void
      stossc()
      {
 if (this->gptr() < this->egptr())
   this->gbump(1);
 else
   this->uflow();
      }



      void
      __safe_gbump(streamsize __n) { _M_in_cur += __n; }

      void
      __safe_pbump(streamsize __n) { _M_out_cur += __n; }




    protected:

      basic_streambuf(const basic_streambuf&);

      basic_streambuf&
      operator=(const basic_streambuf&);


      void
      swap(basic_streambuf& __sb)
      {
 std::swap(_M_in_beg, __sb._M_in_beg);
 std::swap(_M_in_cur, __sb._M_in_cur);
 std::swap(_M_in_end, __sb._M_in_end);
 std::swap(_M_out_beg, __sb._M_out_beg);
 std::swap(_M_out_cur, __sb._M_out_cur);
 std::swap(_M_out_end, __sb._M_out_end);
 std::swap(_M_buf_locale, __sb._M_buf_locale);
      }

    };


  template<typename _CharT, typename _Traits>
    std::basic_streambuf<_CharT, _Traits>::
    basic_streambuf(const basic_streambuf&) = default;

  template<typename _CharT, typename _Traits>
    std::basic_streambuf<_CharT, _Traits>&
    std::basic_streambuf<_CharT, _Traits>::
    operator=(const basic_streambuf&) = default;



  template<>
    streamsize
    __copy_streambufs_eof(basic_streambuf<char>* __sbin,
     basic_streambuf<char>* __sbout, bool& __ineof);

  template<>
    streamsize
    __copy_streambufs_eof(basic_streambuf<wchar_t>* __sbin,
     basic_streambuf<wchar_t>* __sbout, bool& __ineof);





}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf.tcc" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf.tcc" 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _CharT, typename _Traits>
    streamsize
    basic_streambuf<_CharT, _Traits>::
    xsgetn(char_type* __s, streamsize __n)
    {
      streamsize __ret = 0;
      while (__ret < __n)
 {
   const streamsize __buf_len = this->egptr() - this->gptr();
   if (__buf_len)
     {
       const streamsize __remaining = __n - __ret;
       const streamsize __len = std::min(__buf_len, __remaining);
       traits_type::copy(__s, this->gptr(), __len);
       __ret += __len;
       __s += __len;
       this->__safe_gbump(__len);
     }

   if (__ret < __n)
     {
       const int_type __c = this->uflow();
       if (!traits_type::eq_int_type(__c, traits_type::eof()))
  {
    traits_type::assign(*__s++, traits_type::to_char_type(__c));
    ++__ret;
  }
       else
  break;
     }
 }
      return __ret;
    }

  template<typename _CharT, typename _Traits>
    streamsize
    basic_streambuf<_CharT, _Traits>::
    xsputn(const char_type* __s, streamsize __n)
    {
      streamsize __ret = 0;
      while (__ret < __n)
 {
   const streamsize __buf_len = this->epptr() - this->pptr();
   if (__buf_len)
     {
       const streamsize __remaining = __n - __ret;
       const streamsize __len = std::min(__buf_len, __remaining);
       traits_type::copy(this->pptr(), __s, __len);
       __ret += __len;
       __s += __len;
       this->__safe_pbump(__len);
     }

   if (__ret < __n)
     {
       int_type __c = this->overflow(traits_type::to_int_type(*__s));
       if (!traits_type::eq_int_type(__c, traits_type::eof()))
  {
    ++__ret;
    ++__s;
  }
       else
  break;
     }
 }
      return __ret;
    }




  template<typename _CharT, typename _Traits>
    streamsize
    __copy_streambufs_eof(basic_streambuf<_CharT, _Traits>* __sbin,
     basic_streambuf<_CharT, _Traits>* __sbout,
     bool& __ineof)
    {
      streamsize __ret = 0;
      __ineof = true;
      typename _Traits::int_type __c = __sbin->sgetc();
      while (!_Traits::eq_int_type(__c, _Traits::eof()))
 {
   __c = __sbout->sputc(_Traits::to_char_type(__c));
   if (_Traits::eq_int_type(__c, _Traits::eof()))
     {
       __ineof = false;
       break;
     }
   ++__ret;
   __c = __sbin->snextc();
 }
      return __ret;
    }

  template<typename _CharT, typename _Traits>
    inline streamsize
    __copy_streambufs(basic_streambuf<_CharT, _Traits>* __sbin,
        basic_streambuf<_CharT, _Traits>* __sbout)
    {
      bool __ineof;
      return __copy_streambufs_eof(__sbin, __sbout, __ineof);
    }




  extern template class basic_streambuf<char>;

  extern template
    streamsize
    __copy_streambufs(basic_streambuf<char>*,
        basic_streambuf<char>*);


  extern template class basic_streambuf<wchar_t>;

  extern template
    streamsize
    __copy_streambufs(basic_streambuf<wchar_t>*,
        basic_streambuf<wchar_t>*);




}
# 859 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/streambuf" 2 3
# 44 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ios" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwctype" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwctype" 3
# 50 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwctype" 3
# 1 "/usr/include/wctype.h" 1 3 4
# 38 "/usr/include/wctype.h" 3 4
# 1 "/usr/include/x86_64-linux-gnu/bits/wctype-wchar.h" 1 3 4
# 38 "/usr/include/x86_64-linux-gnu/bits/wctype-wchar.h" 3 4
typedef unsigned long int wctype_t;
# 56 "/usr/include/x86_64-linux-gnu/bits/wctype-wchar.h" 3 4
enum
{
  __ISwupper = 0,
  __ISwlower = 1,
  __ISwalpha = 2,
  __ISwdigit = 3,
  __ISwxdigit = 4,
  __ISwspace = 5,
  __ISwprint = 6,
  __ISwgraph = 7,
  __ISwblank = 8,
  __ISwcntrl = 9,
  __ISwpunct = 10,
  __ISwalnum = 11,

  _ISwupper = ((__ISwupper) < 8 ? (int) ((1UL << (__ISwupper)) << 24) : ((__ISwupper) < 16 ? (int) ((1UL << (__ISwupper)) << 8) : ((__ISwupper) < 24 ? (int) ((1UL << (__ISwupper)) >> 8) : (int) ((1UL << (__ISwupper)) >> 24)))),
  _ISwlower = ((__ISwlower) < 8 ? (int) ((1UL << (__ISwlower)) << 24) : ((__ISwlower) < 16 ? (int) ((1UL << (__ISwlower)) << 8) : ((__ISwlower) < 24 ? (int) ((1UL << (__ISwlower)) >> 8) : (int) ((1UL << (__ISwlower)) >> 24)))),
  _ISwalpha = ((__ISwalpha) < 8 ? (int) ((1UL << (__ISwalpha)) << 24) : ((__ISwalpha) < 16 ? (int) ((1UL << (__ISwalpha)) << 8) : ((__ISwalpha) < 24 ? (int) ((1UL << (__ISwalpha)) >> 8) : (int) ((1UL << (__ISwalpha)) >> 24)))),
  _ISwdigit = ((__ISwdigit) < 8 ? (int) ((1UL << (__ISwdigit)) << 24) : ((__ISwdigit) < 16 ? (int) ((1UL << (__ISwdigit)) << 8) : ((__ISwdigit) < 24 ? (int) ((1UL << (__ISwdigit)) >> 8) : (int) ((1UL << (__ISwdigit)) >> 24)))),
  _ISwxdigit = ((__ISwxdigit) < 8 ? (int) ((1UL << (__ISwxdigit)) << 24) : ((__ISwxdigit) < 16 ? (int) ((1UL << (__ISwxdigit)) << 8) : ((__ISwxdigit) < 24 ? (int) ((1UL << (__ISwxdigit)) >> 8) : (int) ((1UL << (__ISwxdigit)) >> 24)))),
  _ISwspace = ((__ISwspace) < 8 ? (int) ((1UL << (__ISwspace)) << 24) : ((__ISwspace) < 16 ? (int) ((1UL << (__ISwspace)) << 8) : ((__ISwspace) < 24 ? (int) ((1UL << (__ISwspace)) >> 8) : (int) ((1UL << (__ISwspace)) >> 24)))),
  _ISwprint = ((__ISwprint) < 8 ? (int) ((1UL << (__ISwprint)) << 24) : ((__ISwprint) < 16 ? (int) ((1UL << (__ISwprint)) << 8) : ((__ISwprint) < 24 ? (int) ((1UL << (__ISwprint)) >> 8) : (int) ((1UL << (__ISwprint)) >> 24)))),
  _ISwgraph = ((__ISwgraph) < 8 ? (int) ((1UL << (__ISwgraph)) << 24) : ((__ISwgraph) < 16 ? (int) ((1UL << (__ISwgraph)) << 8) : ((__ISwgraph) < 24 ? (int) ((1UL << (__ISwgraph)) >> 8) : (int) ((1UL << (__ISwgraph)) >> 24)))),
  _ISwblank = ((__ISwblank) < 8 ? (int) ((1UL << (__ISwblank)) << 24) : ((__ISwblank) < 16 ? (int) ((1UL << (__ISwblank)) << 8) : ((__ISwblank) < 24 ? (int) ((1UL << (__ISwblank)) >> 8) : (int) ((1UL << (__ISwblank)) >> 24)))),
  _ISwcntrl = ((__ISwcntrl) < 8 ? (int) ((1UL << (__ISwcntrl)) << 24) : ((__ISwcntrl) < 16 ? (int) ((1UL << (__ISwcntrl)) << 8) : ((__ISwcntrl) < 24 ? (int) ((1UL << (__ISwcntrl)) >> 8) : (int) ((1UL << (__ISwcntrl)) >> 24)))),
  _ISwpunct = ((__ISwpunct) < 8 ? (int) ((1UL << (__ISwpunct)) << 24) : ((__ISwpunct) < 16 ? (int) ((1UL << (__ISwpunct)) << 8) : ((__ISwpunct) < 24 ? (int) ((1UL << (__ISwpunct)) >> 8) : (int) ((1UL << (__ISwpunct)) >> 24)))),
  _ISwalnum = ((__ISwalnum) < 8 ? (int) ((1UL << (__ISwalnum)) << 24) : ((__ISwalnum) < 16 ? (int) ((1UL << (__ISwalnum)) << 8) : ((__ISwalnum) < 24 ? (int) ((1UL << (__ISwalnum)) >> 8) : (int) ((1UL << (__ISwalnum)) >> 24))))
};



extern "C" {







extern int iswalnum (wint_t __wc) noexcept (true);





extern int iswalpha (wint_t __wc) noexcept (true);


extern int iswcntrl (wint_t __wc) noexcept (true);



extern int iswdigit (wint_t __wc) noexcept (true);



extern int iswgraph (wint_t __wc) noexcept (true);




extern int iswlower (wint_t __wc) noexcept (true);


extern int iswprint (wint_t __wc) noexcept (true);




extern int iswpunct (wint_t __wc) noexcept (true);




extern int iswspace (wint_t __wc) noexcept (true);




extern int iswupper (wint_t __wc) noexcept (true);




extern int iswxdigit (wint_t __wc) noexcept (true);





extern int iswblank (wint_t __wc) noexcept (true);
# 155 "/usr/include/x86_64-linux-gnu/bits/wctype-wchar.h" 3 4
extern wctype_t wctype (const char *__property) noexcept (true);



extern int iswctype (wint_t __wc, wctype_t __desc) noexcept (true);






extern wint_t towlower (wint_t __wc) noexcept (true);


extern wint_t towupper (wint_t __wc) noexcept (true);

}
# 39 "/usr/include/wctype.h" 2 3 4





extern "C" {



typedef const __int32_t *wctrans_t;



extern wctrans_t wctrans (const char *__property) noexcept (true);


extern wint_t towctrans (wint_t __wc, wctrans_t __desc) noexcept (true);







extern int iswalnum_l (wint_t __wc, locale_t __locale) noexcept (true);





extern int iswalpha_l (wint_t __wc, locale_t __locale) noexcept (true);


extern int iswcntrl_l (wint_t __wc, locale_t __locale) noexcept (true);



extern int iswdigit_l (wint_t __wc, locale_t __locale) noexcept (true);



extern int iswgraph_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswlower_l (wint_t __wc, locale_t __locale) noexcept (true);


extern int iswprint_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswpunct_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswspace_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswupper_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswxdigit_l (wint_t __wc, locale_t __locale) noexcept (true);




extern int iswblank_l (wint_t __wc, locale_t __locale) noexcept (true);



extern wctype_t wctype_l (const char *__property, locale_t __locale)
     noexcept (true);



extern int iswctype_l (wint_t __wc, wctype_t __desc, locale_t __locale)
     noexcept (true);






extern wint_t towlower_l (wint_t __wc, locale_t __locale) noexcept (true);


extern wint_t towupper_l (wint_t __wc, locale_t __locale) noexcept (true);



extern wctrans_t wctrans_l (const char *__property, locale_t __locale)
     noexcept (true);


extern wint_t towctrans_l (wint_t __wc, wctrans_t __desc,
      locale_t __locale) noexcept (true);



}
# 51 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwctype" 2 3
# 80 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cwctype" 3
namespace std
{
  using ::wctrans_t;
  using ::wctype_t;
  using ::wint_t;

  using ::iswalnum;
  using ::iswalpha;

  using ::iswblank;

  using ::iswcntrl;
  using ::iswctype;
  using ::iswdigit;
  using ::iswgraph;
  using ::iswlower;
  using ::iswprint;
  using ::iswpunct;
  using ::iswspace;
  using ::iswupper;
  using ::iswxdigit;
  using ::towctrans;
  using ::towlower;
  using ::towupper;
  using ::wctrans;
  using ::wctype;
}
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cctype" 3
# 41 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/ctype_base.h" 1 3
# 36 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/ctype_base.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{



  struct ctype_base
  {

    typedef const int* __to_type;



    typedef unsigned short mask;
    static const mask upper = _ISupper;
    static const mask lower = _ISlower;
    static const mask alpha = _ISalpha;
    static const mask digit = _ISdigit;
    static const mask xdigit = _ISxdigit;
    static const mask space = _ISspace;
    static const mask print = _ISprint;
    static const mask graph = _ISalpha | _ISdigit | _ISpunct;
    static const mask cntrl = _IScntrl;
    static const mask punct = _ISpunct;
    static const mask alnum = _ISalpha | _ISdigit;

    static const mask blank = _ISblank;

  };


}
# 42 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3






# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf_iterator.h" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf_iterator.h" 3




namespace std __attribute__ ((__visibility__ ("default")))
{








#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"


  template<typename _CharT, typename _Traits>
    class istreambuf_iterator
    : public iterator<input_iterator_tag, _CharT, typename _Traits::off_type,
        _CharT*, _CharT>
    {
    public:
# 69 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf_iterator.h" 3
      typedef _CharT char_type;
      typedef _Traits traits_type;
      typedef typename _Traits::int_type int_type;
      typedef basic_streambuf<_CharT, _Traits> streambuf_type;
      typedef basic_istream<_CharT, _Traits> istream_type;


      template<typename _CharT2>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
        ostreambuf_iterator<_CharT2> >::__type
 copy(istreambuf_iterator<_CharT2>, istreambuf_iterator<_CharT2>,
      ostreambuf_iterator<_CharT2>);

      template<bool _IsMove, typename _CharT2>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
            _CharT2*>::__type
 __copy_move_a2(istreambuf_iterator<_CharT2>,
         istreambuf_iterator<_CharT2>, _CharT2*);

      template<typename _CharT2, typename _Size>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
            _CharT2*>::__type
 __copy_n_a(istreambuf_iterator<_CharT2>, _Size, _CharT2*, bool);

      template<typename _CharT2>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
        istreambuf_iterator<_CharT2> >::__type
 find(istreambuf_iterator<_CharT2>, istreambuf_iterator<_CharT2>,
      const _CharT2&);

      template<typename _CharT2, typename _Distance>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
            void>::__type
 advance(istreambuf_iterator<_CharT2>&, _Distance);

    private:







      mutable streambuf_type* _M_sbuf;
      int_type _M_c;

    public:

      constexpr istreambuf_iterator() noexcept
      : _M_sbuf(0), _M_c(traits_type::eof()) { }







      istreambuf_iterator(const istreambuf_iterator&) noexcept = default;

      ~istreambuf_iterator() = default;



      istreambuf_iterator(istream_type& __s) noexcept
      : _M_sbuf(__s.rdbuf()), _M_c(traits_type::eof()) { }


      istreambuf_iterator(streambuf_type* __s) noexcept
      : _M_sbuf(__s), _M_c(traits_type::eof()) { }


      istreambuf_iterator&
      operator=(const istreambuf_iterator&) noexcept = default;






      char_type
      operator*() const
      {
 int_type __c = _M_get();
# 160 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf_iterator.h" 3
 return traits_type::to_char_type(__c);
      }


      istreambuf_iterator&
      operator++()
      {



                        ;

 _M_sbuf->sbumpc();
 _M_c = traits_type::eof();
 return *this;
      }


      istreambuf_iterator
      operator++(int)
      {



                        ;

 istreambuf_iterator __old = *this;
 __old._M_c = _M_sbuf->sbumpc();
 _M_c = traits_type::eof();
 return __old;
      }






      bool
      equal(const istreambuf_iterator& __b) const
      { return _M_at_eof() == __b._M_at_eof(); }

    private:
      int_type
      _M_get() const
      {
 int_type __ret = _M_c;
 if (_M_sbuf && _S_is_eof(__ret) && _S_is_eof(__ret = _M_sbuf->sgetc()))
   _M_sbuf = 0;
 return __ret;
      }

      bool
      _M_at_eof() const
      { return _S_is_eof(_M_get()); }

      static bool
      _S_is_eof(int_type __c)
      {
 const int_type __eof = traits_type::eof();
 return traits_type::eq_int_type(__c, __eof);
      }







    };

  template<typename _CharT, typename _Traits>

    inline bool
    operator==(const istreambuf_iterator<_CharT, _Traits>& __a,
        const istreambuf_iterator<_CharT, _Traits>& __b)
    { return __a.equal(__b); }


  template<typename _CharT, typename _Traits>

    inline bool
    operator!=(const istreambuf_iterator<_CharT, _Traits>& __a,
        const istreambuf_iterator<_CharT, _Traits>& __b)
    { return !__a.equal(__b); }



  template<typename _CharT, typename _Traits>
    class ostreambuf_iterator
    : public iterator<output_iterator_tag, void, void, void, void>
    {
    public:






      typedef _CharT char_type;
      typedef _Traits traits_type;
      typedef basic_streambuf<_CharT, _Traits> streambuf_type;
      typedef basic_ostream<_CharT, _Traits> ostream_type;


      template<typename _CharT2>
 friend typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value,
        ostreambuf_iterator<_CharT2> >::__type
 copy(istreambuf_iterator<_CharT2>, istreambuf_iterator<_CharT2>,
      ostreambuf_iterator<_CharT2>);

    private:
      streambuf_type* _M_sbuf;
      bool _M_failed;

    public:
# 283 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/streambuf_iterator.h" 3
      ostreambuf_iterator(ostream_type& __s) noexcept
      : _M_sbuf(__s.rdbuf()), _M_failed(!_M_sbuf) { }


      ostreambuf_iterator(streambuf_type* __s) noexcept
      : _M_sbuf(__s), _M_failed(!_M_sbuf) { }


      ostreambuf_iterator&
      operator=(_CharT __c)
      {
 if (!_M_failed &&
     _Traits::eq_int_type(_M_sbuf->sputc(__c), _Traits::eof()))
   _M_failed = true;
 return *this;
      }



      ostreambuf_iterator&
      operator*()
      { return *this; }


      ostreambuf_iterator&
      operator++(int)
      { return *this; }


      ostreambuf_iterator&
      operator++()
      { return *this; }



      bool
      failed() const noexcept
      { return _M_failed; }

      ostreambuf_iterator&
      _M_put(const _CharT* __ws, streamsize __len)
      {
 if (__builtin_expect(!_M_failed, true)
     && __builtin_expect(this->_M_sbuf->sputn(__ws, __len) != __len,
    false))
   _M_failed = true;
 return *this;
      }
    };
#pragma GCC diagnostic pop


  template<typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        ostreambuf_iterator<_CharT> >::__type
    copy(istreambuf_iterator<_CharT> __first,
  istreambuf_iterator<_CharT> __last,
  ostreambuf_iterator<_CharT> __result)
    {
      if (__first._M_sbuf && !__last._M_sbuf && !__result._M_failed)
 {
   bool __ineof;
   __copy_streambufs_eof(__first._M_sbuf, __result._M_sbuf, __ineof);
   if (!__ineof)
     __result._M_failed = true;
 }
      return __result;
    }

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        ostreambuf_iterator<_CharT> >::__type
    __copy_move_a2(_CharT* __first, _CharT* __last,
     ostreambuf_iterator<_CharT> __result)
    {
      const streamsize __num = __last - __first;
      if (__num > 0)
 __result._M_put(__first, __num);
      return __result;
    }

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        ostreambuf_iterator<_CharT> >::__type
    __copy_move_a2(const _CharT* __first, const _CharT* __last,
     ostreambuf_iterator<_CharT> __result)
    {
      const streamsize __num = __last - __first;
      if (__num > 0)
 __result._M_put(__first, __num);
      return __result;
    }

  template<bool _IsMove, typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        _CharT*>::__type
    __copy_move_a2(istreambuf_iterator<_CharT> __first,
     istreambuf_iterator<_CharT> __last, _CharT* __result)
    {
      typedef istreambuf_iterator<_CharT> __is_iterator_type;
      typedef typename __is_iterator_type::traits_type traits_type;
      typedef typename __is_iterator_type::streambuf_type streambuf_type;
      typedef typename traits_type::int_type int_type;

      if (__first._M_sbuf && !__last._M_sbuf)
 {
   streambuf_type* __sb = __first._M_sbuf;
   int_type __c = __sb->sgetc();
   while (!traits_type::eq_int_type(__c, traits_type::eof()))
     {
       const streamsize __n = __sb->egptr() - __sb->gptr();
       if (__n > 1)
  {
    traits_type::copy(__result, __sb->gptr(), __n);
    __sb->__safe_gbump(__n);
    __result += __n;
    __c = __sb->underflow();
  }
       else
  {
    *__result++ = traits_type::to_char_type(__c);
    __c = __sb->snextc();
  }
     }
 }
      return __result;
    }

  template<typename _CharT, typename _Size>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        _CharT*>::__type
    __copy_n_a(istreambuf_iterator<_CharT> __it, _Size __n, _CharT* __result,
        bool __strict __attribute__((__unused__)))
    {
      if (__n == 0)
 return __result;



                            ;
      _CharT* __beg = __result;
      __result += __it._M_sbuf->sgetn(__beg, __n);


                            ;
      return __result;
    }

  template<typename _CharT>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
          istreambuf_iterator<_CharT> >::__type
    find(istreambuf_iterator<_CharT> __first,
  istreambuf_iterator<_CharT> __last, const _CharT& __val)
    {
      typedef istreambuf_iterator<_CharT> __is_iterator_type;
      typedef typename __is_iterator_type::traits_type traits_type;
      typedef typename __is_iterator_type::streambuf_type streambuf_type;
      typedef typename traits_type::int_type int_type;
      const int_type __eof = traits_type::eof();

      if (__first._M_sbuf && !__last._M_sbuf)
 {
   const int_type __ival = traits_type::to_int_type(__val);
   streambuf_type* __sb = __first._M_sbuf;
   int_type __c = __sb->sgetc();
   while (!traits_type::eq_int_type(__c, __eof)
   && !traits_type::eq_int_type(__c, __ival))
     {
       streamsize __n = __sb->egptr() - __sb->gptr();
       if (__n > 1)
  {
    const _CharT* __p = traits_type::find(__sb->gptr(),
       __n, __val);
    if (__p)
      __n = __p - __sb->gptr();
    __sb->__safe_gbump(__n);
    __c = __sb->sgetc();
  }
       else
  __c = __sb->snextc();
     }

   __first._M_c = __eof;
 }

      return __first;
    }

  template<typename _CharT, typename _Distance>
    typename __gnu_cxx::__enable_if<__is_char<_CharT>::__value,
        void>::__type
    advance(istreambuf_iterator<_CharT>& __i, _Distance __n)
    {
      if (__n == 0)
 return;

      do { if (std::__is_constant_evaluated() && !bool(__n > 0)) __builtin_unreachable(); } while (false);


                           ;

      typedef istreambuf_iterator<_CharT> __is_iterator_type;
      typedef typename __is_iterator_type::traits_type traits_type;
      typedef typename __is_iterator_type::streambuf_type streambuf_type;
      typedef typename traits_type::int_type int_type;
      const int_type __eof = traits_type::eof();

      streambuf_type* __sb = __i._M_sbuf;
      while (__n > 0)
 {
   streamsize __size = __sb->egptr() - __sb->gptr();
   if (__size > __n)
     {
       __sb->__safe_gbump(__n);
       break;
     }

   __sb->__safe_gbump(__size);
   __n -= __size;
   if (traits_type::eq_int_type(__sb->underflow(), __eof))
     {


                      ;
       break;
     }
 }

      __i._M_c = __eof;
    }




}
# 49 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{
# 74 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _Tp>
    void
    __convert_to_v(const char*, _Tp&, ios_base::iostate&,
     const __c_locale&) throw();


  template<>
    void
    __convert_to_v(const char*, float&, ios_base::iostate&,
     const __c_locale&) throw();

  template<>
    void
    __convert_to_v(const char*, double&, ios_base::iostate&,
     const __c_locale&) throw();

  template<>
    void
    __convert_to_v(const char*, long double&, ios_base::iostate&,
     const __c_locale&) throw();



  template<typename _CharT, typename _Traits>
    struct __pad
    {
      static void
      _S_pad(ios_base& __io, _CharT __fill, _CharT* __news,
      const _CharT* __olds, streamsize __newlen, streamsize __oldlen);
    };






  template<typename _CharT>
    _CharT*
    __add_grouping(_CharT* __s, _CharT __sep,
     const char* __gbeg, size_t __gsize,
     const _CharT* __first, const _CharT* __last);




  template<typename _CharT>
    inline
    ostreambuf_iterator<_CharT>
    __write(ostreambuf_iterator<_CharT> __s, const _CharT* __ws, int __len)
    {
      __s._M_put(__ws, __len);
      return __s;
    }


  template<typename _CharT, typename _OutIter>
    inline
    _OutIter
    __write(_OutIter __s, const _CharT* __ws, int __len)
    {
      for (int __j = 0; __j < __len; __j++, ++__s)
 *__s = __ws[__j];
      return __s;
    }
# 152 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT>
    class __ctype_abstract_base : public locale::facet, public ctype_base
    {
    public:


      typedef _CharT char_type;
# 171 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      bool
      is(mask __m, char_type __c) const
      { return this->do_is(__m, __c); }
# 188 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      is(const char_type *__lo, const char_type *__hi, mask *__vec) const
      { return this->do_is(__lo, __hi, __vec); }
# 204 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      scan_is(mask __m, const char_type* __lo, const char_type* __hi) const
      { return this->do_scan_is(__m, __lo, __hi); }
# 220 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      scan_not(mask __m, const char_type* __lo, const char_type* __hi) const
      { return this->do_scan_not(__m, __lo, __hi); }
# 234 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      toupper(char_type __c) const
      { return this->do_toupper(__c); }
# 249 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      toupper(char_type *__lo, const char_type* __hi) const
      { return this->do_toupper(__lo, __hi); }
# 263 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      tolower(char_type __c) const
      { return this->do_tolower(__c); }
# 278 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      tolower(char_type* __lo, const char_type* __hi) const
      { return this->do_tolower(__lo, __hi); }
# 295 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      widen(char __c) const
      { return this->do_widen(__c); }
# 314 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char*
      widen(const char* __lo, const char* __hi, char_type* __to) const
      { return this->do_widen(__lo, __hi, __to); }
# 333 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char
      narrow(char_type __c, char __dfault) const
      { return this->do_narrow(__c, __dfault); }
# 355 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      narrow(const char_type* __lo, const char_type* __hi,
       char __dfault, char* __to) const
      { return this->do_narrow(__lo, __hi, __dfault, __to); }

    protected:
      explicit
      __ctype_abstract_base(size_t __refs = 0): facet(__refs) { }

      virtual
      ~__ctype_abstract_base() { }
# 380 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual bool
      do_is(mask __m, char_type __c) const = 0;
# 399 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_is(const char_type* __lo, const char_type* __hi,
     mask* __vec) const = 0;
# 418 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_scan_is(mask __m, const char_type* __lo,
   const char_type* __hi) const = 0;
# 437 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_scan_not(mask __m, const char_type* __lo,
    const char_type* __hi) const = 0;
# 455 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_toupper(char_type __c) const = 0;
# 472 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_toupper(char_type* __lo, const char_type* __hi) const = 0;
# 488 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_tolower(char_type __c) const = 0;
# 505 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_tolower(char_type* __lo, const char_type* __hi) const = 0;
# 524 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_widen(char __c) const = 0;
# 545 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char*
      do_widen(const char* __lo, const char* __hi, char_type* __to) const = 0;
# 566 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char
      do_narrow(char_type __c, char __dfault) const = 0;
# 591 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_narrow(const char_type* __lo, const char_type* __hi,
  char __dfault, char* __to) const = 0;
    };
# 614 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT>
    class ctype : public __ctype_abstract_base<_CharT>
    {
    public:

      typedef _CharT char_type;
      typedef typename __ctype_abstract_base<_CharT>::mask mask;


      static locale::id id;

      explicit
      ctype(size_t __refs = 0) : __ctype_abstract_base<_CharT>(__refs) { }

   protected:
      virtual
      ~ctype();

      virtual bool
      do_is(mask __m, char_type __c) const;

      virtual const char_type*
      do_is(const char_type* __lo, const char_type* __hi, mask* __vec) const;

      virtual const char_type*
      do_scan_is(mask __m, const char_type* __lo, const char_type* __hi) const;

      virtual const char_type*
      do_scan_not(mask __m, const char_type* __lo,
    const char_type* __hi) const;

      virtual char_type
      do_toupper(char_type __c) const;

      virtual const char_type*
      do_toupper(char_type* __lo, const char_type* __hi) const;

      virtual char_type
      do_tolower(char_type __c) const;

      virtual const char_type*
      do_tolower(char_type* __lo, const char_type* __hi) const;

      virtual char_type
      do_widen(char __c) const;

      virtual const char*
      do_widen(const char* __lo, const char* __hi, char_type* __dest) const;

      virtual char
      do_narrow(char_type, char __dfault) const;

      virtual const char_type*
      do_narrow(const char_type* __lo, const char_type* __hi,
  char __dfault, char* __to) const;
    };

  template<typename _CharT>
    locale::id ctype<_CharT>::id;



  template<typename _CharT, typename _Traits, typename _Alloc>
    class ctype<basic_string<_CharT, _Traits, _Alloc> >;
# 688 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<>
    class ctype<char> : public locale::facet, public ctype_base
    {
    public:


      typedef char char_type;

    protected:

      __c_locale _M_c_locale_ctype;
      bool _M_del;
      __to_type _M_toupper;
      __to_type _M_tolower;
      const mask* _M_table;
      mutable char _M_widen_ok;
      mutable char _M_widen[1 + static_cast<unsigned char>(-1)];
      mutable char _M_narrow[1 + static_cast<unsigned char>(-1)];
      mutable char _M_narrow_ok;


    public:

      static locale::id id;

      static const size_t table_size = 1 + static_cast<unsigned char>(-1);
# 725 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      ctype(const mask* __table = 0, bool __del = false, size_t __refs = 0);
# 738 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      ctype(__c_locale __cloc, const mask* __table = 0, bool __del = false,
     size_t __refs = 0);
# 751 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      inline bool
      is(mask __m, char __c) const;
# 766 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      inline const char*
      is(const char* __lo, const char* __hi, mask* __vec) const;
# 780 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      inline const char*
      scan_is(mask __m, const char* __lo, const char* __hi) const;
# 794 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      inline const char*
      scan_not(mask __m, const char* __lo, const char* __hi) const;
# 809 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      toupper(char_type __c) const
      { return this->do_toupper(__c); }
# 826 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      toupper(char_type *__lo, const char_type* __hi) const
      { return this->do_toupper(__lo, __hi); }
# 842 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      tolower(char_type __c) const
      { return this->do_tolower(__c); }
# 859 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      tolower(char_type* __lo, const char_type* __hi) const
      { return this->do_tolower(__lo, __hi); }
# 879 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      widen(char __c) const
      {
 if (_M_widen_ok)
   return _M_widen[static_cast<unsigned char>(__c)];
 this->_M_widen_init();
 return this->do_widen(__c);
      }
# 906 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char*
      widen(const char* __lo, const char* __hi, char_type* __to) const
      {
 if (_M_widen_ok == 1)
   {
     if (__builtin_expect(__hi != __lo, true))
       __builtin_memcpy(__to, __lo, __hi - __lo);
     return __hi;
   }
 if (!_M_widen_ok)
   _M_widen_init();
 return this->do_widen(__lo, __hi, __to);
      }
# 938 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char
      narrow(char_type __c, char __dfault) const
      {
 if (_M_narrow[static_cast<unsigned char>(__c)])
   return _M_narrow[static_cast<unsigned char>(__c)];
 const char __t = do_narrow(__c, __dfault);
 if (__t != __dfault)
   _M_narrow[static_cast<unsigned char>(__c)] = __t;
 return __t;
      }
# 971 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      const char_type*
      narrow(const char_type* __lo, const char_type* __hi,
      char __dfault, char* __to) const
      {
 if (__builtin_expect(_M_narrow_ok == 1, true))
   {
     if (__builtin_expect(__hi != __lo, true))
       __builtin_memcpy(__to, __lo, __hi - __lo);
     return __hi;
   }
 if (!_M_narrow_ok)
   _M_narrow_init();
 return this->do_narrow(__lo, __hi, __dfault, __to);
      }





      const mask*
      table() const throw()
      { return _M_table; }


      static const mask*
      classic_table() throw();
    protected:







      virtual
      ~ctype();
# 1021 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_toupper(char_type __c) const;
# 1038 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_toupper(char_type* __lo, const char_type* __hi) const;
# 1054 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_tolower(char_type __c) const;
# 1071 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_tolower(char_type* __lo, const char_type* __hi) const;
# 1091 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_widen(char __c) const
      { return __c; }
# 1114 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char*
      do_widen(const char* __lo, const char* __hi, char_type* __to) const
      {
 if (__builtin_expect(__hi != __lo, true))
   __builtin_memcpy(__to, __lo, __hi - __lo);
 return __hi;
      }
# 1141 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char
      do_narrow(char_type __c, char __dfault __attribute__((__unused__))) const
      { return __c; }
# 1167 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_narrow(const char_type* __lo, const char_type* __hi,
  char __dfault __attribute__((__unused__)), char* __to) const
      {
 if (__builtin_expect(__hi != __lo, true))
   __builtin_memcpy(__to, __lo, __hi - __lo);
 return __hi;
      }

    private:
      void _M_narrow_init() const;
      void _M_widen_init() const;
    };
# 1193 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<>
    class ctype<wchar_t> : public __ctype_abstract_base<wchar_t>
    {
    public:


      typedef wchar_t char_type;
      typedef wctype_t __wmask_type;

    protected:
      __c_locale _M_c_locale_ctype;


      bool _M_narrow_ok;
      char _M_narrow[128];
      wint_t _M_widen[1 + static_cast<unsigned char>(-1)];


      mask _M_bit[16];
      __wmask_type _M_wmask[16];

    public:


      static locale::id id;
# 1226 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      ctype(size_t __refs = 0);
# 1237 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      ctype(__c_locale __cloc, size_t __refs = 0);

    protected:
      __wmask_type
      _M_convert_to_wmask(const mask __m) const throw();


      virtual
      ~ctype();
# 1261 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual bool
      do_is(mask __m, char_type __c) const;
# 1280 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_is(const char_type* __lo, const char_type* __hi, mask* __vec) const;
# 1298 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_scan_is(mask __m, const char_type* __lo, const char_type* __hi) const;
# 1316 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_scan_not(mask __m, const char_type* __lo,
    const char_type* __hi) const;
# 1333 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_toupper(char_type __c) const;
# 1350 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_toupper(char_type* __lo, const char_type* __hi) const;
# 1366 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_tolower(char_type __c) const;
# 1383 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_tolower(char_type* __lo, const char_type* __hi) const;
# 1403 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_widen(char __c) const;
# 1425 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char*
      do_widen(const char* __lo, const char* __hi, char_type* __to) const;
# 1448 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char
      do_narrow(char_type __c, char __dfault) const;
# 1474 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual const char_type*
      do_narrow(const char_type* __lo, const char_type* __hi,
  char __dfault, char* __to) const;


      void
      _M_initialize_ctype() throw();
    };



  template<typename _CharT>
    class ctype_byname : public ctype<_CharT>
    {
    public:
      typedef typename ctype<_CharT>::mask mask;

      explicit
      ctype_byname(const char* __s, size_t __refs = 0);


      explicit
      ctype_byname(const string& __s, size_t __refs = 0)
      : ctype_byname(__s.c_str(), __refs) { }


    protected:
      virtual
      ~ctype_byname() { }
    };


  template<>
    class ctype_byname<char> : public ctype<char>
    {
    public:
      explicit
      ctype_byname(const char* __s, size_t __refs = 0);


      explicit
      ctype_byname(const string& __s, size_t __refs = 0);


    protected:
      virtual
      ~ctype_byname();
    };


  template<>
    class ctype_byname<wchar_t> : public ctype<wchar_t>
    {
    public:
      explicit
      ctype_byname(const char* __s, size_t __refs = 0);


      explicit
      ctype_byname(const string& __s, size_t __refs = 0);


    protected:
      virtual
      ~ctype_byname();
    };



}


# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/ctype_inline.h" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/x86_64-linux-gnu/c++/12/bits/ctype_inline.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{


  bool
  ctype<char>::
  is(mask __m, char __c) const
  { return _M_table[static_cast<unsigned char>(__c)] & __m; }

  const char*
  ctype<char>::
  is(const char* __low, const char* __high, mask* __vec) const
  {
    while (__low < __high)
      *__vec++ = _M_table[static_cast<unsigned char>(*__low++)];
    return __high;
  }

  const char*
  ctype<char>::
  scan_is(mask __m, const char* __low, const char* __high) const
  {
    while (__low < __high
    && !(_M_table[static_cast<unsigned char>(*__low)] & __m))
      ++__low;
    return __low;
  }

  const char*
  ctype<char>::
  scan_not(mask __m, const char* __low, const char* __high) const
  {
    while (__low < __high
    && (_M_table[static_cast<unsigned char>(*__low)] & __m) != 0)
      ++__low;
    return __low;
  }


}
# 1547 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{



  class __num_base
  {
  public:


    enum
      {
 _S_ominus,
 _S_oplus,
 _S_ox,
 _S_oX,
 _S_odigits,
 _S_odigits_end = _S_odigits + 16,
 _S_oudigits = _S_odigits_end,
 _S_oudigits_end = _S_oudigits + 16,
 _S_oe = _S_odigits + 14,
 _S_oE = _S_oudigits + 14,
 _S_oend = _S_oudigits_end
      };






    static const char* _S_atoms_out;



    static const char* _S_atoms_in;

    enum
    {
      _S_iminus,
      _S_iplus,
      _S_ix,
      _S_iX,
      _S_izero,
      _S_ie = _S_izero + 14,
      _S_iE = _S_izero + 20,
      _S_iend = 26
    };



    static void
    _S_format_float(const ios_base& __io, char* __fptr, char __mod) throw();
  };

  template<typename _CharT>
    struct __numpunct_cache : public locale::facet
    {
      const char* _M_grouping;
      size_t _M_grouping_size;
      bool _M_use_grouping;
      const _CharT* _M_truename;
      size_t _M_truename_size;
      const _CharT* _M_falsename;
      size_t _M_falsename_size;
      _CharT _M_decimal_point;
      _CharT _M_thousands_sep;





      _CharT _M_atoms_out[__num_base::_S_oend];





      _CharT _M_atoms_in[__num_base::_S_iend];

      bool _M_allocated;

      __numpunct_cache(size_t __refs = 0)
      : facet(__refs), _M_grouping(0), _M_grouping_size(0),
 _M_use_grouping(false),
 _M_truename(0), _M_truename_size(0), _M_falsename(0),
 _M_falsename_size(0), _M_decimal_point(_CharT()),
 _M_thousands_sep(_CharT()), _M_allocated(false)
 { }

      ~__numpunct_cache();

      void
      _M_cache(const locale& __loc);

    private:
      __numpunct_cache&
      operator=(const __numpunct_cache&);

      explicit
      __numpunct_cache(const __numpunct_cache&);
    };

  template<typename _CharT>
    __numpunct_cache<_CharT>::~__numpunct_cache()
    {
      if (_M_allocated)
 {
   delete [] _M_grouping;
   delete [] _M_truename;
   delete [] _M_falsename;
 }
    }

namespace __cxx11 {
# 1677 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT>
    class numpunct : public locale::facet
    {
    public:



      typedef _CharT char_type;
      typedef basic_string<_CharT> string_type;

      typedef __numpunct_cache<_CharT> __cache_type;

    protected:
      __cache_type* _M_data;

    public:

      static locale::id id;






      explicit
      numpunct(size_t __refs = 0)
      : facet(__refs), _M_data(0)
      { _M_initialize_numpunct(); }
# 1715 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      numpunct(__cache_type* __cache, size_t __refs = 0)
      : facet(__refs), _M_data(__cache)
      { _M_initialize_numpunct(); }
# 1729 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      numpunct(__c_locale __cloc, size_t __refs = 0)
      : facet(__refs), _M_data(0)
      { _M_initialize_numpunct(__cloc); }
# 1743 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      decimal_point() const
      { return this->do_decimal_point(); }
# 1756 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      char_type
      thousands_sep() const
      { return this->do_thousands_sep(); }
# 1787 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      string
      grouping() const
      { return this->do_grouping(); }
# 1800 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      string_type
      truename() const
      { return this->do_truename(); }
# 1813 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      string_type
      falsename() const
      { return this->do_falsename(); }

    protected:

      virtual
      ~numpunct();
# 1830 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_decimal_point() const
      { return _M_data->_M_decimal_point; }
# 1842 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual char_type
      do_thousands_sep() const
      { return _M_data->_M_thousands_sep; }
# 1855 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual string
      do_grouping() const
      { return _M_data->_M_grouping; }
# 1868 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual string_type
      do_truename() const
      { return _M_data->_M_truename; }
# 1881 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual string_type
      do_falsename() const
      { return _M_data->_M_falsename; }


      void
      _M_initialize_numpunct(__c_locale __cloc = 0);
    };

  template<typename _CharT>
    locale::id numpunct<_CharT>::id;

  template<>
    numpunct<char>::~numpunct();

  template<>
    void
    numpunct<char>::_M_initialize_numpunct(__c_locale __cloc);


  template<>
    numpunct<wchar_t>::~numpunct();

  template<>
    void
    numpunct<wchar_t>::_M_initialize_numpunct(__c_locale __cloc);



  template<typename _CharT>
    class numpunct_byname : public numpunct<_CharT>
    {
    public:
      typedef _CharT char_type;
      typedef basic_string<_CharT> string_type;

      explicit
      numpunct_byname(const char* __s, size_t __refs = 0)
      : numpunct<_CharT>(__refs)
      {
 if (__builtin_strcmp(__s, "C") != 0
     && __builtin_strcmp(__s, "POSIX") != 0)
   {
     __c_locale __tmp;
     this->_S_create_c_locale(__tmp, __s);
     this->_M_initialize_numpunct(__tmp);
     this->_S_destroy_c_locale(__tmp);
   }
      }


      explicit
      numpunct_byname(const string& __s, size_t __refs = 0)
      : numpunct_byname(__s.c_str(), __refs) { }


    protected:
      virtual
      ~numpunct_byname() { }
    };

}
# 1959 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT, typename _InIter>
    class num_get : public locale::facet
    {
    public:



      typedef _CharT char_type;
      typedef _InIter iter_type;



      static locale::id id;
# 1980 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      num_get(size_t __refs = 0) : facet(__refs) { }
# 2006 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, bool& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }
# 2043 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, long& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, unsigned short& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, unsigned int& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, unsigned long& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }


      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, long long& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, unsigned long long& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }
# 2103 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, float& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, double& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, long double& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }
# 2146 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      get(iter_type __in, iter_type __end, ios_base& __io,
   ios_base::iostate& __err, void*& __v) const
      { return this->do_get(__in, __end, __io, __err, __v); }

    protected:

      virtual ~num_get() { }

      __attribute ((__abi_tag__ ("cxx11")))
      iter_type
      _M_extract_float(iter_type, iter_type, ios_base&, ios_base::iostate&,
         string&) const;

      template<typename _ValueT>
 __attribute ((__abi_tag__ ("cxx11")))
 iter_type
 _M_extract_int(iter_type, iter_type, ios_base&, ios_base::iostate&,
         _ValueT&) const;

      template<typename _CharT2>
      typename __gnu_cxx::__enable_if<__is_char<_CharT2>::__value, int>::__type
 _M_find(const _CharT2*, size_t __len, _CharT2 __c) const
 {
   int __ret = -1;
   if (__len <= 10)
     {
       if (__c >= _CharT2('0') && __c < _CharT2(_CharT2('0') + __len))
  __ret = __c - _CharT2('0');
     }
   else
     {
       if (__c >= _CharT2('0') && __c <= _CharT2('9'))
  __ret = __c - _CharT2('0');
       else if (__c >= _CharT2('a') && __c <= _CharT2('f'))
  __ret = 10 + (__c - _CharT2('a'));
       else if (__c >= _CharT2('A') && __c <= _CharT2('F'))
  __ret = 10 + (__c - _CharT2('A'));
     }
   return __ret;
 }

      template<typename _CharT2>
      typename __gnu_cxx::__enable_if<!__is_char<_CharT2>::__value,
          int>::__type
 _M_find(const _CharT2* __zero, size_t __len, _CharT2 __c) const
 {
   int __ret = -1;
   const char_type* __q = char_traits<_CharT2>::find(__zero, __len, __c);
   if (__q)
     {
       __ret = __q - __zero;
       if (__ret > 15)
  __ret -= 6;
     }
   return __ret;
 }
# 2219 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&, bool&) const;

      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, long& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }

      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, unsigned short& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }

      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, unsigned int& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }

      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, unsigned long& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }


      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, long long& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }

      virtual iter_type
      do_get(iter_type __beg, iter_type __end, ios_base& __io,
      ios_base::iostate& __err, unsigned long long& __v) const
      { return _M_extract_int(__beg, __end, __io, __err, __v); }


      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&, float&) const;

      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&,
      double&) const;
# 2271 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&,
      long double&) const;


      virtual iter_type
      do_get(iter_type, iter_type, ios_base&, ios_base::iostate&, void*&) const;
# 2299 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
    };

  template<typename _CharT, typename _InIter>
    locale::id num_get<_CharT, _InIter>::id;
# 2317 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT, typename _OutIter>
    class num_put : public locale::facet
    {
    public:



      typedef _CharT char_type;
      typedef _OutIter iter_type;



      static locale::id id;
# 2338 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      explicit
      num_put(size_t __refs = 0) : facet(__refs) { }
# 2356 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill, bool __v) const
      { return this->do_put(__s, __io, __fill, __v); }
# 2398 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill, long __v) const
      { return this->do_put(__s, __io, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill,
   unsigned long __v) const
      { return this->do_put(__s, __io, __fill, __v); }


      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill, long long __v) const
      { return this->do_put(__s, __io, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill,
   unsigned long long __v) const
      { return this->do_put(__s, __io, __fill, __v); }
# 2461 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill, double __v) const
      { return this->do_put(__s, __io, __fill, __v); }

      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill,
   long double __v) const
      { return this->do_put(__s, __io, __fill, __v); }
# 2486 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      iter_type
      put(iter_type __s, ios_base& __io, char_type __fill,
   const void* __v) const
      { return this->do_put(__s, __io, __fill, __v); }

    protected:
      template<typename _ValueT>
 iter_type
 _M_insert_float(iter_type, ios_base& __io, char_type __fill,
   char __mod, _ValueT __v) const;

      void
      _M_group_float(const char* __grouping, size_t __grouping_size,
       char_type __sep, const char_type* __p, char_type* __new,
       char_type* __cs, int& __len) const;

      template<typename _ValueT>
 iter_type
 _M_insert_int(iter_type, ios_base& __io, char_type __fill,
        _ValueT __v) const;

      void
      _M_group_int(const char* __grouping, size_t __grouping_size,
     char_type __sep, ios_base& __io, char_type* __new,
     char_type* __cs, int& __len) const;

      void
      _M_pad(char_type __fill, streamsize __w, ios_base& __io,
      char_type* __new, const char_type* __cs, int& __len) const;


      virtual
      ~num_put() { }
# 2534 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
      virtual iter_type
      do_put(iter_type __s, ios_base& __io, char_type __fill, bool __v) const;

      virtual iter_type
      do_put(iter_type __s, ios_base& __io, char_type __fill, long __v) const
      { return _M_insert_int(__s, __io, __fill, __v); }

      virtual iter_type
      do_put(iter_type __s, ios_base& __io, char_type __fill,
      unsigned long __v) const
      { return _M_insert_int(__s, __io, __fill, __v); }


      virtual iter_type
      do_put(iter_type __s, ios_base& __io, char_type __fill,
      long long __v) const
      { return _M_insert_int(__s, __io, __fill, __v); }

      virtual iter_type
      do_put(iter_type __s, ios_base& __io, char_type __fill,
      unsigned long long __v) const
      { return _M_insert_int(__s, __io, __fill, __v); }


      virtual iter_type
      do_put(iter_type, ios_base&, char_type, double) const;






      virtual iter_type
      do_put(iter_type, ios_base&, char_type, long double) const;


      virtual iter_type
      do_put(iter_type, ios_base&, char_type, const void*) const;
# 2586 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
    };

  template <typename _CharT, typename _OutIter>
    locale::id num_put<_CharT, _OutIter>::id;
# 2599 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 3
  template<typename _CharT>
    inline bool
    isspace(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::space, __c); }


  template<typename _CharT>
    inline bool
    isprint(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::print, __c); }


  template<typename _CharT>
    inline bool
    iscntrl(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::cntrl, __c); }


  template<typename _CharT>
    inline bool
    isupper(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::upper, __c); }


  template<typename _CharT>
    inline bool
    islower(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::lower, __c); }


  template<typename _CharT>
    inline bool
    isalpha(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::alpha, __c); }


  template<typename _CharT>
    inline bool
    isdigit(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::digit, __c); }


  template<typename _CharT>
    inline bool
    ispunct(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::punct, __c); }


  template<typename _CharT>
    inline bool
    isxdigit(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::xdigit, __c); }


  template<typename _CharT>
    inline bool
    isalnum(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::alnum, __c); }


  template<typename _CharT>
    inline bool
    isgraph(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::graph, __c); }



  template<typename _CharT>
    inline bool
    isblank(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).is(ctype_base::blank, __c); }



  template<typename _CharT>
    inline _CharT
    toupper(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).toupper(__c); }


  template<typename _CharT>
    inline _CharT
    tolower(_CharT __c, const locale& __loc)
    { return use_facet<ctype<_CharT> >(__loc).tolower(__c); }


}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3

namespace std __attribute__ ((__visibility__ ("default")))
{




  template<typename _Facet>
    struct __use_cache
    {
      const _Facet*
      operator() (const locale& __loc) const;
    };


  template<typename _CharT>
    struct __use_cache<__numpunct_cache<_CharT> >
    {
      const __numpunct_cache<_CharT>*
      operator() (const locale& __loc) const
      {
 const size_t __i = numpunct<_CharT>::id._M_id();
 const locale::facet** __caches = __loc._M_impl->_M_caches;
 if (!__caches[__i])
   {
     __numpunct_cache<_CharT>* __tmp = 0;
     try
       {
  __tmp = new __numpunct_cache<_CharT>;
  __tmp->_M_cache(__loc);
       }
     catch(...)
       {
  delete __tmp;
  throw;
       }
     __loc._M_impl->_M_install_cache(__tmp, __i);
   }
 return static_cast<const __numpunct_cache<_CharT>*>(__caches[__i]);
      }
    };

  template<typename _CharT>
    void
    __numpunct_cache<_CharT>::_M_cache(const locale& __loc)
    {
      const numpunct<_CharT>& __np = use_facet<numpunct<_CharT> >(__loc);

      char* __grouping = 0;
      _CharT* __truename = 0;
      _CharT* __falsename = 0;
      try
 {
   const string& __g = __np.grouping();
   _M_grouping_size = __g.size();
   __grouping = new char[_M_grouping_size];
   __g.copy(__grouping, _M_grouping_size);
   _M_use_grouping = (_M_grouping_size
        && static_cast<signed char>(__grouping[0]) > 0
        && (__grouping[0]
     != __gnu_cxx::__numeric_traits<char>::__max));

   const basic_string<_CharT>& __tn = __np.truename();
   _M_truename_size = __tn.size();
   __truename = new _CharT[_M_truename_size];
   __tn.copy(__truename, _M_truename_size);

   const basic_string<_CharT>& __fn = __np.falsename();
   _M_falsename_size = __fn.size();
   __falsename = new _CharT[_M_falsename_size];
   __fn.copy(__falsename, _M_falsename_size);

   _M_decimal_point = __np.decimal_point();
   _M_thousands_sep = __np.thousands_sep();

   const ctype<_CharT>& __ct = use_facet<ctype<_CharT> >(__loc);
   __ct.widen(__num_base::_S_atoms_out,
       __num_base::_S_atoms_out
       + __num_base::_S_oend, _M_atoms_out);
   __ct.widen(__num_base::_S_atoms_in,
       __num_base::_S_atoms_in
       + __num_base::_S_iend, _M_atoms_in);

   _M_grouping = __grouping;
   _M_truename = __truename;
   _M_falsename = __falsename;
   _M_allocated = true;
 }
      catch(...)
 {
   delete [] __grouping;
   delete [] __truename;
   delete [] __falsename;
   throw;
 }
    }
# 139 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  __attribute__ ((__pure__)) bool
  __verify_grouping(const char* __grouping, size_t __grouping_size,
      const string& __grouping_tmp) throw ();



  template<typename _CharT, typename _InIter>
    __attribute ((__abi_tag__ ("cxx11")))
    _InIter
    num_get<_CharT, _InIter>::
    _M_extract_float(_InIter __beg, _InIter __end, ios_base& __io,
       ios_base::iostate& __err, string& __xtrc) const
    {
      typedef char_traits<_CharT> __traits_type;
      typedef __numpunct_cache<_CharT> __cache_type;
      __use_cache<__cache_type> __uc;
      const locale& __loc = __io._M_getloc();
      const __cache_type* __lc = __uc(__loc);
      const _CharT* __lit = __lc->_M_atoms_in;
      char_type __c = char_type();


      bool __testeof = __beg == __end;


      if (!__testeof)
 {
   __c = *__beg;
   const bool __plus = __c == __lit[__num_base::_S_iplus];
   if ((__plus || __c == __lit[__num_base::_S_iminus])
       && !(__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
       && !(__c == __lc->_M_decimal_point))
     {
       __xtrc += __plus ? '+' : '-';
       if (++__beg != __end)
  __c = *__beg;
       else
  __testeof = true;
     }
 }


      bool __found_mantissa = false;
      int __sep_pos = 0;
      while (!__testeof)
 {
   if ((__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
       || __c == __lc->_M_decimal_point)
     break;
   else if (__c == __lit[__num_base::_S_izero])
     {
       if (!__found_mantissa)
  {
    __xtrc += '0';
    __found_mantissa = true;
  }
       ++__sep_pos;

       if (++__beg != __end)
  __c = *__beg;
       else
  __testeof = true;
     }
   else
     break;
 }


      bool __found_dec = false;
      bool __found_sci = false;
      string __found_grouping;
      if (__lc->_M_use_grouping)
 __found_grouping.reserve(32);
      const char_type* __lit_zero = __lit + __num_base::_S_izero;

      if (!__lc->_M_allocated)

 while (!__testeof)
   {
     const int __digit = _M_find(__lit_zero, 10, __c);
     if (__digit != -1)
       {
  __xtrc += '0' + __digit;
  __found_mantissa = true;
       }
     else if (__c == __lc->_M_decimal_point
       && !__found_dec && !__found_sci)
       {
  __xtrc += '.';
  __found_dec = true;
       }
     else if ((__c == __lit[__num_base::_S_ie]
        || __c == __lit[__num_base::_S_iE])
       && !__found_sci && __found_mantissa)
       {

  __xtrc += 'e';
  __found_sci = true;


  if (++__beg != __end)
    {
      __c = *__beg;
      const bool __plus = __c == __lit[__num_base::_S_iplus];
      if (__plus || __c == __lit[__num_base::_S_iminus])
        __xtrc += __plus ? '+' : '-';
      else
        continue;
    }
  else
    {
      __testeof = true;
      break;
    }
       }
     else
       break;

     if (++__beg != __end)
       __c = *__beg;
     else
       __testeof = true;
   }
      else
 while (!__testeof)
   {


     if (__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
       {
  if (!__found_dec && !__found_sci)
    {


      if (__sep_pos)
        {
   __found_grouping += static_cast<char>(__sep_pos);
   __sep_pos = 0;
        }
      else
        {


   __xtrc.clear();
   break;
        }
    }
  else
    break;
       }
     else if (__c == __lc->_M_decimal_point)
       {
  if (!__found_dec && !__found_sci)
    {



      if (__found_grouping.size())
        __found_grouping += static_cast<char>(__sep_pos);
      __xtrc += '.';
      __found_dec = true;
    }
  else
    break;
       }
     else
       {
  const char_type* __q =
    __traits_type::find(__lit_zero, 10, __c);
  if (__q)
    {
      __xtrc += '0' + (__q - __lit_zero);
      __found_mantissa = true;
      ++__sep_pos;
    }
  else if ((__c == __lit[__num_base::_S_ie]
     || __c == __lit[__num_base::_S_iE])
    && !__found_sci && __found_mantissa)
    {

      if (__found_grouping.size() && !__found_dec)
        __found_grouping += static_cast<char>(__sep_pos);
      __xtrc += 'e';
      __found_sci = true;


      if (++__beg != __end)
        {
   __c = *__beg;
   const bool __plus = __c == __lit[__num_base::_S_iplus];
   if ((__plus || __c == __lit[__num_base::_S_iminus])
       && !(__lc->_M_use_grouping
     && __c == __lc->_M_thousands_sep)
       && !(__c == __lc->_M_decimal_point))
        __xtrc += __plus ? '+' : '-';
   else
     continue;
        }
      else
        {
   __testeof = true;
   break;
        }
    }
  else
    break;
       }

     if (++__beg != __end)
       __c = *__beg;
     else
       __testeof = true;
   }



      if (__found_grouping.size())
        {

   if (!__found_dec && !__found_sci)
     __found_grouping += static_cast<char>(__sep_pos);

          if (!std::__verify_grouping(__lc->_M_grouping,
          __lc->_M_grouping_size,
          __found_grouping))
     __err = ios_base::failbit;
        }

      return __beg;
    }

  template<typename _CharT, typename _InIter>
    template<typename _ValueT>
      __attribute ((__abi_tag__ ("cxx11")))
      _InIter
      num_get<_CharT, _InIter>::
      _M_extract_int(_InIter __beg, _InIter __end, ios_base& __io,
       ios_base::iostate& __err, _ValueT& __v) const
      {
        typedef char_traits<_CharT> __traits_type;
 using __gnu_cxx::__add_unsigned;
 typedef typename __add_unsigned<_ValueT>::__type __unsigned_type;
 typedef __numpunct_cache<_CharT> __cache_type;
 __use_cache<__cache_type> __uc;
 const locale& __loc = __io._M_getloc();
 const __cache_type* __lc = __uc(__loc);
 const _CharT* __lit = __lc->_M_atoms_in;
 char_type __c = char_type();


 const ios_base::fmtflags __basefield = __io.flags()
                                        & ios_base::basefield;
 const bool __oct = __basefield == ios_base::oct;
 int __base = __oct ? 8 : (__basefield == ios_base::hex ? 16 : 10);


 bool __testeof = __beg == __end;


 bool __negative = false;
 if (!__testeof)
   {
     __c = *__beg;
     __negative = __c == __lit[__num_base::_S_iminus];
     if ((__negative || __c == __lit[__num_base::_S_iplus])
  && !(__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
  && !(__c == __lc->_M_decimal_point))
       {
  if (++__beg != __end)
    __c = *__beg;
  else
    __testeof = true;
       }
   }



 bool __found_zero = false;
 int __sep_pos = 0;
 while (!__testeof)
   {
     if ((__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
  || __c == __lc->_M_decimal_point)
       break;
     else if (__c == __lit[__num_base::_S_izero]
       && (!__found_zero || __base == 10))
       {
  __found_zero = true;
  ++__sep_pos;
  if (__basefield == 0)
    __base = 8;
  if (__base == 8)
    __sep_pos = 0;
       }
     else if (__found_zero
       && (__c == __lit[__num_base::_S_ix]
    || __c == __lit[__num_base::_S_iX]))
       {
  if (__basefield == 0)
    __base = 16;
  if (__base == 16)
    {
      __found_zero = false;
      __sep_pos = 0;
    }
  else
    break;
       }
     else
       break;

     if (++__beg != __end)
       {
  __c = *__beg;
  if (!__found_zero)
    break;
       }
     else
       __testeof = true;
   }



 const size_t __len = (__base == 16 ? __num_base::_S_iend
         - __num_base::_S_izero : __base);


 typedef __gnu_cxx::__numeric_traits<_ValueT> __num_traits;
 string __found_grouping;
 if (__lc->_M_use_grouping)
   __found_grouping.reserve(32);
 bool __testfail = false;
 bool __testoverflow = false;
 const __unsigned_type __max =
   (__negative && __num_traits::__is_signed)
   ? -static_cast<__unsigned_type>(__num_traits::__min)
   : __num_traits::__max;
 const __unsigned_type __smax = __max / __base;
 __unsigned_type __result = 0;
 int __digit = 0;
 const char_type* __lit_zero = __lit + __num_base::_S_izero;

 if (!__lc->_M_allocated)

   while (!__testeof)
     {
       __digit = _M_find(__lit_zero, __len, __c);
       if (__digit == -1)
  break;

       if (__result > __smax)
  __testoverflow = true;
       else
  {
    __result *= __base;
    __testoverflow |= __result > __max - __digit;
    __result += __digit;
    ++__sep_pos;
  }

       if (++__beg != __end)
  __c = *__beg;
       else
  __testeof = true;
     }
 else
   while (!__testeof)
     {


       if (__lc->_M_use_grouping && __c == __lc->_M_thousands_sep)
  {


    if (__sep_pos)
      {
        __found_grouping += static_cast<char>(__sep_pos);
        __sep_pos = 0;
      }
    else
      {
        __testfail = true;
        break;
      }
  }
       else if (__c == __lc->_M_decimal_point)
  break;
       else
  {
    const char_type* __q =
      __traits_type::find(__lit_zero, __len, __c);
    if (!__q)
      break;

    __digit = __q - __lit_zero;
    if (__digit > 15)
      __digit -= 6;
    if (__result > __smax)
      __testoverflow = true;
    else
      {
        __result *= __base;
        __testoverflow |= __result > __max - __digit;
        __result += __digit;
        ++__sep_pos;
      }
  }

       if (++__beg != __end)
  __c = *__beg;
       else
  __testeof = true;
     }



 if (__found_grouping.size())
   {

     __found_grouping += static_cast<char>(__sep_pos);

     if (!std::__verify_grouping(__lc->_M_grouping,
     __lc->_M_grouping_size,
     __found_grouping))
       __err = ios_base::failbit;
   }



 if ((!__sep_pos && !__found_zero && !__found_grouping.size())
     || __testfail)
   {
     __v = 0;
     __err = ios_base::failbit;
   }
 else if (__testoverflow)
   {
     if (__negative && __num_traits::__is_signed)
       __v = __num_traits::__min;
     else
       __v = __num_traits::__max;
     __err = ios_base::failbit;
   }
 else
   __v = __negative ? -__result : __result;

 if (__testeof)
   __err |= ios_base::eofbit;
 return __beg;
      }



  template<typename _CharT, typename _InIter>
    _InIter
    num_get<_CharT, _InIter>::
    do_get(iter_type __beg, iter_type __end, ios_base& __io,
           ios_base::iostate& __err, bool& __v) const
    {
      if (!(__io.flags() & ios_base::boolalpha))
        {



   long __l = -1;
          __beg = _M_extract_int(__beg, __end, __io, __err, __l);
   if (__l == 0 || __l == 1)
     __v = bool(__l);
   else
     {


       __v = true;
       __err = ios_base::failbit;
       if (__beg == __end)
  __err |= ios_base::eofbit;
     }
        }
      else
        {

   typedef __numpunct_cache<_CharT> __cache_type;
   __use_cache<__cache_type> __uc;
   const locale& __loc = __io._M_getloc();
   const __cache_type* __lc = __uc(__loc);

   bool __testf = true;
   bool __testt = true;
   bool __donef = __lc->_M_falsename_size == 0;
   bool __donet = __lc->_M_truename_size == 0;
   bool __testeof = false;
   size_t __n = 0;
   while (!__donef || !__donet)
     {
       if (__beg == __end)
  {
    __testeof = true;
    break;
  }

       const char_type __c = *__beg;

       if (!__donef)
  __testf = __c == __lc->_M_falsename[__n];

       if (!__testf && __donet)
  break;

       if (!__donet)
  __testt = __c == __lc->_M_truename[__n];

       if (!__testt && __donef)
  break;

       if (!__testt && !__testf)
  break;

       ++__n;
       ++__beg;

       __donef = !__testf || __n >= __lc->_M_falsename_size;
       __donet = !__testt || __n >= __lc->_M_truename_size;
     }
   if (__testf && __n == __lc->_M_falsename_size && __n)
     {
       __v = false;
       if (__testt && __n == __lc->_M_truename_size)
  __err = ios_base::failbit;
       else
  __err = __testeof ? ios_base::eofbit : ios_base::goodbit;
     }
   else if (__testt && __n == __lc->_M_truename_size && __n)
     {
       __v = true;
       __err = __testeof ? ios_base::eofbit : ios_base::goodbit;
     }
   else
     {


       __v = false;
       __err = ios_base::failbit;
       if (__testeof)
  __err |= ios_base::eofbit;
     }
 }
      return __beg;
    }

  template<typename _CharT, typename _InIter>
    _InIter
    num_get<_CharT, _InIter>::
    do_get(iter_type __beg, iter_type __end, ios_base& __io,
    ios_base::iostate& __err, float& __v) const
    {
      string __xtrc;
      __xtrc.reserve(32);
      __beg = _M_extract_float(__beg, __end, __io, __err, __xtrc);
      std::__convert_to_v(__xtrc.c_str(), __v, __err, _S_get_c_locale());
      if (__beg == __end)
 __err |= ios_base::eofbit;
      return __beg;
    }

  template<typename _CharT, typename _InIter>
    _InIter
    num_get<_CharT, _InIter>::
    do_get(iter_type __beg, iter_type __end, ios_base& __io,
           ios_base::iostate& __err, double& __v) const
    {
      string __xtrc;
      __xtrc.reserve(32);
      __beg = _M_extract_float(__beg, __end, __io, __err, __xtrc);
      std::__convert_to_v(__xtrc.c_str(), __v, __err, _S_get_c_locale());
      if (__beg == __end)
 __err |= ios_base::eofbit;
      return __beg;
    }
# 735 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  template<typename _CharT, typename _InIter>
    _InIter
    num_get<_CharT, _InIter>::
    do_get(iter_type __beg, iter_type __end, ios_base& __io,
           ios_base::iostate& __err, long double& __v) const
    {
      string __xtrc;
      __xtrc.reserve(32);
      __beg = _M_extract_float(__beg, __end, __io, __err, __xtrc);
      std::__convert_to_v(__xtrc.c_str(), __v, __err, _S_get_c_locale());
      if (__beg == __end)
 __err |= ios_base::eofbit;
      return __beg;
    }

  template<typename _CharT, typename _InIter>
    _InIter
    num_get<_CharT, _InIter>::
    do_get(iter_type __beg, iter_type __end, ios_base& __io,
           ios_base::iostate& __err, void*& __v) const
    {

      typedef ios_base::fmtflags fmtflags;
      const fmtflags __fmt = __io.flags();
      __io.flags((__fmt & ~ios_base::basefield) | ios_base::hex);

      typedef __gnu_cxx::__conditional_type<(sizeof(void*)
          <= sizeof(unsigned long)),
 unsigned long, unsigned long long>::__type _UIntPtrType;

      _UIntPtrType __ul;
      __beg = _M_extract_int(__beg, __end, __io, __err, __ul);


      __io.flags(__fmt);

      __v = reinterpret_cast<void*>(__ul);
      return __beg;
    }
# 795 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  template<typename _CharT, typename _OutIter>
    void
    num_put<_CharT, _OutIter>::
    _M_pad(_CharT __fill, streamsize __w, ios_base& __io,
    _CharT* __new, const _CharT* __cs, int& __len) const
    {


      __pad<_CharT, char_traits<_CharT> >::_S_pad(__io, __fill, __new,
        __cs, __w, __len);
      __len = static_cast<int>(__w);
    }



  template<typename _CharT, typename _ValueT>
    int
    __int_to_char(_CharT* __bufend, _ValueT __v, const _CharT* __lit,
    ios_base::fmtflags __flags, bool __dec)
    {
      _CharT* __buf = __bufend;
      if (__builtin_expect(__dec, true))
 {

   do
     {
       *--__buf = __lit[(__v % 10) + __num_base::_S_odigits];
       __v /= 10;
     }
   while (__v != 0);
 }
      else if ((__flags & ios_base::basefield) == ios_base::oct)
 {

   do
     {
       *--__buf = __lit[(__v & 0x7) + __num_base::_S_odigits];
       __v >>= 3;
     }
   while (__v != 0);
 }
      else
 {

   const bool __uppercase = __flags & ios_base::uppercase;
   const int __case_offset = __uppercase ? __num_base::_S_oudigits
                                         : __num_base::_S_odigits;
   do
     {
       *--__buf = __lit[(__v & 0xf) + __case_offset];
       __v >>= 4;
     }
   while (__v != 0);
 }
      return __bufend - __buf;
    }



  template<typename _CharT, typename _OutIter>
    void
    num_put<_CharT, _OutIter>::
    _M_group_int(const char* __grouping, size_t __grouping_size, _CharT __sep,
   ios_base&, _CharT* __new, _CharT* __cs, int& __len) const
    {
      _CharT* __p = std::__add_grouping(__new, __sep, __grouping,
     __grouping_size, __cs, __cs + __len);
      __len = __p - __new;
    }

  template<typename _CharT, typename _OutIter>
    template<typename _ValueT>
      _OutIter
      num_put<_CharT, _OutIter>::
      _M_insert_int(_OutIter __s, ios_base& __io, _CharT __fill,
      _ValueT __v) const
      {
 using __gnu_cxx::__add_unsigned;
 typedef typename __add_unsigned<_ValueT>::__type __unsigned_type;
 typedef __numpunct_cache<_CharT> __cache_type;
 __use_cache<__cache_type> __uc;
 const locale& __loc = __io._M_getloc();
 const __cache_type* __lc = __uc(__loc);
 const _CharT* __lit = __lc->_M_atoms_out;
 const ios_base::fmtflags __flags = __io.flags();


 const int __ilen = 5 * sizeof(_ValueT);
 _CharT* __cs = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
            * __ilen));



 const ios_base::fmtflags __basefield = __flags & ios_base::basefield;
 const bool __dec = (__basefield != ios_base::oct
       && __basefield != ios_base::hex);
 const __unsigned_type __u = ((__v > 0 || !__dec)
         ? __unsigned_type(__v)
         : -__unsigned_type(__v));
  int __len = __int_to_char(__cs + __ilen, __u, __lit, __flags, __dec);
 __cs += __ilen - __len;


 if (__lc->_M_use_grouping)
   {


     _CharT* __cs2 = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
          * (__len + 1)
          * 2));
     _M_group_int(__lc->_M_grouping, __lc->_M_grouping_size,
    __lc->_M_thousands_sep, __io, __cs2 + 2, __cs, __len);
     __cs = __cs2 + 2;
   }


 if (__builtin_expect(__dec, true))
   {

     if (__v >= 0)
       {
  if (bool(__flags & ios_base::showpos)
      && __gnu_cxx::__numeric_traits<_ValueT>::__is_signed)
    *--__cs = __lit[__num_base::_S_oplus], ++__len;
       }
     else
       *--__cs = __lit[__num_base::_S_ominus], ++__len;
   }
 else if (bool(__flags & ios_base::showbase) && __v)
   {
     if (__basefield == ios_base::oct)
       *--__cs = __lit[__num_base::_S_odigits], ++__len;
     else
       {

  const bool __uppercase = __flags & ios_base::uppercase;
  *--__cs = __lit[__num_base::_S_ox + __uppercase];

  *--__cs = __lit[__num_base::_S_odigits];
  __len += 2;
       }
   }


 const streamsize __w = __io.width();
 if (__w > static_cast<streamsize>(__len))
   {
     _CharT* __cs3 = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
          * __w));
     _M_pad(__fill, __w, __io, __cs3, __cs, __len);
     __cs = __cs3;
   }
 __io.width(0);



 return std::__write(__s, __cs, __len);
      }

  template<typename _CharT, typename _OutIter>
    void
    num_put<_CharT, _OutIter>::
    _M_group_float(const char* __grouping, size_t __grouping_size,
     _CharT __sep, const _CharT* __p, _CharT* __new,
     _CharT* __cs, int& __len) const
    {



      const int __declen = __p ? __p - __cs : __len;
      _CharT* __p2 = std::__add_grouping(__new, __sep, __grouping,
      __grouping_size,
      __cs, __cs + __declen);


      int __newlen = __p2 - __new;
      if (__p)
 {
   char_traits<_CharT>::copy(__p2, __p, __len - __declen);
   __newlen += __len - __declen;
 }
      __len = __newlen;
    }
# 989 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  template<typename _CharT, typename _OutIter>
    template<typename _ValueT>
      _OutIter
      num_put<_CharT, _OutIter>::
      _M_insert_float(_OutIter __s, ios_base& __io, _CharT __fill, char __mod,
         _ValueT __v) const
      {
 typedef __numpunct_cache<_CharT> __cache_type;
 __use_cache<__cache_type> __uc;
 const locale& __loc = __io._M_getloc();
 const __cache_type* __lc = __uc(__loc);


 const streamsize __prec = __io.precision() < 0 ? 6 : __io.precision();

 const int __max_digits =
   __gnu_cxx::__numeric_traits<_ValueT>::__digits10;


 int __len;

 char __fbuf[16];
 __num_base::_S_format_float(__io, __fbuf, __mod);



 const bool __use_prec =
   (__io.flags() & ios_base::floatfield) != ios_base::floatfield;



 int __cs_size = __max_digits * 3;
 char* __cs = static_cast<char*>(__builtin_alloca(__cs_size));
 if (__use_prec)
   __len = std::__convert_from_v(_S_get_c_locale(), __cs, __cs_size,
     __fbuf, __prec, __v);
 else
   __len = std::__convert_from_v(_S_get_c_locale(), __cs, __cs_size,
     __fbuf, __v);


 if (__len >= __cs_size)
   {
     __cs_size = __len + 1;
     __cs = static_cast<char*>(__builtin_alloca(__cs_size));
     if (__use_prec)
       __len = std::__convert_from_v(_S_get_c_locale(), __cs, __cs_size,
         __fbuf, __prec, __v);
     else
       __len = std::__convert_from_v(_S_get_c_locale(), __cs, __cs_size,
         __fbuf, __v);
   }
# 1062 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
 const ctype<_CharT>& __ctype = use_facet<ctype<_CharT> >(__loc);

 _CharT* __ws = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
            * __len));
 __ctype.widen(__cs, __cs + __len, __ws);


 _CharT* __wp = 0;
 const char* __p = char_traits<char>::find(__cs, __len, '.');
 if (__p)
   {
     __wp = __ws + (__p - __cs);
     *__wp = __lc->_M_decimal_point;
   }




 if (__lc->_M_use_grouping
     && (__wp || __len < 3 || (__cs[1] <= '9' && __cs[2] <= '9'
          && __cs[1] >= '0' && __cs[2] >= '0')))
   {


     _CharT* __ws2 = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
          * __len * 2));

     streamsize __off = 0;
     if (__cs[0] == '-' || __cs[0] == '+')
       {
  __off = 1;
  __ws2[0] = __ws[0];
  __len -= 1;
       }

     _M_group_float(__lc->_M_grouping, __lc->_M_grouping_size,
      __lc->_M_thousands_sep, __wp, __ws2 + __off,
      __ws + __off, __len);
     __len += __off;

     __ws = __ws2;
   }


 const streamsize __w = __io.width();
 if (__w > static_cast<streamsize>(__len))
   {
     _CharT* __ws3 = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
          * __w));
     _M_pad(__fill, __w, __io, __ws3, __ws, __len);
     __ws = __ws3;
   }
 __io.width(0);



 return std::__write(__s, __ws, __len);
      }

  template<typename _CharT, typename _OutIter>
    _OutIter
    num_put<_CharT, _OutIter>::
    do_put(iter_type __s, ios_base& __io, char_type __fill, bool __v) const
    {
      const ios_base::fmtflags __flags = __io.flags();
      if ((__flags & ios_base::boolalpha) == 0)
        {
          const long __l = __v;
          __s = _M_insert_int(__s, __io, __fill, __l);
        }
      else
        {
   typedef __numpunct_cache<_CharT> __cache_type;
   __use_cache<__cache_type> __uc;
   const locale& __loc = __io._M_getloc();
   const __cache_type* __lc = __uc(__loc);

   const _CharT* __name = __v ? __lc->_M_truename
                              : __lc->_M_falsename;
   int __len = __v ? __lc->_M_truename_size
                   : __lc->_M_falsename_size;

   const streamsize __w = __io.width();
   if (__w > static_cast<streamsize>(__len))
     {
       const streamsize __plen = __w - __len;
       _CharT* __ps
  = static_cast<_CharT*>(__builtin_alloca(sizeof(_CharT)
       * __plen));

       char_traits<_CharT>::assign(__ps, __plen, __fill);
       __io.width(0);

       if ((__flags & ios_base::adjustfield) == ios_base::left)
  {
    __s = std::__write(__s, __name, __len);
    __s = std::__write(__s, __ps, __plen);
  }
       else
  {
    __s = std::__write(__s, __ps, __plen);
    __s = std::__write(__s, __name, __len);
  }
       return __s;
     }
   __io.width(0);
   __s = std::__write(__s, __name, __len);
 }
      return __s;
    }

  template<typename _CharT, typename _OutIter>
    _OutIter
    num_put<_CharT, _OutIter>::
    do_put(iter_type __s, ios_base& __io, char_type __fill, double __v) const
    { return _M_insert_float(__s, __io, __fill, char(), __v); }
# 1187 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  template<typename _CharT, typename _OutIter>
    _OutIter
    num_put<_CharT, _OutIter>::
    do_put(iter_type __s, ios_base& __io, char_type __fill,
    long double __v) const
    { return _M_insert_float(__s, __io, __fill, 'L', __v); }

  template<typename _CharT, typename _OutIter>
    _OutIter
    num_put<_CharT, _OutIter>::
    do_put(iter_type __s, ios_base& __io, char_type __fill,
           const void* __v) const
    {
      const ios_base::fmtflags __flags = __io.flags();
      const ios_base::fmtflags __fmt = ~(ios_base::basefield
      | ios_base::uppercase);
      __io.flags((__flags & __fmt) | (ios_base::hex | ios_base::showbase));

      typedef __gnu_cxx::__conditional_type<(sizeof(const void*)
          <= sizeof(unsigned long)),
 unsigned long, unsigned long long>::__type _UIntPtrType;

      __s = _M_insert_int(__s, __io, __fill,
     reinterpret_cast<_UIntPtrType>(__v));
      __io.flags(__flags);
      return __s;
    }
# 1233 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.tcc" 3
  template<typename _CharT, typename _Traits>
    void
    __pad<_CharT, _Traits>::_S_pad(ios_base& __io, _CharT __fill,
       _CharT* __news, const _CharT* __olds,
       streamsize __newlen, streamsize __oldlen)
    {
      const size_t __plen = static_cast<size_t>(__newlen - __oldlen);
      const ios_base::fmtflags __adjust = __io.flags() & ios_base::adjustfield;


      if (__adjust == ios_base::left)
 {
   _Traits::copy(__news, __olds, __oldlen);
   _Traits::assign(__news + __oldlen, __plen, __fill);
   return;
 }

      size_t __mod = 0;
      if (__adjust == ios_base::internal)
 {



          const locale& __loc = __io._M_getloc();
   const ctype<_CharT>& __ctype = use_facet<ctype<_CharT> >(__loc);

   if (__ctype.widen('-') == __olds[0]
       || __ctype.widen('+') == __olds[0])
     {
       __news[0] = __olds[0];
       __mod = 1;
       ++__news;
     }
   else if (__ctype.widen('0') == __olds[0]
     && __oldlen > 1
     && (__ctype.widen('x') == __olds[1]
         || __ctype.widen('X') == __olds[1]))
     {
       __news[0] = __olds[0];
       __news[1] = __olds[1];
       __mod = 2;
       __news += 2;
     }

 }
      _Traits::assign(__news, __plen, __fill);
      _Traits::copy(__news + __plen, __olds + __mod, __oldlen - __mod);
    }

  template<typename _CharT>
    _CharT*
    __add_grouping(_CharT* __s, _CharT __sep,
     const char* __gbeg, size_t __gsize,
     const _CharT* __first, const _CharT* __last)
    {
      size_t __idx = 0;
      size_t __ctr = 0;

      while (__last - __first > __gbeg[__idx]
      && static_cast<signed char>(__gbeg[__idx]) > 0
      && __gbeg[__idx] != __gnu_cxx::__numeric_traits<char>::__max)
 {
   __last -= __gbeg[__idx];
   __idx < __gsize - 1 ? ++__idx : ++__ctr;
 }

      while (__first != __last)
 *__s++ = *__first++;

      while (__ctr--)
 {
   *__s++ = __sep;
   for (char __i = __gbeg[__idx]; __i > 0; --__i)
     *__s++ = *__first++;
 }

      while (__idx--)
 {
   *__s++ = __sep;
   for (char __i = __gbeg[__idx]; __i > 0; --__i)
     *__s++ = *__first++;
 }

      return __s;
    }




  extern template class __cxx11:: numpunct<char>;
  extern template class __cxx11:: numpunct_byname<char>;
  extern template class num_get<char>;
  extern template class num_put<char>;
  extern template class ctype_byname<char>;

  extern template
    const ctype<char>&
    use_facet<ctype<char> >(const locale&);

  extern template
    const numpunct<char>&
    use_facet<numpunct<char> >(const locale&);

  extern template
    const num_put<char>&
    use_facet<num_put<char> >(const locale&);

  extern template
    const num_get<char>&
    use_facet<num_get<char> >(const locale&);

  extern template
    bool
    has_facet<ctype<char> >(const locale&);

  extern template
    bool
    has_facet<numpunct<char> >(const locale&);

  extern template
    bool
    has_facet<num_put<char> >(const locale&);

  extern template
    bool
    has_facet<num_get<char> >(const locale&);


  extern template class __cxx11:: numpunct<wchar_t>;
  extern template class __cxx11:: numpunct_byname<wchar_t>;
  extern template class num_get<wchar_t>;
  extern template class num_put<wchar_t>;
  extern template class ctype_byname<wchar_t>;

  extern template
    const ctype<wchar_t>&
    use_facet<ctype<wchar_t> >(const locale&);

  extern template
    const numpunct<wchar_t>&
    use_facet<numpunct<wchar_t> >(const locale&);

  extern template
    const num_put<wchar_t>&
    use_facet<num_put<wchar_t> >(const locale&);

  extern template
    const num_get<wchar_t>&
    use_facet<num_get<wchar_t> >(const locale&);

 extern template
    bool
    has_facet<ctype<wchar_t> >(const locale&);

  extern template
    bool
    has_facet<numpunct<wchar_t> >(const locale&);

  extern template
    bool
    has_facet<num_put<wchar_t> >(const locale&);

  extern template
    bool
    has_facet<num_get<wchar_t> >(const locale&);




}
# 2688 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/locale_facets.h" 2 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 2 3



namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _Facet>
    inline const _Facet&
    __check_facet(const _Facet* __f)
    {
      if (!__f)
 __throw_bad_cast();
      return *__f;
    }
# 66 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
  template<typename _CharT, typename _Traits>
    class basic_ios : public ios_base
    {
    public:






      typedef _CharT char_type;
      typedef typename _Traits::int_type int_type;
      typedef typename _Traits::pos_type pos_type;
      typedef typename _Traits::off_type off_type;
      typedef _Traits traits_type;






      typedef ctype<_CharT> __ctype_type;
      typedef num_put<_CharT, ostreambuf_iterator<_CharT, _Traits> >
           __num_put_type;
      typedef num_get<_CharT, istreambuf_iterator<_CharT, _Traits> >
           __num_get_type;



    protected:
      basic_ostream<_CharT, _Traits>* _M_tie;
      mutable char_type _M_fill;
      mutable bool _M_fill_init;
      basic_streambuf<_CharT, _Traits>* _M_streambuf;


      const __ctype_type* _M_ctype;

      const __num_put_type* _M_num_put;

      const __num_get_type* _M_num_get;

    public:
# 117 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      explicit operator bool() const
      { return !this->fail(); }





      bool
      operator!() const
      { return this->fail(); }
# 136 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      iostate
      rdstate() const
      { return _M_streambuf_state; }
# 147 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      void
      clear(iostate __state = goodbit);







      void
      setstate(iostate __state)
      { this->clear(this->rdstate() | __state); }




      void
      _M_setstate(iostate __state)
      {


 _M_streambuf_state |= __state;
 if (this->exceptions() & __state)
   throw;
      }







      bool
      good() const
      { return this->rdstate() == 0; }







      bool
      eof() const
      { return (this->rdstate() & eofbit) != 0; }
# 200 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      bool
      fail() const
      { return (this->rdstate() & (badbit | failbit)) != 0; }







      bool
      bad() const
      { return (this->rdstate() & badbit) != 0; }
# 221 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      iostate
      exceptions() const
      { return _M_exception; }
# 256 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      void
      exceptions(iostate __except)
      {
        _M_exception = __except;
        this->clear(_M_streambuf_state);
      }







      explicit
      basic_ios(basic_streambuf<_CharT, _Traits>* __sb)
      : ios_base(), _M_tie(0), _M_fill(), _M_fill_init(false), _M_streambuf(0),
 _M_ctype(0), _M_num_put(0), _M_num_get(0)
      { this->init(__sb); }







      virtual
      ~basic_ios() { }
# 294 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      basic_ostream<_CharT, _Traits>*
      tie() const
      { return _M_tie; }
# 306 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      basic_ostream<_CharT, _Traits>*
      tie(basic_ostream<_CharT, _Traits>* __tiestr)
      {
        basic_ostream<_CharT, _Traits>* __old = _M_tie;
        _M_tie = __tiestr;
        return __old;
      }







      basic_streambuf<_CharT, _Traits>*
      rdbuf() const
      { return _M_streambuf; }
# 346 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      basic_streambuf<_CharT, _Traits>*
      rdbuf(basic_streambuf<_CharT, _Traits>* __sb);
# 360 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      basic_ios&
      copyfmt(const basic_ios& __rhs);







      char_type
      fill() const
      {
 if (!_M_fill_init)
   {
     _M_fill = this->widen(' ');
     _M_fill_init = true;
   }
 return _M_fill;
      }
# 389 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      char_type
      fill(char_type __ch)
      {
 char_type __old = this->fill();
 _M_fill = __ch;
 return __old;
      }
# 409 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      locale
      imbue(const locale& __loc);
# 429 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      char
      narrow(char_type __c, char __dfault) const
      { return __check_facet(_M_ctype).narrow(__c, __dfault); }
# 448 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 3
      char_type
      widen(char __c) const
      { return __check_facet(_M_ctype).widen(__c); }

    protected:







      basic_ios()
      : ios_base(), _M_tie(0), _M_fill(char_type()), _M_fill_init(false),
 _M_streambuf(0), _M_ctype(0), _M_num_put(0), _M_num_get(0)
      { }







      void
      init(basic_streambuf<_CharT, _Traits>* __sb);


      basic_ios(const basic_ios&) = delete;
      basic_ios& operator=(const basic_ios&) = delete;

      void
      move(basic_ios& __rhs)
      {
 ios_base::_M_move(__rhs);
 _M_cache_locale(_M_ios_locale);
 this->tie(__rhs.tie(nullptr));
 _M_fill = __rhs._M_fill;
 _M_fill_init = __rhs._M_fill_init;
 _M_streambuf = nullptr;
      }

      void
      move(basic_ios&& __rhs)
      { this->move(__rhs); }

      void
      swap(basic_ios& __rhs) noexcept
      {
 ios_base::_M_swap(__rhs);
 _M_cache_locale(_M_ios_locale);
 __rhs._M_cache_locale(__rhs._M_ios_locale);
 std::swap(_M_tie, __rhs._M_tie);
 std::swap(_M_fill, __rhs._M_fill);
 std::swap(_M_fill_init, __rhs._M_fill_init);
      }

      void
      set_rdbuf(basic_streambuf<_CharT, _Traits>* __sb)
      { _M_streambuf = __sb; }


      void
      _M_cache_locale(const locale& __loc);
    };


}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.tcc" 1 3
# 34 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.tcc" 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _CharT, typename _Traits>
    void
    basic_ios<_CharT, _Traits>::clear(iostate __state)
    {
      if (this->rdbuf())
 _M_streambuf_state = __state;
      else
 _M_streambuf_state = __state | badbit;
      if (this->exceptions() & this->rdstate())
 __throw_ios_failure(("basic_ios::clear"));
    }

  template<typename _CharT, typename _Traits>
    basic_streambuf<_CharT, _Traits>*
    basic_ios<_CharT, _Traits>::rdbuf(basic_streambuf<_CharT, _Traits>* __sb)
    {
      basic_streambuf<_CharT, _Traits>* __old = _M_streambuf;
      _M_streambuf = __sb;
      this->clear();
      return __old;
    }

  template<typename _CharT, typename _Traits>
    basic_ios<_CharT, _Traits>&
    basic_ios<_CharT, _Traits>::copyfmt(const basic_ios& __rhs)
    {


      if (this != std::__addressof(__rhs))
 {




   _Words* __words = (__rhs._M_word_size <= _S_local_word_size) ?
                      _M_local_word : new _Words[__rhs._M_word_size];


   _Callback_list* __cb = __rhs._M_callbacks;
   if (__cb)
     __cb->_M_add_reference();
   _M_call_callbacks(erase_event);
   if (_M_word != _M_local_word)
     {
       delete [] _M_word;
       _M_word = 0;
     }
   _M_dispose_callbacks();


   _M_callbacks = __cb;
   for (int __i = 0; __i < __rhs._M_word_size; ++__i)
     __words[__i] = __rhs._M_word[__i];
   _M_word = __words;
   _M_word_size = __rhs._M_word_size;

   this->flags(__rhs.flags());
   this->width(__rhs.width());
   this->precision(__rhs.precision());
   this->tie(__rhs.tie());
   this->fill(__rhs.fill());
   _M_ios_locale = __rhs.getloc();
   _M_cache_locale(_M_ios_locale);

   _M_call_callbacks(copyfmt_event);


   this->exceptions(__rhs.exceptions());
 }
      return *this;
    }


  template<typename _CharT, typename _Traits>
    locale
    basic_ios<_CharT, _Traits>::imbue(const locale& __loc)
    {
      locale __old(this->getloc());
      ios_base::imbue(__loc);
      _M_cache_locale(__loc);
      if (this->rdbuf() != 0)
 this->rdbuf()->pubimbue(__loc);
      return __old;
    }

  template<typename _CharT, typename _Traits>
    void
    basic_ios<_CharT, _Traits>::init(basic_streambuf<_CharT, _Traits>* __sb)
    {

      ios_base::_M_init();


      _M_cache_locale(_M_ios_locale);
# 146 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.tcc" 3
      _M_fill = _CharT();
      _M_fill_init = false;

      _M_tie = 0;
      _M_exception = goodbit;
      _M_streambuf = __sb;
      _M_streambuf_state = __sb ? goodbit : badbit;
    }

  template<typename _CharT, typename _Traits>
    void
    basic_ios<_CharT, _Traits>::_M_cache_locale(const locale& __loc)
    {
      if (__builtin_expect(has_facet<__ctype_type>(__loc), true))
 _M_ctype = std::__addressof(use_facet<__ctype_type>(__loc));
      else
 _M_ctype = 0;

      if (__builtin_expect(has_facet<__num_put_type>(__loc), true))
 _M_num_put = std::__addressof(use_facet<__num_put_type>(__loc));
      else
 _M_num_put = 0;

      if (__builtin_expect(has_facet<__num_get_type>(__loc), true))
 _M_num_get = std::__addressof(use_facet<__num_get_type>(__loc));
      else
 _M_num_get = 0;
    }




  extern template class basic_ios<char>;


  extern template class basic_ios<wchar_t>;




}
# 517 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/basic_ios.h" 2 3
# 45 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ios" 2 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3




namespace std __attribute__ ((__visibility__ ("default")))
{
# 57 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _CharT, typename _Traits>
    class basic_ostream : virtual public basic_ios<_CharT, _Traits>
    {
    public:

      typedef _CharT char_type;
      typedef typename _Traits::int_type int_type;
      typedef typename _Traits::pos_type pos_type;
      typedef typename _Traits::off_type off_type;
      typedef _Traits traits_type;


      typedef basic_streambuf<_CharT, _Traits> __streambuf_type;
      typedef basic_ios<_CharT, _Traits> __ios_type;
      typedef basic_ostream<_CharT, _Traits> __ostream_type;
      typedef num_put<_CharT, ostreambuf_iterator<_CharT, _Traits> >
             __num_put_type;
      typedef ctype<_CharT> __ctype_type;
# 83 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      explicit
      basic_ostream(__streambuf_type* __sb)
      { this->init(__sb); }






      virtual
      ~basic_ostream() { }


      class sentry;
      friend class sentry;
# 107 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      operator<<(__ostream_type& (*__pf)(__ostream_type&))
      {



 return __pf(*this);
      }

      __ostream_type&
      operator<<(__ios_type& (*__pf)(__ios_type&))
      {



 __pf(*this);
 return *this;
      }

      __ostream_type&
      operator<<(ios_base& (*__pf) (ios_base&))
      {



 __pf(*this);
 return *this;
      }
# 165 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      operator<<(long __n)
      { return _M_insert(__n); }

      __ostream_type&
      operator<<(unsigned long __n)
      { return _M_insert(__n); }

      __ostream_type&
      operator<<(bool __n)
      { return _M_insert(__n); }

      __ostream_type&
      operator<<(short __n);

      __ostream_type&
      operator<<(unsigned short __n)
      {


 return _M_insert(static_cast<unsigned long>(__n));
      }

      __ostream_type&
      operator<<(int __n);

      __ostream_type&
      operator<<(unsigned int __n)
      {


 return _M_insert(static_cast<unsigned long>(__n));
      }


      __ostream_type&
      operator<<(long long __n)
      { return _M_insert(__n); }

      __ostream_type&
      operator<<(unsigned long long __n)
      { return _M_insert(__n); }
# 219 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      operator<<(double __f)
      { return _M_insert(__f); }

      __ostream_type&
      operator<<(float __f)
      {


 return _M_insert(static_cast<double>(__f));
      }

      __ostream_type&
      operator<<(long double __f)
      { return _M_insert(__f); }
# 244 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      operator<<(const void* __p)
      { return _M_insert(__p); }
# 282 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      operator<<(__streambuf_type* __sb);
# 315 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      put(char_type __c);
# 334 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      write(const char_type* __s, streamsize __n);
# 347 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      flush();
# 357 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      pos_type
      tellp();
# 368 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      __ostream_type&
      seekp(pos_type);
# 380 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
       __ostream_type&
      seekp(off_type, ios_base::seekdir);

    protected:
      basic_ostream()
      { this->init(0); }



      basic_ostream(basic_iostream<_CharT, _Traits>&) { }

      basic_ostream(const basic_ostream&) = delete;

      basic_ostream(basic_ostream&& __rhs)
      : __ios_type()
      { __ios_type::move(__rhs); }



      basic_ostream& operator=(const basic_ostream&) = delete;

      basic_ostream&
      operator=(basic_ostream&& __rhs)
      {
 swap(__rhs);
 return *this;
      }

      void
      swap(basic_ostream& __rhs)
      { __ios_type::swap(__rhs); }


      template<typename _ValueT>
 __ostream_type&
 _M_insert(_ValueT __v);

    private:

      void
      _M_write(const char_type* __s, streamsize __n)
      { std::__ostream_insert(*this, __s, __n); }

    };
# 432 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template <typename _CharT, typename _Traits>
    class basic_ostream<_CharT, _Traits>::sentry
    {

      bool _M_ok;
      basic_ostream<_CharT, _Traits>& _M_os;

    public:
# 451 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      explicit
      sentry(basic_ostream<_CharT, _Traits>& __os);

#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"







      ~sentry()
      {

 if (bool(_M_os.flags() & ios_base::unitbuf) && !uncaught_exception())
   {

     if (_M_os.rdbuf() && _M_os.rdbuf()->pubsync() == -1)
       _M_os.setstate(ios_base::badbit);
   }
      }
#pragma GCC diagnostic pop
# 483 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
      explicit

      operator bool() const
      { return _M_ok; }
    };
# 505 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __out, _CharT __c)
    {
      if (__out.width() != 0)
 return __ostream_insert(__out, &__c, 1);
      __out.put(__c);
      return __out;
    }

  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __out, char __c)
    { return (__out << __out.widen(__c)); }


  template<typename _Traits>
    inline basic_ostream<char, _Traits>&
    operator<<(basic_ostream<char, _Traits>& __out, char __c)
    {
      if (__out.width() != 0)
 return __ostream_insert(__out, &__c, 1);
      __out.put(__c);
      return __out;
    }


  template<typename _Traits>
    inline basic_ostream<char, _Traits>&
    operator<<(basic_ostream<char, _Traits>& __out, signed char __c)
    { return (__out << static_cast<char>(__c)); }

  template<typename _Traits>
    inline basic_ostream<char, _Traits>&
    operator<<(basic_ostream<char, _Traits>& __out, unsigned char __c)
    { return (__out << static_cast<char>(__c)); }
# 596 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __out, const _CharT* __s)
    {
      if (!__s)
 __out.setstate(ios_base::badbit);
      else
 __ostream_insert(__out, __s,
    static_cast<streamsize>(_Traits::length(__s)));
      return __out;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits> &
    operator<<(basic_ostream<_CharT, _Traits>& __out, const char* __s);


  template<typename _Traits>
    inline basic_ostream<char, _Traits>&
    operator<<(basic_ostream<char, _Traits>& __out, const char* __s)
    {
      if (!__s)
 __out.setstate(ios_base::badbit);
      else
 __ostream_insert(__out, __s,
    static_cast<streamsize>(_Traits::length(__s)));
      return __out;
    }


  template<typename _Traits>
    inline basic_ostream<char, _Traits>&
    operator<<(basic_ostream<char, _Traits>& __out, const signed char* __s)
    { return (__out << reinterpret_cast<const char*>(__s)); }

  template<typename _Traits>
    inline basic_ostream<char, _Traits> &
    operator<<(basic_ostream<char, _Traits>& __out, const unsigned char* __s)
    { return (__out << reinterpret_cast<const char*>(__s)); }
# 686 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    endl(basic_ostream<_CharT, _Traits>& __os)
    { return flush(__os.put(__os.widen('\n'))); }
# 698 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    ends(basic_ostream<_CharT, _Traits>& __os)
    { return __os.put(_CharT()); }






  template<typename _CharT, typename _Traits>
    inline basic_ostream<_CharT, _Traits>&
    flush(basic_ostream<_CharT, _Traits>& __os)
    { return __os.flush(); }
# 730 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _Tp>
    using _Require_derived_from_ios_base
      = _Require<is_class<_Tp>, __not_<is_same<_Tp, ios_base>>,
   is_convertible<typename add_pointer<_Tp>::type, ios_base*>>;

  template<typename _Os, typename _Tp,
    typename = _Require_derived_from_ios_base<_Os>,
    typename
      = decltype(std::declval<_Os&>() << std::declval<const _Tp&>())>
    using __rvalue_stream_insertion_t = _Os&&;
# 752 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
  template<typename _Ostream, typename _Tp>
    inline __rvalue_stream_insertion_t<_Ostream, _Tp>
    operator<<(_Ostream&& __os, const _Tp& __x)
    {
      __os << __x;
      return std::move(__os);
    }
# 831 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 3
}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ostream.tcc" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/ostream.tcc" 3



namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>::sentry::
    sentry(basic_ostream<_CharT, _Traits>& __os)
    : _M_ok(false), _M_os(__os)
    {

      if (__os.tie() && __os.good())
 __os.tie()->flush();

      if (__os.good())
 _M_ok = true;
      else if (__os.bad())
 __os.setstate(ios_base::failbit);
    }

  template<typename _CharT, typename _Traits>
    template<typename _ValueT>
      basic_ostream<_CharT, _Traits>&
      basic_ostream<_CharT, _Traits>::
      _M_insert(_ValueT __v)
      {
 sentry __cerb(*this);
 if (__cerb)
   {
     ios_base::iostate __err = ios_base::goodbit;
     try
       {
  const __num_put_type& __np = __check_facet(this->_M_num_put);
  if (__np.put(*this, *this, this->fill(), __v).failed())
    __err |= ios_base::badbit;
       }
     catch(__cxxabiv1::__forced_unwind&)
       {
  this->_M_setstate(ios_base::badbit);
  throw;
       }
     catch(...)
       { this->_M_setstate(ios_base::badbit); }
     if (__err)
       this->setstate(__err);
   }
 return *this;
      }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    operator<<(short __n)
    {


      const ios_base::fmtflags __fmt = this->flags() & ios_base::basefield;
      if (__fmt == ios_base::oct || __fmt == ios_base::hex)
 return _M_insert(static_cast<long>(static_cast<unsigned short>(__n)));
      else
 return _M_insert(static_cast<long>(__n));
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    operator<<(int __n)
    {


      const ios_base::fmtflags __fmt = this->flags() & ios_base::basefield;
      if (__fmt == ios_base::oct || __fmt == ios_base::hex)
 return _M_insert(static_cast<long>(static_cast<unsigned int>(__n)));
      else
 return _M_insert(static_cast<long>(__n));
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    operator<<(__streambuf_type* __sbin)
    {
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this);
      if (__cerb && __sbin)
 {
   try
     {
       if (!__copy_streambufs(__sbin, this->rdbuf()))
  __err |= ios_base::failbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::failbit); }
 }
      else if (!__sbin)
 __err |= ios_base::badbit;
      if (__err)
 this->setstate(__err);
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    put(char_type __c)
    {






      sentry __cerb(*this);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const int_type __put = this->rdbuf()->sputc(__c);
       if (traits_type::eq_int_type(__put, traits_type::eof()))
  __err |= ios_base::badbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    write(const _CharT* __s, streamsize __n)
    {







      sentry __cerb(*this);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       if (this->rdbuf()->sputn(__s, __n) != __n)
  __err = ios_base::badbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(ios_base::badbit);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    flush()
    {





      if (__streambuf_type* __buf = this->rdbuf())
 {
   sentry __cerb(*this);
   if (__cerb)
     {
       ios_base::iostate __err = ios_base::goodbit;
       try
  {
    if (this->rdbuf()->pubsync() == -1)
      __err |= ios_base::badbit;
  }
       catch(__cxxabiv1::__forced_unwind&)
  {
    this->_M_setstate(ios_base::badbit);
    throw;
  }
       catch(...)
  { this->_M_setstate(ios_base::badbit); }
       if (__err)
  this->setstate(__err);
     }
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    typename basic_ostream<_CharT, _Traits>::pos_type
    basic_ostream<_CharT, _Traits>::
    tellp()
    {
      sentry __cerb(*this);
      pos_type __ret = pos_type(-1);
      if (!this->fail())
 __ret = this->rdbuf()->pubseekoff(0, ios_base::cur, ios_base::out);
      return __ret;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    seekp(pos_type __pos)
    {
      sentry __cerb(*this);
      if (!this->fail())
 {


   const pos_type __p = this->rdbuf()->pubseekpos(__pos, ios_base::out);


   if (__p == pos_type(off_type(-1)))
     this->setstate(ios_base::failbit);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    basic_ostream<_CharT, _Traits>::
    seekp(off_type __off, ios_base::seekdir __dir)
    {
      sentry __cerb(*this);
      if (!this->fail())
 {


   const pos_type __p = this->rdbuf()->pubseekoff(__off, __dir,
        ios_base::out);


   if (__p == pos_type(off_type(-1)))
     this->setstate(ios_base::failbit);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __out, const char* __s)
    {
      if (!__s)
 __out.setstate(ios_base::badbit);
      else
 {


   const size_t __clen = char_traits<char>::length(__s);
   try
     {
       struct __ptr_guard
       {
  _CharT *__p;
  __ptr_guard (_CharT *__ip): __p(__ip) { }
  ~__ptr_guard() { delete[] __p; }
  _CharT* __get() { return __p; }
       } __pg (new _CharT[__clen]);

       _CharT *__ws = __pg.__get();
       for (size_t __i = 0; __i < __clen; ++__i)
  __ws[__i] = __out.widen(__s[__i]);
       __ostream_insert(__out, __ws, __clen);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __out._M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { __out._M_setstate(ios_base::badbit); }
 }
      return __out;
    }




  extern template class basic_ostream<char>;
  extern template ostream& endl(ostream&);
  extern template ostream& ends(ostream&);
  extern template ostream& flush(ostream&);
  extern template ostream& operator<<(ostream&, char);
  extern template ostream& operator<<(ostream&, unsigned char);
  extern template ostream& operator<<(ostream&, signed char);
  extern template ostream& operator<<(ostream&, const char*);
  extern template ostream& operator<<(ostream&, const unsigned char*);
  extern template ostream& operator<<(ostream&, const signed char*);

  extern template ostream& ostream::_M_insert(long);
  extern template ostream& ostream::_M_insert(unsigned long);
  extern template ostream& ostream::_M_insert(bool);

  extern template ostream& ostream::_M_insert(long long);
  extern template ostream& ostream::_M_insert(unsigned long long);

  extern template ostream& ostream::_M_insert(double);
  extern template ostream& ostream::_M_insert(long double);
  extern template ostream& ostream::_M_insert(const void*);


  extern template class basic_ostream<wchar_t>;
  extern template wostream& endl(wostream&);
  extern template wostream& ends(wostream&);
  extern template wostream& flush(wostream&);
  extern template wostream& operator<<(wostream&, wchar_t);
  extern template wostream& operator<<(wostream&, char);
  extern template wostream& operator<<(wostream&, const wchar_t*);
  extern template wostream& operator<<(wostream&, const char*);

  extern template wostream& wostream::_M_insert(long);
  extern template wostream& wostream::_M_insert(unsigned long);
  extern template wostream& wostream::_M_insert(bool);

  extern template wostream& wostream::_M_insert(long long);
  extern template wostream& wostream::_M_insert(unsigned long long);

  extern template wostream& wostream::_M_insert(double);
  extern template wostream& wostream::_M_insert(long double);
  extern template wostream& wostream::_M_insert(const void*);




}
# 834 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/ostream" 2 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 2 3

namespace std __attribute__ ((__visibility__ ("default")))
{
# 57 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    class basic_istream : virtual public basic_ios<_CharT, _Traits>
    {
    public:

      typedef _CharT char_type;
      typedef typename _Traits::int_type int_type;
      typedef typename _Traits::pos_type pos_type;
      typedef typename _Traits::off_type off_type;
      typedef _Traits traits_type;


      typedef basic_streambuf<_CharT, _Traits> __streambuf_type;
      typedef basic_ios<_CharT, _Traits> __ios_type;
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef num_get<_CharT, istreambuf_iterator<_CharT, _Traits> >
        __num_get_type;
      typedef ctype<_CharT> __ctype_type;

    protected:





      streamsize _M_gcount;

    public:







      explicit
      basic_istream(__streambuf_type* __sb)
      : _M_gcount(streamsize(0))
      { this->init(__sb); }






      virtual
      ~basic_istream()
      { _M_gcount = streamsize(0); }


      class sentry;
      friend class sentry;
# 119 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      operator>>(__istream_type& (*__pf)(__istream_type&))
      { return __pf(*this); }

      __istream_type&
      operator>>(__ios_type& (*__pf)(__ios_type&))
      {
 __pf(*this);
 return *this;
      }

      __istream_type&
      operator>>(ios_base& (*__pf)(ios_base&))
      {
 __pf(*this);
 return *this;
      }
# 167 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      operator>>(bool& __n)
      { return _M_extract(__n); }

      __istream_type&
      operator>>(short& __n);

      __istream_type&
      operator>>(unsigned short& __n)
      { return _M_extract(__n); }

      __istream_type&
      operator>>(int& __n);

      __istream_type&
      operator>>(unsigned int& __n)
      { return _M_extract(__n); }

      __istream_type&
      operator>>(long& __n)
      { return _M_extract(__n); }

      __istream_type&
      operator>>(unsigned long& __n)
      { return _M_extract(__n); }


      __istream_type&
      operator>>(long long& __n)
      { return _M_extract(__n); }

      __istream_type&
      operator>>(unsigned long long& __n)
      { return _M_extract(__n); }
# 213 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      operator>>(float& __f)
      { return _M_extract(__f); }

      __istream_type&
      operator>>(double& __f)
      { return _M_extract(__f); }

      __istream_type&
      operator>>(long double& __f)
      { return _M_extract(__f); }
# 234 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      operator>>(void*& __p)
      { return _M_extract(__p); }
# 258 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      operator>>(__streambuf_type* __sb);
# 268 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      streamsize
      gcount() const
      { return _M_gcount; }
# 301 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      int_type
      get();
# 315 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      get(char_type& __c);
# 342 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      get(char_type* __s, streamsize __n, char_type __delim);
# 353 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      get(char_type* __s, streamsize __n)
      { return this->get(__s, __n, this->widen('\n')); }
# 376 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      get(__streambuf_type& __sb, char_type __delim);
# 386 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      get(__streambuf_type& __sb)
      { return this->get(__sb, this->widen('\n')); }
# 415 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      getline(char_type* __s, streamsize __n, char_type __delim);
# 426 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      getline(char_type* __s, streamsize __n)
      { return this->getline(__s, __n, this->widen('\n')); }
# 450 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      ignore(streamsize __n, int_type __delim);

      __istream_type&
      ignore(streamsize __n);

      __istream_type&
      ignore();
# 467 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      int_type
      peek();
# 485 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      read(char_type* __s, streamsize __n);
# 504 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      streamsize
      readsome(char_type* __s, streamsize __n);
# 521 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      putback(char_type __c);
# 537 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      unget();
# 555 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      int
      sync();
# 570 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      pos_type
      tellg();
# 585 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      seekg(pos_type);
# 601 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      __istream_type&
      seekg(off_type, ios_base::seekdir);


    protected:
      basic_istream()
      : _M_gcount(streamsize(0))
      { this->init(0); }


      basic_istream(const basic_istream&) = delete;

      basic_istream(basic_istream&& __rhs)
      : __ios_type(), _M_gcount(__rhs._M_gcount)
      {
 __ios_type::move(__rhs);
 __rhs._M_gcount = 0;
      }



      basic_istream& operator=(const basic_istream&) = delete;

      basic_istream&
      operator=(basic_istream&& __rhs)
      {
 swap(__rhs);
 return *this;
      }

      void
      swap(basic_istream& __rhs)
      {
 __ios_type::swap(__rhs);
 std::swap(_M_gcount, __rhs._M_gcount);
      }


      template<typename _ValueT>
 __istream_type&
 _M_extract(_ValueT& __v);
    };


  template<>
    basic_istream<char>&
    basic_istream<char>::
    getline(char_type* __s, streamsize __n, char_type __delim);

  template<>
    basic_istream<char>&
    basic_istream<char>::
    ignore(streamsize __n);

  template<>
    basic_istream<char>&
    basic_istream<char>::
    ignore(streamsize __n, int_type __delim);


  template<>
    basic_istream<wchar_t>&
    basic_istream<wchar_t>::
    getline(char_type* __s, streamsize __n, char_type __delim);

  template<>
    basic_istream<wchar_t>&
    basic_istream<wchar_t>::
    ignore(streamsize __n);

  template<>
    basic_istream<wchar_t>&
    basic_istream<wchar_t>::
    ignore(streamsize __n, int_type __delim);
# 685 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    class basic_istream<_CharT, _Traits>::sentry
    {

      bool _M_ok;

    public:

      typedef _Traits traits_type;
      typedef basic_streambuf<_CharT, _Traits> __streambuf_type;
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef typename __istream_type::__ctype_type __ctype_type;
      typedef typename _Traits::int_type __int_type;
# 721 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      explicit
      sentry(basic_istream<_CharT, _Traits>& __is, bool __noskipws = false);
# 732 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
      explicit

      operator bool() const
      { return _M_ok; }
    };
# 750 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __in, _CharT& __c);

  template<class _Traits>
    inline basic_istream<char, _Traits>&
    operator>>(basic_istream<char, _Traits>& __in, unsigned char& __c)
    { return (__in >> reinterpret_cast<char&>(__c)); }

  template<class _Traits>
    inline basic_istream<char, _Traits>&
    operator>>(basic_istream<char, _Traits>& __in, signed char& __c)
    { return (__in >> reinterpret_cast<char&>(__c)); }



  template<typename _CharT, typename _Traits>
    void
    __istream_extract(basic_istream<_CharT, _Traits>&, _CharT*, streamsize);

  void __istream_extract(istream&, char*, streamsize);
# 800 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    __attribute__((__nonnull__(2), __access__(__write_only__, 2)))
    inline basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __in, _CharT* __s)
    {
# 834 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
 {

   streamsize __n = __gnu_cxx::__numeric_traits<streamsize>::__max;
   __n /= sizeof(_CharT);
   std::__istream_extract(__in, __s, __n);
 }
      return __in;
    }

  template<class _Traits>
    __attribute__((__nonnull__(2), __access__(__write_only__, 2)))
    inline basic_istream<char, _Traits>&
    operator>>(basic_istream<char, _Traits>& __in, unsigned char* __s)
    { return __in >> reinterpret_cast<char*>(__s); }

  template<class _Traits>
    __attribute__((__nonnull__(2), __access__(__write_only__, 2)))
    inline basic_istream<char, _Traits>&
    operator>>(basic_istream<char, _Traits>& __in, signed char* __s)
    { return __in >> reinterpret_cast<char*>(__s); }
# 889 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    class basic_iostream
    : public basic_istream<_CharT, _Traits>,
      public basic_ostream<_CharT, _Traits>
    {
    public:



      typedef _CharT char_type;
      typedef typename _Traits::int_type int_type;
      typedef typename _Traits::pos_type pos_type;
      typedef typename _Traits::off_type off_type;
      typedef _Traits traits_type;


      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef basic_ostream<_CharT, _Traits> __ostream_type;







      explicit
      basic_iostream(basic_streambuf<_CharT, _Traits>* __sb)
      : __istream_type(__sb), __ostream_type(__sb) { }




      virtual
      ~basic_iostream() { }

    protected:
      basic_iostream()
      : __istream_type(), __ostream_type() { }


      basic_iostream(const basic_iostream&) = delete;

      basic_iostream(basic_iostream&& __rhs)
      : __istream_type(std::move(__rhs)), __ostream_type(*this)
      { }



      basic_iostream& operator=(const basic_iostream&) = delete;

      basic_iostream&
      operator=(basic_iostream&& __rhs)
      {
 swap(__rhs);
 return *this;
      }

      void
      swap(basic_iostream& __rhs)
      { __istream_type::swap(__rhs); }

    };
# 972 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    ws(basic_istream<_CharT, _Traits>& __is);
# 988 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _Is, typename _Tp,
    typename = _Require_derived_from_ios_base<_Is>,
    typename = decltype(std::declval<_Is&>() >> std::declval<_Tp>())>
    using __rvalue_stream_extraction_t = _Is&&;
# 1004 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 3
  template<typename _Istream, typename _Tp>
    inline __rvalue_stream_extraction_t<_Istream, _Tp>
    operator>>(_Istream&& __is, _Tp&& __x)
    {
      __is >> std::forward<_Tp>(__x);
      return std::move(__is);
    }



}

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/istream.tcc" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/istream.tcc" 3



namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>::sentry::
    sentry(basic_istream<_CharT, _Traits>& __in, bool __noskip) : _M_ok(false)
    {
      ios_base::iostate __err = ios_base::goodbit;
      if (__in.good())
 {
   try
     {
       if (__in.tie())
  __in.tie()->flush();
       if (!__noskip && bool(__in.flags() & ios_base::skipws))
  {
    const __int_type __eof = traits_type::eof();
    __streambuf_type* __sb = __in.rdbuf();
    __int_type __c = __sb->sgetc();

    const __ctype_type& __ct = __check_facet(__in._M_ctype);
    while (!traits_type::eq_int_type(__c, __eof)
    && __ct.is(ctype_base::space,
        traits_type::to_char_type(__c)))
      __c = __sb->snextc();




    if (traits_type::eq_int_type(__c, __eof))
      __err |= ios_base::eofbit;
  }
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { __in._M_setstate(ios_base::badbit); }
 }

      if (__in.good() && __err == ios_base::goodbit)
 _M_ok = true;
      else
 {
   __err |= ios_base::failbit;
   __in.setstate(__err);
 }
    }

  template<typename _CharT, typename _Traits>
    template<typename _ValueT>
      basic_istream<_CharT, _Traits>&
      basic_istream<_CharT, _Traits>::
      _M_extract(_ValueT& __v)
      {
 sentry __cerb(*this, false);
 if (__cerb)
   {
     ios_base::iostate __err = ios_base::goodbit;
     try
       {
  const __num_get_type& __ng = __check_facet(this->_M_num_get);
  __ng.get(*this, 0, *this, __err, __v);
       }
     catch(__cxxabiv1::__forced_unwind&)
       {
  this->_M_setstate(ios_base::badbit);
  throw;
       }
     catch(...)
       { this->_M_setstate(ios_base::badbit); }
     if (__err)
       this->setstate(__err);
   }
 return *this;
      }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    operator>>(short& __n)
    {


      sentry __cerb(*this, false);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       long __l;
       const __num_get_type& __ng = __check_facet(this->_M_num_get);
       __ng.get(*this, 0, *this, __err, __l);



       if (__l < __gnu_cxx::__numeric_traits<short>::__min)
  {
    __err |= ios_base::failbit;
    __n = __gnu_cxx::__numeric_traits<short>::__min;
  }
       else if (__l > __gnu_cxx::__numeric_traits<short>::__max)
  {
    __err |= ios_base::failbit;
    __n = __gnu_cxx::__numeric_traits<short>::__max;
  }
       else
  __n = short(__l);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    operator>>(int& __n)
    {


      sentry __cerb(*this, false);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       long __l;
       const __num_get_type& __ng = __check_facet(this->_M_num_get);
       __ng.get(*this, 0, *this, __err, __l);



       if (__l < __gnu_cxx::__numeric_traits<int>::__min)
  {
    __err |= ios_base::failbit;
    __n = __gnu_cxx::__numeric_traits<int>::__min;
  }
       else if (__l > __gnu_cxx::__numeric_traits<int>::__max)
  {
    __err |= ios_base::failbit;
    __n = __gnu_cxx::__numeric_traits<int>::__max;
  }
       else
  __n = int(__l);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    operator>>(__streambuf_type* __sbout)
    {
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, false);
      if (__cerb && __sbout)
 {
   try
     {
       bool __ineof;
       if (!__copy_streambufs_eof(this->rdbuf(), __sbout, __ineof))
  __err |= ios_base::failbit;
       if (__ineof)
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::failbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::failbit); }
 }
      else if (!__sbout)
 __err |= ios_base::failbit;
      if (__err)
 this->setstate(__err);
      return *this;
    }

  template<typename _CharT, typename _Traits>
    typename basic_istream<_CharT, _Traits>::int_type
    basic_istream<_CharT, _Traits>::
    get(void)
    {
      const int_type __eof = traits_type::eof();
      int_type __c = __eof;
      _M_gcount = 0;
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   try
     {
       __c = this->rdbuf()->sbumpc();

       if (!traits_type::eq_int_type(__c, __eof))
  _M_gcount = 1;
       else
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
 }
      if (!_M_gcount)
 __err |= ios_base::failbit;
      if (__err)
 this->setstate(__err);
      return __c;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    get(char_type& __c)
    {
      _M_gcount = 0;
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   try
     {
       const int_type __cb = this->rdbuf()->sbumpc();

       if (!traits_type::eq_int_type(__cb, traits_type::eof()))
  {
    _M_gcount = 1;
    __c = traits_type::to_char_type(__cb);
  }
       else
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
 }
      if (!_M_gcount)
 __err |= ios_base::failbit;
      if (__err)
 this->setstate(__err);
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    get(char_type* __s, streamsize __n, char_type __delim)
    {
      _M_gcount = 0;
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   try
     {
       const int_type __idelim = traits_type::to_int_type(__delim);
       const int_type __eof = traits_type::eof();
       __streambuf_type* __sb = this->rdbuf();
       int_type __c = __sb->sgetc();

       while (_M_gcount + 1 < __n
       && !traits_type::eq_int_type(__c, __eof)
       && !traits_type::eq_int_type(__c, __idelim))
  {
    *__s++ = traits_type::to_char_type(__c);
    ++_M_gcount;
    __c = __sb->snextc();
  }
       if (traits_type::eq_int_type(__c, __eof))
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
 }


      if (__n > 0)
 *__s = char_type();
      if (!_M_gcount)
 __err |= ios_base::failbit;
      if (__err)
 this->setstate(__err);
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    get(__streambuf_type& __sb, char_type __delim)
    {
      _M_gcount = 0;
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   try
     {
       const int_type __idelim = traits_type::to_int_type(__delim);
       const int_type __eof = traits_type::eof();
       __streambuf_type* __this_sb = this->rdbuf();
       int_type __c = __this_sb->sgetc();
       char_type __c2 = traits_type::to_char_type(__c);
       unsigned long long __gcount = 0;

       while (!traits_type::eq_int_type(__c, __eof)
       && !traits_type::eq_int_type(__c, __idelim)
       && !traits_type::eq_int_type(__sb.sputc(__c2), __eof))
  {
    ++__gcount;
    __c = __this_sb->snextc();
    __c2 = traits_type::to_char_type(__c);
  }
       if (traits_type::eq_int_type(__c, __eof))
  __err |= ios_base::eofbit;


       if (__gcount <= __gnu_cxx::__numeric_traits<streamsize>::__max)
  _M_gcount = __gcount;
       else
  _M_gcount = __gnu_cxx::__numeric_traits<streamsize>::__max;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
 }
      if (!_M_gcount)
 __err |= ios_base::failbit;
      if (__err)
 this->setstate(__err);
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    getline(char_type* __s, streamsize __n, char_type __delim)
    {
      _M_gcount = 0;
      ios_base::iostate __err = ios_base::goodbit;
      sentry __cerb(*this, true);
      if (__cerb)
        {
          try
            {
              const int_type __idelim = traits_type::to_int_type(__delim);
              const int_type __eof = traits_type::eof();
              __streambuf_type* __sb = this->rdbuf();
              int_type __c = __sb->sgetc();

              while (_M_gcount + 1 < __n
                     && !traits_type::eq_int_type(__c, __eof)
                     && !traits_type::eq_int_type(__c, __idelim))
                {
                  *__s++ = traits_type::to_char_type(__c);
                  __c = __sb->snextc();
                  ++_M_gcount;
                }
              if (traits_type::eq_int_type(__c, __eof))
                __err |= ios_base::eofbit;
              else
                {
                  if (traits_type::eq_int_type(__c, __idelim))
                    {
                      __sb->sbumpc();
                      ++_M_gcount;
                    }
                  else
                    __err |= ios_base::failbit;
                }
            }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
          catch(...)
            { this->_M_setstate(ios_base::badbit); }
        }


      if (__n > 0)
 *__s = char_type();
      if (!_M_gcount)
        __err |= ios_base::failbit;
      if (__err)
        this->setstate(__err);
      return *this;
    }




  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    ignore(void)
    {
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const int_type __eof = traits_type::eof();
       __streambuf_type* __sb = this->rdbuf();

       if (traits_type::eq_int_type(__sb->sbumpc(), __eof))
  __err |= ios_base::eofbit;
       else
  _M_gcount = 1;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    ignore(streamsize __n)
    {
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb && __n > 0)
        {
          ios_base::iostate __err = ios_base::goodbit;
          try
            {
              const int_type __eof = traits_type::eof();
              __streambuf_type* __sb = this->rdbuf();
              int_type __c = __sb->sgetc();
# 530 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/istream.tcc" 3
       bool __large_ignore = false;
       while (true)
  {
    while (_M_gcount < __n
    && !traits_type::eq_int_type(__c, __eof))
      {
        ++_M_gcount;
        __c = __sb->snextc();
      }
    if (__n == __gnu_cxx::__numeric_traits<streamsize>::__max
        && !traits_type::eq_int_type(__c, __eof))
      {
        _M_gcount =
   __gnu_cxx::__numeric_traits<streamsize>::__min;
        __large_ignore = true;
      }
    else
      break;
  }

       if (__n == __gnu_cxx::__numeric_traits<streamsize>::__max)
  {
    if (__large_ignore)
      _M_gcount = __gnu_cxx::__numeric_traits<streamsize>::__max;

    if (traits_type::eq_int_type(__c, __eof))
      __err |= ios_base::eofbit;
  }
       else if (_M_gcount < __n)
  {
    if (traits_type::eq_int_type(__c, __eof))
      __err |= ios_base::eofbit;
  }
            }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
          catch(...)
            { this->_M_setstate(ios_base::badbit); }
          if (__err)
            this->setstate(__err);
        }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    ignore(streamsize __n, int_type __delim)
    {
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb && __n > 0)
        {
          ios_base::iostate __err = ios_base::goodbit;
          try
            {
              const int_type __eof = traits_type::eof();
              __streambuf_type* __sb = this->rdbuf();
              int_type __c = __sb->sgetc();


       bool __large_ignore = false;
       while (true)
  {
    while (_M_gcount < __n
    && !traits_type::eq_int_type(__c, __eof)
    && !traits_type::eq_int_type(__c, __delim))
      {
        ++_M_gcount;
        __c = __sb->snextc();
      }
    if (__n == __gnu_cxx::__numeric_traits<streamsize>::__max
        && !traits_type::eq_int_type(__c, __eof)
        && !traits_type::eq_int_type(__c, __delim))
      {
        _M_gcount =
   __gnu_cxx::__numeric_traits<streamsize>::__min;
        __large_ignore = true;
      }
    else
      break;
  }

       if (__n == __gnu_cxx::__numeric_traits<streamsize>::__max)
  {
    if (__large_ignore)
      _M_gcount = __gnu_cxx::__numeric_traits<streamsize>::__max;

    if (traits_type::eq_int_type(__c, __eof))
      __err |= ios_base::eofbit;
    else
      {
        if (_M_gcount != __n)
   ++_M_gcount;
        __sb->sbumpc();
      }
  }
       else if (_M_gcount < __n)
  {
    if (traits_type::eq_int_type(__c, __eof))
      __err |= ios_base::eofbit;
    else
      {
        ++_M_gcount;
        __sb->sbumpc();
      }
  }
            }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
          catch(...)
            { this->_M_setstate(ios_base::badbit); }
          if (__err)
            this->setstate(__err);
        }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    typename basic_istream<_CharT, _Traits>::int_type
    basic_istream<_CharT, _Traits>::
    peek(void)
    {
      int_type __c = traits_type::eof();
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       __c = this->rdbuf()->sgetc();
       if (traits_type::eq_int_type(__c, traits_type::eof()))
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return __c;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    read(char_type* __s, streamsize __n)
    {
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       _M_gcount = this->rdbuf()->sgetn(__s, __n);
       if (_M_gcount != __n)
  __err |= (ios_base::eofbit | ios_base::failbit);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    streamsize
    basic_istream<_CharT, _Traits>::
    readsome(char_type* __s, streamsize __n)
    {
      _M_gcount = 0;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {

       const streamsize __num = this->rdbuf()->in_avail();
       if (__num > 0)
  _M_gcount = this->rdbuf()->sgetn(__s, std::min(__num, __n));
       else if (__num == -1)
  __err |= ios_base::eofbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return _M_gcount;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    putback(char_type __c)
    {


      _M_gcount = 0;

      this->clear(this->rdstate() & ~ios_base::eofbit);
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const int_type __eof = traits_type::eof();
       __streambuf_type* __sb = this->rdbuf();
       if (!__sb
    || traits_type::eq_int_type(__sb->sputbackc(__c), __eof))
  __err |= ios_base::badbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    unget(void)
    {


      _M_gcount = 0;

      this->clear(this->rdstate() & ~ios_base::eofbit);
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const int_type __eof = traits_type::eof();
       __streambuf_type* __sb = this->rdbuf();
       if (!__sb
    || traits_type::eq_int_type(__sb->sungetc(), __eof))
  __err |= ios_base::badbit;
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    int
    basic_istream<_CharT, _Traits>::
    sync(void)
    {


      int __ret = -1;
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       __streambuf_type* __sb = this->rdbuf();
       if (__sb)
  {
    if (__sb->pubsync() == -1)
      __err |= ios_base::badbit;
    else
      __ret = 0;
  }
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return __ret;
    }

  template<typename _CharT, typename _Traits>
    typename basic_istream<_CharT, _Traits>::pos_type
    basic_istream<_CharT, _Traits>::
    tellg(void)
    {


      pos_type __ret = pos_type(-1);
      sentry __cerb(*this, true);
      if (__cerb)
 {
   try
     {
       if (!this->fail())
  __ret = this->rdbuf()->pubseekoff(0, ios_base::cur,
        ios_base::in);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
 }
      return __ret;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    seekg(pos_type __pos)
    {



      this->clear(this->rdstate() & ~ios_base::eofbit);
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       if (!this->fail())
  {

    const pos_type __p = this->rdbuf()->pubseekpos(__pos,
         ios_base::in);


    if (__p == pos_type(off_type(-1)))
      __err |= ios_base::failbit;
  }
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }

  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    basic_istream<_CharT, _Traits>::
    seekg(off_type __off, ios_base::seekdir __dir)
    {



      this->clear(this->rdstate() & ~ios_base::eofbit);
      sentry __cerb(*this, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       if (!this->fail())
  {

    const pos_type __p = this->rdbuf()->pubseekoff(__off, __dir,
         ios_base::in);


    if (__p == pos_type(off_type(-1)))
      __err |= ios_base::failbit;
  }
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       this->_M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { this->_M_setstate(ios_base::badbit); }
   if (__err)
     this->setstate(__err);
 }
      return *this;
    }


  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __in, _CharT& __c)
    {
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef typename __istream_type::int_type __int_type;

      typename __istream_type::sentry __cerb(__in, false);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const __int_type __cb = __in.rdbuf()->sbumpc();
       if (!_Traits::eq_int_type(__cb, _Traits::eof()))
  __c = _Traits::to_char_type(__cb);
       else
  __err |= (ios_base::eofbit | ios_base::failbit);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { __in._M_setstate(ios_base::badbit); }
   if (__err)
     __in.setstate(__err);
 }
      return __in;
    }

  template<typename _CharT, typename _Traits>
    void
    __istream_extract(basic_istream<_CharT, _Traits>& __in, _CharT* __s,
        streamsize __num)
    {
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef basic_streambuf<_CharT, _Traits> __streambuf_type;
      typedef typename _Traits::int_type int_type;
      typedef _CharT char_type;
      typedef ctype<_CharT> __ctype_type;

      streamsize __extracted = 0;
      ios_base::iostate __err = ios_base::goodbit;
      typename __istream_type::sentry __cerb(__in, false);
      if (__cerb)
 {
   try
     {

       streamsize __width = __in.width();
       if (0 < __width && __width < __num)
  __num = __width;

       const __ctype_type& __ct = use_facet<__ctype_type>(__in.getloc());

       const int_type __eof = _Traits::eof();
       __streambuf_type* __sb = __in.rdbuf();
       int_type __c = __sb->sgetc();

       while (__extracted < __num - 1
       && !_Traits::eq_int_type(__c, __eof)
       && !__ct.is(ctype_base::space,
     _Traits::to_char_type(__c)))
  {
    *__s++ = _Traits::to_char_type(__c);
    ++__extracted;
    __c = __sb->snextc();
  }

       if (__extracted < __num - 1
    && _Traits::eq_int_type(__c, __eof))
  __err |= ios_base::eofbit;



       *__s = char_type();
       __in.width(0);
     }
   catch(__cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     { __in._M_setstate(ios_base::badbit); }
 }
      if (!__extracted)
 __err |= ios_base::failbit;
      if (__err)
 __in.setstate(__err);
    }


  template<typename _CharT, typename _Traits>
    basic_istream<_CharT, _Traits>&
    ws(basic_istream<_CharT, _Traits>& __in)
    {
      typedef basic_istream<_CharT, _Traits> __istream_type;
      typedef basic_streambuf<_CharT, _Traits> __streambuf_type;
      typedef typename __istream_type::int_type __int_type;
      typedef ctype<_CharT> __ctype_type;



      typename __istream_type::sentry __cerb(__in, true);
      if (__cerb)
 {
   ios_base::iostate __err = ios_base::goodbit;
   try
     {
       const __ctype_type& __ct = use_facet<__ctype_type>(__in.getloc());
       const __int_type __eof = _Traits::eof();
       __streambuf_type* __sb = __in.rdbuf();
       __int_type __c = __sb->sgetc();

       while (true)
  {
    if (_Traits::eq_int_type(__c, __eof))
      {
        __err = ios_base::eofbit;
        break;
      }
    if (!__ct.is(ctype_base::space, _Traits::to_char_type(__c)))
      break;
    __c = __sb->snextc();
  }
     }
   catch(const __cxxabiv1::__forced_unwind&)
     {
       __in._M_setstate(ios_base::badbit);
       throw;
     }
   catch(...)
     {
       __in._M_setstate(ios_base::badbit);
     }
   if (__err)
     __in.setstate(__err);
 }
      return __in;
    }




  extern template class basic_istream<char>;
  extern template istream& ws(istream&);
  extern template istream& operator>>(istream&, char&);
  extern template istream& operator>>(istream&, unsigned char&);
  extern template istream& operator>>(istream&, signed char&);

  extern template istream& istream::_M_extract(unsigned short&);
  extern template istream& istream::_M_extract(unsigned int&);
  extern template istream& istream::_M_extract(long&);
  extern template istream& istream::_M_extract(unsigned long&);
  extern template istream& istream::_M_extract(bool&);

  extern template istream& istream::_M_extract(long long&);
  extern template istream& istream::_M_extract(unsigned long long&);

  extern template istream& istream::_M_extract(float&);
  extern template istream& istream::_M_extract(double&);
  extern template istream& istream::_M_extract(long double&);
  extern template istream& istream::_M_extract(void*&);

  extern template class basic_iostream<char>;


  extern template class basic_istream<wchar_t>;
  extern template wistream& ws(wistream&);
  extern template wistream& operator>>(wistream&, wchar_t&);
  extern template void __istream_extract(wistream&, wchar_t*, streamsize);

  extern template wistream& wistream::_M_extract(unsigned short&);
  extern template wistream& wistream::_M_extract(unsigned int&);
  extern template wistream& wistream::_M_extract(long&);
  extern template wistream& wistream::_M_extract(unsigned long&);
  extern template wistream& wistream::_M_extract(bool&);

  extern template wistream& wistream::_M_extract(long long&);
  extern template wistream& wistream::_M_extract(unsigned long long&);

  extern template wistream& wistream::_M_extract(float&);
  extern template wistream& wistream::_M_extract(double&);
  extern template wistream& wistream::_M_extract(long double&);
  extern template wistream& wistream::_M_extract(void*&);

  extern template class basic_iostream<wchar_t>;




}
# 1017 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/istream" 2 3
# 39 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 2 3
# 48 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
namespace std __attribute__ ((__visibility__ ("default")))
{

namespace __cxx11 {
# 71 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    class basic_stringbuf : public basic_streambuf<_CharT, _Traits>
    {
      struct __xfer_bufptrs;


      using allocator_traits = std::allocator_traits<_Alloc>;
      using _Noexcept_swap
 = __or_<typename allocator_traits::propagate_on_container_swap,
  typename allocator_traits::is_always_equal>;


    public:

      typedef _CharT char_type;
      typedef _Traits traits_type;


      typedef _Alloc allocator_type;
      typedef typename traits_type::int_type int_type;
      typedef typename traits_type::pos_type pos_type;
      typedef typename traits_type::off_type off_type;

      typedef basic_streambuf<char_type, traits_type> __streambuf_type;
      typedef basic_string<char_type, _Traits, _Alloc> __string_type;
      typedef typename __string_type::size_type __size_type;

    protected:

      ios_base::openmode _M_mode;


      __string_type _M_string;

    public:
# 114 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_stringbuf()
      : __streambuf_type(), _M_mode(ios_base::in | ios_base::out), _M_string()
      { }
# 125 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_stringbuf(ios_base::openmode __mode)
      : __streambuf_type(), _M_mode(__mode), _M_string()
      { }
# 138 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_stringbuf(const __string_type& __str,
        ios_base::openmode __mode = ios_base::in | ios_base::out)
      : __streambuf_type(), _M_mode(),
 _M_string(__str.data(), __str.size(), __str.get_allocator())
      { _M_stringbuf_init(__mode); }


      basic_stringbuf(const basic_stringbuf&) = delete;

      basic_stringbuf(basic_stringbuf&& __rhs)
      : basic_stringbuf(std::move(__rhs), __xfer_bufptrs(__rhs, this))
      { __rhs._M_sync(const_cast<char_type*>(__rhs._M_string.data()), 0, 0); }
# 202 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_stringbuf&
      operator=(const basic_stringbuf&) = delete;

      basic_stringbuf&
      operator=(basic_stringbuf&& __rhs)
      {
 __xfer_bufptrs __st{__rhs, this};
 const __streambuf_type& __base = __rhs;
 __streambuf_type::operator=(__base);
 this->pubimbue(__rhs.getloc());
 _M_mode = __rhs._M_mode;
 _M_string = std::move(__rhs._M_string);
 __rhs._M_sync(const_cast<char_type*>(__rhs._M_string.data()), 0, 0);
 return *this;
      }

      void
      swap(basic_stringbuf& __rhs) noexcept(_Noexcept_swap::value)
      {
 __xfer_bufptrs __l_st{*this, std::__addressof(__rhs)};
 __xfer_bufptrs __r_st{__rhs, this};
 __streambuf_type& __base = __rhs;
 __streambuf_type::swap(__base);
 __rhs.pubimbue(this->pubimbue(__rhs.getloc()));
 std::swap(_M_mode, __rhs._M_mode);
 std::swap(_M_string, __rhs._M_string);
      }
# 241 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      __string_type
      str() const
      {
 __string_type __ret(_M_string.get_allocator());
 if (char_type* __hi = _M_high_mark())
   __ret.assign(this->pbase(), __hi);
 else
   __ret = _M_string;
 return __ret;
      }
# 294 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      void
      str(const __string_type& __s)
      {


 _M_string.assign(__s.data(), __s.size());
 _M_stringbuf_init(_M_mode);
      }
# 323 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
    protected:

      void
      _M_stringbuf_init(ios_base::openmode __mode)
      {
 _M_mode = __mode;
 __size_type __len = 0;
 if (_M_mode & (ios_base::ate | ios_base::app))
   __len = _M_string.size();
 _M_sync(const_cast<char_type*>(_M_string.data()), 0, __len);
      }

      virtual streamsize
      showmanyc()
      {
 streamsize __ret = -1;
 if (_M_mode & ios_base::in)
   {
     _M_update_egptr();
     __ret = this->egptr() - this->gptr();
   }
 return __ret;
      }

      virtual int_type
      underflow();

      virtual int_type
      pbackfail(int_type __c = traits_type::eof());

      virtual int_type
      overflow(int_type __c = traits_type::eof());
# 367 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      virtual __streambuf_type*
      setbuf(char_type* __s, streamsize __n)
      {
 if (__s && __n >= 0)
   {






     _M_string.clear();


     _M_sync(__s, __n, 0);
   }
 return this;
      }

      virtual pos_type
      seekoff(off_type __off, ios_base::seekdir __way,
       ios_base::openmode __mode = ios_base::in | ios_base::out);

      virtual pos_type
      seekpos(pos_type __sp,
       ios_base::openmode __mode = ios_base::in | ios_base::out);




      void
      _M_sync(char_type* __base, __size_type __i, __size_type __o);



      void
      _M_update_egptr()
      {
 if (char_type* __pptr = this->pptr())
   {
     char_type* __egptr = this->egptr();
     if (!__egptr || __pptr > __egptr)
       {
  if (_M_mode & ios_base::in)
    this->setg(this->eback(), this->gptr(), __pptr);
  else
    this->setg(__pptr, __pptr, __pptr);
       }
   }
      }



      void
      _M_pbump(char_type* __pbeg, char_type* __pend, off_type __off);

    private:




      __attribute__((__always_inline__))
      char_type*
      _M_high_mark() const noexcept
      {
 if (char_type* __pptr = this->pptr())
   {
     char_type* __egptr = this->egptr();
     if (!__egptr || __pptr > __egptr)
       return __pptr;
     else
       return __egptr;
   }
 return 0;
      }





      struct __xfer_bufptrs
      {
 __xfer_bufptrs(const basic_stringbuf& __from, basic_stringbuf* __to)
 : _M_to{__to}, _M_goff{-1, -1, -1}, _M_poff{-1, -1, -1}
 {
   const _CharT* const __str = __from._M_string.data();
   const _CharT* __end = nullptr;
   if (__from.eback())
     {
       _M_goff[0] = __from.eback() - __str;
       _M_goff[1] = __from.gptr() - __str;
       _M_goff[2] = __from.egptr() - __str;
       __end = __from.egptr();
     }
   if (__from.pbase())
     {
       _M_poff[0] = __from.pbase() - __str;
       _M_poff[1] = __from.pptr() - __from.pbase();
       _M_poff[2] = __from.epptr() - __str;
       if (!__end || __from.pptr() > __end)
  __end = __from.pptr();
     }


   if (__end)
     {


       auto& __mut_from = const_cast<basic_stringbuf&>(__from);
       __mut_from._M_string._M_length(__end - __str);
     }
 }

 ~__xfer_bufptrs()
 {
   char_type* __str = const_cast<char_type*>(_M_to->_M_string.data());
   if (_M_goff[0] != -1)
     _M_to->setg(__str+_M_goff[0], __str+_M_goff[1], __str+_M_goff[2]);
   if (_M_poff[0] != -1)
     _M_to->_M_pbump(__str+_M_poff[0], __str+_M_poff[2], _M_poff[1]);
 }

 basic_stringbuf* _M_to;
 off_type _M_goff[3];
 off_type _M_poff[3];
      };
# 503 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_stringbuf(basic_stringbuf&& __rhs, __xfer_bufptrs&&)
      : __streambuf_type(static_cast<const __streambuf_type&>(__rhs)),
      _M_mode(__rhs._M_mode), _M_string(std::move(__rhs._M_string))
      { }
# 518 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
    };
# 536 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
  template<typename _CharT, typename _Traits, typename _Alloc>
    class basic_istringstream : public basic_istream<_CharT, _Traits>
    {
    public:

      typedef _CharT char_type;
      typedef _Traits traits_type;


      typedef _Alloc allocator_type;
      typedef typename traits_type::int_type int_type;
      typedef typename traits_type::pos_type pos_type;
      typedef typename traits_type::off_type off_type;


      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef basic_stringbuf<_CharT, _Traits, _Alloc> __stringbuf_type;
      typedef basic_istream<char_type, traits_type> __istream_type;

    private:
      __stringbuf_type _M_stringbuf;

    public:
# 570 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_istringstream()
      : __istream_type(), _M_stringbuf(ios_base::in)
      { this->init(&_M_stringbuf); }
# 586 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_istringstream(ios_base::openmode __mode)
      : __istream_type(), _M_stringbuf(__mode | ios_base::in)
      { this->init(&_M_stringbuf); }
# 604 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_istringstream(const __string_type& __str,
     ios_base::openmode __mode = ios_base::in)
      : __istream_type(), _M_stringbuf(__str, __mode | ios_base::in)
      { this->init(&_M_stringbuf); }







      ~basic_istringstream()
      { }


      basic_istringstream(const basic_istringstream&) = delete;

      basic_istringstream(basic_istringstream&& __rhs)
      : __istream_type(std::move(__rhs)),
      _M_stringbuf(std::move(__rhs._M_stringbuf))
      { __istream_type::set_rdbuf(&_M_stringbuf); }
# 661 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_istringstream&
      operator=(const basic_istringstream&) = delete;

      basic_istringstream&
      operator=(basic_istringstream&& __rhs)
      {
 __istream_type::operator=(std::move(__rhs));
 _M_stringbuf = std::move(__rhs._M_stringbuf);
 return *this;
      }

      void
      swap(basic_istringstream& __rhs)
      {
 __istream_type::swap(__rhs);
 _M_stringbuf.swap(__rhs._M_stringbuf);
      }
# 687 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      __stringbuf_type*
      rdbuf() const
      { return const_cast<__stringbuf_type*>(&_M_stringbuf); }





      __string_type
      str() const
      { return _M_stringbuf.str(); }
# 722 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      void
      str(const __string_type& __s)
      { _M_stringbuf.str(__s); }
# 739 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
    };
# 757 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
  template <typename _CharT, typename _Traits, typename _Alloc>
    class basic_ostringstream : public basic_ostream<_CharT, _Traits>
    {
    public:

      typedef _CharT char_type;
      typedef _Traits traits_type;


      typedef _Alloc allocator_type;
      typedef typename traits_type::int_type int_type;
      typedef typename traits_type::pos_type pos_type;
      typedef typename traits_type::off_type off_type;


      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef basic_stringbuf<_CharT, _Traits, _Alloc> __stringbuf_type;
      typedef basic_ostream<char_type, traits_type> __ostream_type;

    private:
      __stringbuf_type _M_stringbuf;

    public:
# 791 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_ostringstream()
      : __ostream_type(), _M_stringbuf(ios_base::out)
      { this->init(&_M_stringbuf); }
# 807 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_ostringstream(ios_base::openmode __mode)
      : __ostream_type(), _M_stringbuf(__mode | ios_base::out)
      { this->init(&_M_stringbuf); }
# 825 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_ostringstream(const __string_type& __str,
     ios_base::openmode __mode = ios_base::out)
      : __ostream_type(), _M_stringbuf(__str, __mode | ios_base::out)
      { this->init(&_M_stringbuf); }







      ~basic_ostringstream()
      { }


      basic_ostringstream(const basic_ostringstream&) = delete;

      basic_ostringstream(basic_ostringstream&& __rhs)
      : __ostream_type(std::move(__rhs)),
      _M_stringbuf(std::move(__rhs._M_stringbuf))
      { __ostream_type::set_rdbuf(&_M_stringbuf); }
# 882 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_ostringstream&
      operator=(const basic_ostringstream&) = delete;

      basic_ostringstream&
      operator=(basic_ostringstream&& __rhs)
      {
 __ostream_type::operator=(std::move(__rhs));
 _M_stringbuf = std::move(__rhs._M_stringbuf);
 return *this;
      }

      void
      swap(basic_ostringstream& __rhs)
      {
 __ostream_type::swap(__rhs);
 _M_stringbuf.swap(__rhs._M_stringbuf);
      }
# 908 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      __stringbuf_type*
      rdbuf() const
      { return const_cast<__stringbuf_type*>(&_M_stringbuf); }





      __string_type
      str() const
      { return _M_stringbuf.str(); }
# 943 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      void
      str(const __string_type& __s)
      { _M_stringbuf.str(__s); }
# 960 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
    };
# 978 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
  template <typename _CharT, typename _Traits, typename _Alloc>
    class basic_stringstream : public basic_iostream<_CharT, _Traits>
    {
    public:

      typedef _CharT char_type;
      typedef _Traits traits_type;


      typedef _Alloc allocator_type;
      typedef typename traits_type::int_type int_type;
      typedef typename traits_type::pos_type pos_type;
      typedef typename traits_type::off_type off_type;


      typedef basic_string<_CharT, _Traits, _Alloc> __string_type;
      typedef basic_stringbuf<_CharT, _Traits, _Alloc> __stringbuf_type;
      typedef basic_iostream<char_type, traits_type> __iostream_type;

    private:
      __stringbuf_type _M_stringbuf;

    public:
# 1012 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_stringstream()
      : __iostream_type(), _M_stringbuf(ios_base::out | ios_base::in)
      { this->init(&_M_stringbuf); }
# 1026 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_stringstream(ios_base::openmode __m)
      : __iostream_type(), _M_stringbuf(__m)
      { this->init(&_M_stringbuf); }
# 1042 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      explicit
      basic_stringstream(const __string_type& __str,
    ios_base::openmode __m = ios_base::out | ios_base::in)
      : __iostream_type(), _M_stringbuf(__str, __m)
      { this->init(&_M_stringbuf); }







      ~basic_stringstream()
      { }


      basic_stringstream(const basic_stringstream&) = delete;

      basic_stringstream(basic_stringstream&& __rhs)
      : __iostream_type(std::move(__rhs)),
      _M_stringbuf(std::move(__rhs._M_stringbuf))
      { __iostream_type::set_rdbuf(&_M_stringbuf); }
# 1101 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      basic_stringstream&
      operator=(const basic_stringstream&) = delete;

      basic_stringstream&
      operator=(basic_stringstream&& __rhs)
      {
 __iostream_type::operator=(std::move(__rhs));
 _M_stringbuf = std::move(__rhs._M_stringbuf);
 return *this;
      }

      void
      swap(basic_stringstream& __rhs)
      {
 __iostream_type::swap(__rhs);
 _M_stringbuf.swap(__rhs._M_stringbuf);
      }
# 1127 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      __stringbuf_type*
      rdbuf() const
      { return const_cast<__stringbuf_type*>(&_M_stringbuf); }





      __string_type
      str() const
      { return _M_stringbuf.str(); }
# 1162 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
      void
      str(const __string_type& __s)
      { _M_stringbuf.str(__s); }
# 1179 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 3
    };



  template <class _CharT, class _Traits, class _Allocator>
    inline void
    swap(basic_stringbuf<_CharT, _Traits, _Allocator>& __x,
  basic_stringbuf<_CharT, _Traits, _Allocator>& __y)
    noexcept(noexcept(__x.swap(__y)))
    { __x.swap(__y); }


  template <class _CharT, class _Traits, class _Allocator>
    inline void
    swap(basic_istringstream<_CharT, _Traits, _Allocator>& __x,
  basic_istringstream<_CharT, _Traits, _Allocator>& __y)
    { __x.swap(__y); }


  template <class _CharT, class _Traits, class _Allocator>
    inline void
    swap(basic_ostringstream<_CharT, _Traits, _Allocator>& __x,
  basic_ostringstream<_CharT, _Traits, _Allocator>& __y)
    { __x.swap(__y); }


  template <class _CharT, class _Traits, class _Allocator>
    inline void
    swap(basic_stringstream<_CharT, _Traits, _Allocator>& __x,
  basic_stringstream<_CharT, _Traits, _Allocator>& __y)
    { __x.swap(__y); }


}

}



# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/sstream.tcc" 1 3
# 38 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/sstream.tcc" 3

namespace std __attribute__ ((__visibility__ ("default")))
{


  template <class _CharT, class _Traits, class _Alloc>
    typename basic_stringbuf<_CharT, _Traits, _Alloc>::int_type
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    pbackfail(int_type __c)
    {
      int_type __ret = traits_type::eof();
      if (this->eback() < this->gptr())
 {


   const bool __testeof = traits_type::eq_int_type(__c, __ret);
   if (!__testeof)
     {
       const bool __testeq = traits_type::eq(traits_type::
          to_char_type(__c),
          this->gptr()[-1]);
       const bool __testout = this->_M_mode & ios_base::out;
       if (__testeq || __testout)
  {
    this->gbump(-1);
    if (!__testeq)
      *this->gptr() = traits_type::to_char_type(__c);
    __ret = __c;
  }
     }
   else
     {
       this->gbump(-1);
       __ret = traits_type::not_eof(__c);
     }
 }
      return __ret;
    }

  template <class _CharT, class _Traits, class _Alloc>
    typename basic_stringbuf<_CharT, _Traits, _Alloc>::int_type
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    overflow(int_type __c)
    {
      const bool __testout = this->_M_mode & ios_base::out;
      if (__builtin_expect(!__testout, false))
 return traits_type::eof();

      const bool __testeof = traits_type::eq_int_type(__c, traits_type::eof());
      if (__builtin_expect(__testeof, false))
 return traits_type::not_eof(__c);

      const __size_type __capacity = _M_string.capacity();


      if (size_t(this->epptr() - this->pbase()) < __capacity)
 {

   char_type* __base = const_cast<char_type*>(_M_string.data());
   _M_pbump(__base, __base + __capacity, this->pptr() - this->pbase());
   if (_M_mode & ios_base::in)
     {
       const __size_type __nget = this->gptr() - this->eback();
       const __size_type __eget = this->egptr() - this->eback();
       this->setg(__base, __base + __nget, __base + __eget + 1);
     }
   *this->pptr() = traits_type::to_char_type(__c);
   this->pbump(1);
   return __c;
 }


      const __size_type __max_size = _M_string.max_size();
      const bool __testput = this->pptr() < this->epptr();
      if (__builtin_expect(!__testput && __capacity == __max_size, false))
 return traits_type::eof();



      const char_type __conv = traits_type::to_char_type(__c);
      if (!__testput)
 {
# 129 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/sstream.tcc" 3
   const __size_type __opt_len = std::max(__size_type(2 * __capacity),
       __size_type(512));
   const __size_type __len = std::min(__opt_len, __max_size);
   __string_type __tmp(_M_string.get_allocator());
   __tmp.reserve(__len);
   if (this->pbase())
     __tmp.assign(this->pbase(), this->epptr() - this->pbase());
   __tmp.push_back(__conv);
   _M_string.swap(__tmp);
   _M_sync(const_cast<char_type*>(_M_string.data()),
    this->gptr() - this->eback(), this->pptr() - this->pbase());
 }
      else
 *this->pptr() = __conv;
      this->pbump(1);
      return __c;
    }

  template <class _CharT, class _Traits, class _Alloc>
    typename basic_stringbuf<_CharT, _Traits, _Alloc>::int_type
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    underflow()
    {
      int_type __ret = traits_type::eof();
      const bool __testin = this->_M_mode & ios_base::in;
      if (__testin)
 {

   _M_update_egptr();

   if (this->gptr() < this->egptr())
     __ret = traits_type::to_int_type(*this->gptr());
 }
      return __ret;
    }

  template <class _CharT, class _Traits, class _Alloc>
    typename basic_stringbuf<_CharT, _Traits, _Alloc>::pos_type
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    seekoff(off_type __off, ios_base::seekdir __way, ios_base::openmode __mode)
    {
      pos_type __ret = pos_type(off_type(-1));
      bool __testin = (ios_base::in & this->_M_mode & __mode) != 0;
      bool __testout = (ios_base::out & this->_M_mode & __mode) != 0;
      const bool __testboth = __testin && __testout && __way != ios_base::cur;
      __testin &= !(__mode & ios_base::out);
      __testout &= !(__mode & ios_base::in);



      const char_type* __beg = __testin ? this->eback() : this->pbase();
      if ((__beg || !__off) && (__testin || __testout || __testboth))
 {
   _M_update_egptr();

   off_type __newoffi = __off;
   off_type __newoffo = __newoffi;
   if (__way == ios_base::cur)
     {
       __newoffi += this->gptr() - __beg;
       __newoffo += this->pptr() - __beg;
     }
   else if (__way == ios_base::end)
     __newoffo = __newoffi += this->egptr() - __beg;

   if ((__testin || __testboth)
       && __newoffi >= 0
       && this->egptr() - __beg >= __newoffi)
     {
       this->setg(this->eback(), this->eback() + __newoffi,
    this->egptr());
       __ret = pos_type(__newoffi);
     }
   if ((__testout || __testboth)
       && __newoffo >= 0
       && this->egptr() - __beg >= __newoffo)
     {
       _M_pbump(this->pbase(), this->epptr(), __newoffo);
       __ret = pos_type(__newoffo);
     }
 }
      return __ret;
    }

  template <class _CharT, class _Traits, class _Alloc>
    typename basic_stringbuf<_CharT, _Traits, _Alloc>::pos_type
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    seekpos(pos_type __sp, ios_base::openmode __mode)
    {
      pos_type __ret = pos_type(off_type(-1));
      const bool __testin = (ios_base::in & this->_M_mode & __mode) != 0;
      const bool __testout = (ios_base::out & this->_M_mode & __mode) != 0;

      const char_type* __beg = __testin ? this->eback() : this->pbase();
      if ((__beg || !off_type(__sp)) && (__testin || __testout))
 {
   _M_update_egptr();

   const off_type __pos(__sp);
   const bool __testpos = (0 <= __pos
      && __pos <= this->egptr() - __beg);
   if (__testpos)
     {
       if (__testin)
  this->setg(this->eback(), this->eback() + __pos,
      this->egptr());
       if (__testout)
  _M_pbump(this->pbase(), this->epptr(), __pos);
       __ret = __sp;
     }
 }
      return __ret;
    }

  template <class _CharT, class _Traits, class _Alloc>
    void
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    _M_sync(char_type* __base, __size_type __i, __size_type __o)
    {
      const bool __testin = _M_mode & ios_base::in;
      const bool __testout = _M_mode & ios_base::out;
      char_type* __endg = __base + _M_string.size();
      char_type* __endp = __base + _M_string.capacity();

      if (__base != _M_string.data())
 {

   __endg += __i;
   __i = 0;
   __endp = __endg;
 }

      if (__testin)
 this->setg(__base, __base + __i, __endg);
      if (__testout)
 {
   _M_pbump(__base, __endp, __o);



   if (!__testin)
     this->setg(__endg, __endg, __endg);
 }
    }

  template <class _CharT, class _Traits, class _Alloc>
    void
    basic_stringbuf<_CharT, _Traits, _Alloc>::
    _M_pbump(char_type* __pbeg, char_type* __pend, off_type __off)
    {
      this->setp(__pbeg, __pend);
      while (__off > __gnu_cxx::__numeric_traits<int>::__max)
 {
   this->pbump(__gnu_cxx::__numeric_traits<int>::__max);
   __off -= __gnu_cxx::__numeric_traits<int>::__max;
 }
      this->pbump(__off);
    }




  extern template class basic_stringbuf<char>;
  extern template class basic_istringstream<char>;
  extern template class basic_ostringstream<char>;
  extern template class basic_stringstream<char>;


  extern template class basic_stringbuf<wchar_t>;
  extern template class basic_istringstream<wchar_t>;
  extern template class basic_ostringstream<wchar_t>;
  extern template class basic_stringstream<wchar_t>;




}
# 1219 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/sstream" 2 3
# 38 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 2 3





#pragma clang force_cuda_host_device begin
# 82 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3




# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 1 3
# 40 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/cmath" 3
# 45 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 2 3
# 54 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 67 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp> class complex;
  template<> class complex<float>;
  template<> class complex<double>;
  template<> class complex<long double>;


  template<typename _Tp> _Tp abs(const complex<_Tp>&);

  template<typename _Tp> _Tp arg(const complex<_Tp>&);

  template<typename _Tp> _Tp norm(const complex<_Tp>&);


  template<typename _Tp>
                         complex<_Tp> conj(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);



  template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);

  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);

  template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
                                          const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);

  template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
# 126 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    class complex
    {
    public:

      typedef _Tp value_type;



      constexpr complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
      : _M_real(__r), _M_imag(__i) { }



      constexpr complex(const complex&) = default;



      template<typename _Up>
        constexpr complex(const complex<_Up>& __z)
 : _M_real(__z.real()), _M_imag(__z.imag()) { }




      __attribute ((__abi_tag__ ("cxx11")))
      constexpr _Tp
      real() const { return _M_real; }

      __attribute ((__abi_tag__ ("cxx11")))
      constexpr _Tp
      imag() const { return _M_imag; }
# 178 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
                           void
      real(_Tp __val) { _M_real = __val; }

                           void
      imag(_Tp __val) { _M_imag = __val; }


                           complex<_Tp>& operator=(const _Tp&);



                           complex<_Tp>&
      operator+=(const _Tp& __t)
      {
 _M_real += __t;
 return *this;
      }



                           complex<_Tp>&
      operator-=(const _Tp& __t)
      {
 _M_real -= __t;
 return *this;
      }


                           complex<_Tp>& operator*=(const _Tp&);

                           complex<_Tp>& operator/=(const _Tp&);



                           complex& operator=(const complex&) = default;



      template<typename _Up>
                             complex<_Tp>& operator=(const complex<_Up>&);

      template<typename _Up>
                             complex<_Tp>& operator+=(const complex<_Up>&);

      template<typename _Up>
                             complex<_Tp>& operator-=(const complex<_Up>&);

      template<typename _Up>
                             complex<_Tp>& operator*=(const complex<_Up>&);

      template<typename _Up>
                             complex<_Tp>& operator/=(const complex<_Up>&);

      constexpr complex __rep() const
      { return *this; }

    private:
      _Tp _M_real;
      _Tp _M_imag;
    };

  template<typename _Tp>
                         complex<_Tp>&
    complex<_Tp>::operator=(const _Tp& __t)
    {
     _M_real = __t;
     _M_imag = _Tp();
     return *this;
    }


  template<typename _Tp>
                         complex<_Tp>&
    complex<_Tp>::operator*=(const _Tp& __t)
    {
      _M_real *= __t;
      _M_imag *= __t;
      return *this;
    }


  template<typename _Tp>
                         complex<_Tp>&
    complex<_Tp>::operator/=(const _Tp& __t)
    {
      _M_real /= __t;
      _M_imag /= __t;
      return *this;
    }

  template<typename _Tp>
    template<typename _Up>
                         complex<_Tp>&
    complex<_Tp>::operator=(const complex<_Up>& __z)
    {
      _M_real = __z.real();
      _M_imag = __z.imag();
      return *this;
    }


  template<typename _Tp>
    template<typename _Up>
                         complex<_Tp>&
    complex<_Tp>::operator+=(const complex<_Up>& __z)
    {
      _M_real += __z.real();
      _M_imag += __z.imag();
      return *this;
    }


  template<typename _Tp>
    template<typename _Up>
                         complex<_Tp>&
    complex<_Tp>::operator-=(const complex<_Up>& __z)
    {
      _M_real -= __z.real();
      _M_imag -= __z.imag();
      return *this;
    }



  template<typename _Tp>
    template<typename _Up>
                         complex<_Tp>&
    complex<_Tp>::operator*=(const complex<_Up>& __z)
    {
      const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
      _M_imag = _M_real * __z.imag() + _M_imag * __z.real();
      _M_real = __r;
      return *this;
    }



  template<typename _Tp>
    template<typename _Up>
                         complex<_Tp>&
    complex<_Tp>::operator/=(const complex<_Up>& __z)
    {
      const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
      const _Tp __n = std::norm(__z);
      _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
      _M_real = __r / __n;
      return *this;
    }




  template<typename _Tp>
    inline complex<_Tp>
    operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r += __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator+(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r += __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator+(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __y;
      __r += __x;
      return __r;
    }




  template<typename _Tp>
    inline complex<_Tp>
    operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r -= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator-(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r -= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator-(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = -__y;
      __r += __x;
      return __r;
    }




  template<typename _Tp>
    inline complex<_Tp>
    operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r *= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator*(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r *= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator*(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __y;
      __r *= __x;
      return __r;
    }




  template<typename _Tp>
    inline complex<_Tp>
    operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r /= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator/(const complex<_Tp>& __x, const _Tp& __y)
    {
      complex<_Tp> __r = __x;
      __r /= __y;
      return __r;
    }

  template<typename _Tp>
    inline complex<_Tp>
    operator/(const _Tp& __x, const complex<_Tp>& __y)
    {
      complex<_Tp> __r = __x;
      __r /= __y;
      return __r;
    }



  template<typename _Tp>
    inline complex<_Tp>
    operator+(const complex<_Tp>& __x)
    { return __x; }


  template<typename _Tp>
    inline complex<_Tp>
    operator-(const complex<_Tp>& __x)
    { return complex<_Tp>(-__x.real(), -__x.imag()); }



  template<typename _Tp>
    inline constexpr bool
    operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
    { return __x.real() == __y.real() && __x.imag() == __y.imag(); }

  template<typename _Tp>
    inline constexpr bool
    operator==(const complex<_Tp>& __x, const _Tp& __y)
    { return __x.real() == __y && __x.imag() == _Tp(); }


  template<typename _Tp>
    inline constexpr bool
    operator==(const _Tp& __x, const complex<_Tp>& __y)
    { return __x == __y.real() && _Tp() == __y.imag(); }




  template<typename _Tp>
    inline constexpr bool
    operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
    { return __x.real() != __y.real() || __x.imag() != __y.imag(); }

  template<typename _Tp>
    inline constexpr bool
    operator!=(const complex<_Tp>& __x, const _Tp& __y)
    { return __x.real() != __y || __x.imag() != _Tp(); }

  template<typename _Tp>
    inline constexpr bool
    operator!=(const _Tp& __x, const complex<_Tp>& __y)
    { return __x != __y.real() || _Tp() != __y.imag(); }




  template<typename _Tp, typename _CharT, class _Traits>
    basic_istream<_CharT, _Traits>&
    operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
    {
      bool __fail = true;
      _CharT __ch;
      if (__is >> __ch)
 {
   if (_Traits::eq(__ch, __is.widen('(')))
     {
       _Tp __u;
       if (__is >> __u >> __ch)
  {
    const _CharT __rparen = __is.widen(')');
    if (_Traits::eq(__ch, __rparen))
      {
        __x = __u;
        __fail = false;
      }
    else if (_Traits::eq(__ch, __is.widen(',')))
      {
        _Tp __v;
        if (__is >> __v >> __ch)
   {
     if (_Traits::eq(__ch, __rparen))
       {
         __x = complex<_Tp>(__u, __v);
         __fail = false;
       }
     else
       __is.putback(__ch);
   }
      }
    else
      __is.putback(__ch);
  }
     }
   else
     {
       __is.putback(__ch);
       _Tp __u;
       if (__is >> __u)
  {
    __x = __u;
    __fail = false;
  }
     }
 }
      if (__fail)
 __is.setstate(ios_base::failbit);
      return __is;
    }


  template<typename _Tp, typename _CharT, class _Traits>
    basic_ostream<_CharT, _Traits>&
    operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
    {
      basic_ostringstream<_CharT, _Traits> __s;
      __s.flags(__os.flags());
      __s.imbue(__os.getloc());
      __s.precision(__os.precision());
      __s << '(' << __x.real() << ',' << __x.imag() << ')';
      return __os << __s.str();
    }



  template<typename _Tp>
    constexpr _Tp
    real(const complex<_Tp>& __z)
    { return __z.real(); }

  template<typename _Tp>
    constexpr _Tp
    imag(const complex<_Tp>& __z)
    { return __z.imag(); }
# 599 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline _Tp
    __complex_abs(const complex<_Tp>& __z)
    {
      _Tp __x = __z.real();
      _Tp __y = __z.imag();
      const _Tp __s = std::max(abs(__x), abs(__y));
      if (__s == _Tp())
        return __s;
      __x /= __s;
      __y /= __s;
      return __s * sqrt(__x * __x + __y * __y);
    }
# 628 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline _Tp
    abs(const complex<_Tp>& __z) { return __complex_abs(__z); }




  template<typename _Tp>
    inline _Tp
    __complex_arg(const complex<_Tp>& __z)
    { return atan2(__z.imag(), __z.real()); }
# 655 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline _Tp
    arg(const complex<_Tp>& __z) { return __complex_arg(__z); }







  template<bool>
    struct _Norm_helper
    {
      template<typename _Tp>
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
        {
          const _Tp __x = __z.real();
          const _Tp __y = __z.imag();
          return __x * __x + __y * __y;
        }
    };

  template<>
    struct _Norm_helper<true>
    {
      template<typename _Tp>
        static inline _Tp _S_do_it(const complex<_Tp>& __z)
        {


          const _Tp __x = __z.real();
          const _Tp __y = __z.imag();
          return __x * __x + __y * __y;
        }
    };

  template<typename _Tp>
    inline _Tp
    norm(const complex<_Tp>& __z)
    {
      return _Norm_helper<__is_floating<_Tp>::__value
 && !0>::_S_do_it(__z);
    }

  template<typename _Tp>
    inline complex<_Tp>
    polar(const _Tp& __rho, const _Tp& __theta)
    {
      do { if (std::__is_constant_evaluated() && !bool(__rho >= 0)) __builtin_unreachable(); } while (false);
      return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
    }

  template<typename _Tp>
    inline complex<_Tp>
    conj(const complex<_Tp>& __z)
    { return complex<_Tp>(__z.real(), -__z.imag()); }




  template<typename _Tp>
    inline complex<_Tp>
    __complex_cos(const complex<_Tp>& __z)
    {
      const _Tp __x = __z.real();
      const _Tp __y = __z.imag();
      return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
    }
# 739 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    cos(const complex<_Tp>& __z) { return __complex_cos(__z); }



  template<typename _Tp>
    inline complex<_Tp>
    __complex_cosh(const complex<_Tp>& __z)
    {
      const _Tp __x = __z.real();
      const _Tp __y = __z.imag();
      return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
    }
# 769 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }



  template<typename _Tp>
    inline complex<_Tp>
    __complex_exp(const complex<_Tp>& __z)
    { return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
# 795 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    exp(const complex<_Tp>& __z) { return __complex_exp(__z); }




  template<typename _Tp>
    inline complex<_Tp>
    __complex_log(const complex<_Tp>& __z)
    { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
# 822 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    log(const complex<_Tp>& __z) { return __complex_log(__z); }


  template<typename _Tp>
    inline complex<_Tp>
    log10(const complex<_Tp>& __z)
    { return std::log(__z) / log(_Tp(10.0)); }


  template<typename _Tp>
    inline complex<_Tp>
    __complex_sin(const complex<_Tp>& __z)
    {
      const _Tp __x = __z.real();
      const _Tp __y = __z.imag();
      return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
    }
# 857 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    sin(const complex<_Tp>& __z) { return __complex_sin(__z); }



  template<typename _Tp>
    inline complex<_Tp>
    __complex_sinh(const complex<_Tp>& __z)
    {
      const _Tp __x = __z.real();
      const _Tp __y = __z.imag();
      return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
    }
# 887 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }




  template<typename _Tp>
    complex<_Tp>
    __complex_sqrt(const complex<_Tp>& __z)
    {
      _Tp __x = __z.real();
      _Tp __y = __z.imag();

      if (__x == _Tp())
        {
          _Tp __t = sqrt(abs(__y) / 2);
          return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
        }
      else
        {
          _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
          _Tp __u = __t / 2;
          return __x > _Tp()
            ? complex<_Tp>(__u, __y / __t)
            : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
        }
    }
# 931 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }




  template<typename _Tp>
    inline complex<_Tp>
    __complex_tan(const complex<_Tp>& __z)
    { return std::sin(__z) / std::cos(__z); }
# 958 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    tan(const complex<_Tp>& __z) { return __complex_tan(__z); }





  template<typename _Tp>
    inline complex<_Tp>
    __complex_tanh(const complex<_Tp>& __z)
    { return std::sinh(__z) / std::cosh(__z); }
# 986 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }






  template<typename _Tp>
    complex<_Tp>
    __complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
    {
      complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);

      while (__n >>= 1)
        {
          __x *= __x;
          if (__n % 2)
            __y *= __x;
        }

      return __y;
    }







  template<typename _Tp>
    inline complex<_Tp>
    pow(const complex<_Tp>& __z, int __n)
    {
      return __n < 0
 ? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
        : std::__complex_pow_unsigned(__z, __n);
    }

  template<typename _Tp>
    complex<_Tp>
    pow(const complex<_Tp>& __x, const _Tp& __y)
    {

      if (__x == _Tp())
 return _Tp();

      if (__x.imag() == _Tp() && __x.real() > _Tp())
        return pow(__x.real(), __y);

      complex<_Tp> __t = std::log(__x);
      return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
    }

  template<typename _Tp>
    inline complex<_Tp>
    __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
    { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
# 1065 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline complex<_Tp>
    pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
    { return __complex_pow(__x, __y); }


  template<typename _Tp>
    inline complex<_Tp>
    pow(const _Tp& __x, const complex<_Tp>& __y)
    {
      return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
        __y.imag() * log(__x))
                  : std::pow(complex<_Tp>(__x), __y);
    }



  template<>
    class complex<float>
    {
    public:
      typedef float value_type;
      typedef __complex__ float _ComplexT;

      constexpr complex(_ComplexT __z) : _M_value(__z) { }

      constexpr complex(float __r = 0.0f, float __i = 0.0f)

      : _M_value{ __r, __i } { }







      explicit constexpr complex(const complex<double>&);
      explicit constexpr complex(const complex<long double>&);




      __attribute ((__abi_tag__ ("cxx11")))
      constexpr float
      real() const { return __real__ _M_value; }

      __attribute ((__abi_tag__ ("cxx11")))
      constexpr float
      imag() const { return __imag__ _M_value; }
# 1130 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
                           void
      real(float __val) { __real__ _M_value = __val; }

                           void
      imag(float __val) { __imag__ _M_value = __val; }

                           complex&
      operator=(float __f)
      {
 _M_value = __f;
 return *this;
      }

                           complex&
      operator+=(float __f)
      {
 _M_value += __f;
 return *this;
      }

                           complex&
      operator-=(float __f)
      {
 _M_value -= __f;
 return *this;
      }

                           complex&
      operator*=(float __f)
      {
 _M_value *= __f;
 return *this;
      }

                           complex&
      operator/=(float __f)
      {
 _M_value /= __f;
 return *this;
      }




                           complex& operator=(const complex&) = default;


      template<typename _Tp>
                             complex&
        operator=(const complex<_Tp>& __z)
 {
   __real__ _M_value = __z.real();
   __imag__ _M_value = __z.imag();
   return *this;
 }

      template<typename _Tp>
                             complex&
        operator+=(const complex<_Tp>& __z)
 {
   _M_value += __z.__rep();
   return *this;
 }

      template<class _Tp>
                             complex&
        operator-=(const complex<_Tp>& __z)
 {
   _M_value -= __z.__rep();
   return *this;
 }

      template<class _Tp>
                             complex&
        operator*=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value *= __t;
   return *this;
 }

      template<class _Tp>
                             complex&
        operator/=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value /= __t;
   return *this;
 }

      constexpr _ComplexT __rep() const { return _M_value; }

    private:
      _ComplexT _M_value;
    };



  template<>
    class complex<double>
    {
    public:
      typedef double value_type;
      typedef __complex__ double _ComplexT;

      constexpr complex(_ComplexT __z) : _M_value(__z) { }

      constexpr complex(double __r = 0.0, double __i = 0.0)

      : _M_value{ __r, __i } { }







      constexpr complex(const complex<float>& __z)
      : _M_value(__z.__rep()) { }

      explicit constexpr complex(const complex<long double>&);




      __attribute ((__abi_tag__ ("cxx11")))
      constexpr double
      real() const { return __real__ _M_value; }

      __attribute ((__abi_tag__ ("cxx11")))
      constexpr double
      imag() const { return __imag__ _M_value; }
# 1278 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
                           void
      real(double __val) { __real__ _M_value = __val; }

                           void
      imag(double __val) { __imag__ _M_value = __val; }

                           complex&
      operator=(double __d)
      {
 _M_value = __d;
 return *this;
      }

                           complex&
      operator+=(double __d)
      {
 _M_value += __d;
 return *this;
      }

                           complex&
      operator-=(double __d)
      {
 _M_value -= __d;
 return *this;
      }

                           complex&
      operator*=(double __d)
      {
 _M_value *= __d;
 return *this;
      }

                           complex&
      operator/=(double __d)
      {
 _M_value /= __d;
 return *this;
      }



                           complex& operator=(const complex&) = default;


      template<typename _Tp>
                             complex&
        operator=(const complex<_Tp>& __z)
 {
   _M_value = __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
        operator+=(const complex<_Tp>& __z)
 {
   _M_value += __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
        operator-=(const complex<_Tp>& __z)
 {
   _M_value -= __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
        operator*=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value *= __t;
   return *this;
 }

      template<typename _Tp>
                             complex&
        operator/=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value /= __t;
   return *this;
 }

      constexpr _ComplexT __rep() const { return _M_value; }

    private:
      _ComplexT _M_value;
    };



  template<>
    class complex<long double>
    {
    public:
      typedef long double value_type;
      typedef __complex__ long double _ComplexT;

      constexpr complex(_ComplexT __z) : _M_value(__z) { }

      constexpr complex(long double __r = 0.0L,
     long double __i = 0.0L)

      : _M_value{ __r, __i } { }







      constexpr complex(const complex<float>& __z)
      : _M_value(__z.__rep()) { }

      constexpr complex(const complex<double>& __z)
      : _M_value(__z.__rep()) { }




      __attribute ((__abi_tag__ ("cxx11")))
      constexpr long double
      real() const { return __real__ _M_value; }

      __attribute ((__abi_tag__ ("cxx11")))
      constexpr long double
      imag() const { return __imag__ _M_value; }
# 1426 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
                           void
      real(long double __val) { __real__ _M_value = __val; }

                           void
      imag(long double __val) { __imag__ _M_value = __val; }

                           complex&
      operator=(long double __r)
      {
 _M_value = __r;
 return *this;
      }

                           complex&
      operator+=(long double __r)
      {
 _M_value += __r;
 return *this;
      }

                           complex&
      operator-=(long double __r)
      {
 _M_value -= __r;
 return *this;
      }

                           complex&
      operator*=(long double __r)
      {
 _M_value *= __r;
 return *this;
      }

                           complex&
      operator/=(long double __r)
      {
 _M_value /= __r;
 return *this;
      }



                           complex& operator=(const complex&) = default;


      template<typename _Tp>
                             complex&
        operator=(const complex<_Tp>& __z)
 {
   _M_value = __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
 operator+=(const complex<_Tp>& __z)
 {
   _M_value += __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
 operator-=(const complex<_Tp>& __z)
 {
   _M_value -= __z.__rep();
   return *this;
 }

      template<typename _Tp>
                             complex&
 operator*=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value *= __t;
   return *this;
 }

      template<typename _Tp>
                             complex&
 operator/=(const complex<_Tp>& __z)
 {
   const _ComplexT __t = __z.__rep();
   _M_value /= __t;
   return *this;
 }

      constexpr _ComplexT __rep() const { return _M_value; }

    private:
      _ComplexT _M_value;
    };



  inline constexpr
  complex<float>::complex(const complex<double>& __z)
  : _M_value(__z.__rep()) { }

  inline constexpr
  complex<float>::complex(const complex<long double>& __z)
  : _M_value(__z.__rep()) { }

  inline constexpr
  complex<double>::complex(const complex<long double>& __z)
  : _M_value(__z.__rep()) { }





  extern template istream& operator>>(istream&, complex<float>&);
  extern template ostream& operator<<(ostream&, const complex<float>&);
  extern template istream& operator>>(istream&, complex<double>&);
  extern template ostream& operator<<(ostream&, const complex<double>&);
  extern template istream& operator>>(istream&, complex<long double>&);
  extern template ostream& operator<<(ostream&, const complex<long double>&);


  extern template wistream& operator>>(wistream&, complex<float>&);
  extern template wostream& operator<<(wostream&, const complex<float>&);
  extern template wistream& operator>>(wistream&, complex<double>&);
  extern template wostream& operator<<(wostream&, const complex<double>&);
  extern template wistream& operator>>(wistream&, complex<long double>&);
  extern template wostream& operator<<(wostream&, const complex<long double>&);






}



namespace std __attribute__ ((__visibility__ ("default")))
{



  template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);

  template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
  template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);

  template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);

  template<typename _Tp>
    inline std::complex<_Tp>
    __complex_acos(const std::complex<_Tp>& __z)
    {
      const std::complex<_Tp> __t = std::asin(__z);
      const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
      return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
    }
# 1607 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    acos(const std::complex<_Tp>& __z)
    { return __complex_acos(__z); }


  template<typename _Tp>
    inline std::complex<_Tp>
    __complex_asin(const std::complex<_Tp>& __z)
    {
      std::complex<_Tp> __t(-__z.imag(), __z.real());
      __t = std::asinh(__t);
      return std::complex<_Tp>(__t.imag(), -__t.real());
    }
# 1643 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    asin(const std::complex<_Tp>& __z)
    { return __complex_asin(__z); }


  template<typename _Tp>
    std::complex<_Tp>
    __complex_atan(const std::complex<_Tp>& __z)
    {
      const _Tp __r2 = __z.real() * __z.real();
      const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();

      _Tp __num = __z.imag() + _Tp(1.0);
      _Tp __den = __z.imag() - _Tp(1.0);

      __num = __r2 + __num * __num;
      __den = __r2 + __den * __den;

      return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
          _Tp(0.25) * log(__num / __den));
    }
# 1687 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    atan(const std::complex<_Tp>& __z)
    { return __complex_atan(__z); }


  template<typename _Tp>
    std::complex<_Tp>
    __complex_acosh(const std::complex<_Tp>& __z)
    {

      return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
     + std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
    }
# 1723 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    acosh(const std::complex<_Tp>& __z)
    { return __complex_acosh(__z); }


  template<typename _Tp>
    std::complex<_Tp>
    __complex_asinh(const std::complex<_Tp>& __z)
    {
      std::complex<_Tp> __t((__z.real() - __z.imag())
       * (__z.real() + __z.imag()) + _Tp(1.0),
       _Tp(2.0) * __z.real() * __z.imag());
      __t = std::sqrt(__t);

      return std::log(__t + __z);
    }
# 1762 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    asinh(const std::complex<_Tp>& __z)
    { return __complex_asinh(__z); }


  template<typename _Tp>
    std::complex<_Tp>
    __complex_atanh(const std::complex<_Tp>& __z)
    {
      const _Tp __i2 = __z.imag() * __z.imag();
      const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();

      _Tp __num = _Tp(1.0) + __z.real();
      _Tp __den = _Tp(1.0) - __z.real();

      __num = __i2 + __num * __num;
      __den = __i2 + __den * __den;

      return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
          _Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
    }
# 1806 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  template<typename _Tp>
    inline std::complex<_Tp>
    atanh(const std::complex<_Tp>& __z)
    { return __complex_atanh(__z); }


  template<typename _Tp>
    inline _Tp



    fabs(const std::complex<_Tp>& __z)
    { return std::abs(__z); }


  template<typename _Tp>
    inline typename __gnu_cxx::__promote<_Tp>::__type
    arg(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;

      return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
                        : __type();



    }

  template<typename _Tp>
    constexpr inline typename __gnu_cxx::__promote<_Tp>::__type
    imag(_Tp)
    { return _Tp(); }

  template<typename _Tp>
                         inline typename __gnu_cxx::__promote<_Tp>::__type
    norm(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __type(__x) * __type(__x);
    }

  template<typename _Tp>
    constexpr inline typename __gnu_cxx::__promote<_Tp>::__type
    real(_Tp __x)
    { return __x; }

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const std::complex<_Tp>& __x, const _Up& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(std::complex<__type>(__x), __type(__y));
    }

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const _Tp& __x, const std::complex<_Up>& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(__type(__x), std::complex<__type>(__y));
    }

  template<typename _Tp, typename _Up>
    inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
    pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return std::pow(std::complex<__type>(__x),
        std::complex<__type>(__y));
    }



  template<typename _Tp>
    std::complex<_Tp> proj(const std::complex<_Tp>&);


  template<typename _Tp>
    inline std::complex<_Tp>
    __complex_proj(const std::complex<_Tp>& __z)
    { return __z; }
# 1901 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
  inline complex<float>
  __complex_proj(const complex<float>& __z)
  {
    if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
      return complex<float>(__builtin_inff(),
       __builtin_copysignf(0.0f, __z.imag()));
    return __z;
  }

  inline complex<double>
  __complex_proj(const complex<double>& __z)
  {
    if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
      return complex<double>(__builtin_inf(),
        __builtin_copysign(0.0, __z.imag()));
    return __z;
  }

  inline complex<long double>
  __complex_proj(const complex<long double>& __z)
  {
    if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
      return complex<long double>(__builtin_infl(),
      __builtin_copysignl(0.0l, __z.imag()));
    return __z;
  }


  template<typename _Tp>
    inline std::complex<_Tp>
    proj(const std::complex<_Tp>& __z)
    { return __complex_proj(__z); }


  template<typename _Tp>
    inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
    proj(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return std::proj(std::complex<__type>(__x));
    }

  template<typename _Tp>
    inline
 std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
    conj(_Tp __x)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return std::complex<__type>(__x, -__type());
    }
# 1991 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/complex" 3
}
# 83 "/usr/lib/llvm-15/lib/clang/15.0.6/include/cuda_wrappers/complex" 2 3





#pragma clang force_cuda_host_device end
# 125 "/usr/lib/llvm-15/lib/clang/15.0.6/include/__clang_hip_runtime_wrapper.h" 2 3
# 2 "<built-in>" 2
# 1 "float16.cpp" 2
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iostream" 1 3
# 37 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iostream" 3





namespace std __attribute__ ((__visibility__ ("default")))
{
# 60 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/iostream" 3
  extern istream cin;
  extern ostream cout;
  extern ostream cerr;
  extern ostream clog;


  extern wistream wcin;
  extern wostream wcout;
  extern wostream wcerr;
  extern wostream wclog;




  static ios_base::Init __ioinit;


}
# 2 "float16.cpp" 2

# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 3




# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 1 3
# 70 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{
# 81 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _ValueType, typename _Tp>
    constexpr bool
    __check_constructible()
    {





      static_assert(is_constructible<_ValueType, _Tp>::value,
   "result type must be constructible from input type");

      return true;
    }
# 110 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _InputIterator, typename _ForwardIterator>

    _ForwardIterator
    __do_uninit_copy(_InputIterator __first, _InputIterator __last,
       _ForwardIterator __result)
    {
      _ForwardIterator __cur = __result;
      try
 {
   for (; __first != __last; ++__first, (void)++__cur)
     std::_Construct(std::__addressof(*__cur), *__first);
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__result, __cur);
   throw;
 }
    }

  template<bool _TrivialValueTypes>
    struct __uninitialized_copy
    {
      template<typename _InputIterator, typename _ForwardIterator>
        static _ForwardIterator
        __uninit_copy(_InputIterator __first, _InputIterator __last,
        _ForwardIterator __result)
 { return std::__do_uninit_copy(__first, __last, __result); }
    };

  template<>
    struct __uninitialized_copy<true>
    {
      template<typename _InputIterator, typename _ForwardIterator>
        static _ForwardIterator
        __uninit_copy(_InputIterator __first, _InputIterator __last,
        _ForwardIterator __result)
        { return std::copy(__first, __last, __result); }
    };
# 161 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _InputIterator, typename _ForwardIterator>
    inline _ForwardIterator
    uninitialized_copy(_InputIterator __first, _InputIterator __last,
         _ForwardIterator __result)
    {
      typedef typename iterator_traits<_InputIterator>::value_type
 _ValueType1;
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType2;




      const bool __can_memmove = __is_trivial(_ValueType1);




      using _From = decltype(*__first);

      const bool __assignable
 = __is_trivial(_ValueType2) && __is_assignable(_ValueType2&, _From) && std::__check_constructible<_ValueType2, _From>();

      return std::__uninitialized_copy<__can_memmove && __assignable>::
 __uninit_copy(__first, __last, __result);
    }



  template<typename _ForwardIterator, typename _Tp>
                         void
    __do_uninit_fill(_ForwardIterator __first, _ForwardIterator __last,
       const _Tp& __x)
    {
      _ForwardIterator __cur = __first;
      try
 {
   for (; __cur != __last; ++__cur)
     std::_Construct(std::__addressof(*__cur), __x);
 }
      catch(...)
 {
   std::_Destroy(__first, __cur);
   throw;
 }
    }

  template<bool _TrivialValueType>
    struct __uninitialized_fill
    {
      template<typename _ForwardIterator, typename _Tp>
        static void
        __uninit_fill(_ForwardIterator __first, _ForwardIterator __last,
        const _Tp& __x)
 { std::__do_uninit_fill(__first, __last, __x); }
    };

  template<>
    struct __uninitialized_fill<true>
    {
      template<typename _ForwardIterator, typename _Tp>
        static void
        __uninit_fill(_ForwardIterator __first, _ForwardIterator __last,
        const _Tp& __x)
        { std::fill(__first, __last, __x); }
    };
# 239 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _ForwardIterator, typename _Tp>
    inline void
    uninitialized_fill(_ForwardIterator __first, _ForwardIterator __last,
         const _Tp& __x)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;



      const bool __can_fill
 = __is_trivial(_ValueType) && __is_assignable(_ValueType&, const _Tp&) && std::__check_constructible<_ValueType, const _Tp&>();

      std::__uninitialized_fill<__can_fill>::
 __uninit_fill(__first, __last, __x);
    }



  template<typename _ForwardIterator, typename _Size, typename _Tp>

    _ForwardIterator
    __do_uninit_fill_n(_ForwardIterator __first, _Size __n, const _Tp& __x)
    {
      _ForwardIterator __cur = __first;
      try
 {
   for (; __n > 0; --__n, (void) ++__cur)
     std::_Construct(std::__addressof(*__cur), __x);
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__first, __cur);
   throw;
 }
    }

  template<bool _TrivialValueType>
    struct __uninitialized_fill_n
    {
      template<typename _ForwardIterator, typename _Size, typename _Tp>
 static _ForwardIterator
        __uninit_fill_n(_ForwardIterator __first, _Size __n,
   const _Tp& __x)
 { return std::__do_uninit_fill_n(__first, __n, __x); }
    };

  template<>
    struct __uninitialized_fill_n<true>
    {
      template<typename _ForwardIterator, typename _Size, typename _Tp>
 static _ForwardIterator
        __uninit_fill_n(_ForwardIterator __first, _Size __n,
   const _Tp& __x)
        { return std::fill_n(__first, __n, __x); }
    };
# 310 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _ForwardIterator, typename _Size, typename _Tp>
    inline _ForwardIterator
    uninitialized_fill_n(_ForwardIterator __first, _Size __n, const _Tp& __x)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;



      const bool __can_fill
 = __is_trivial(_ValueType) && __is_assignable(_ValueType&, const _Tp&) && std::__check_constructible<_ValueType, const _Tp&>()



 && __is_integer<_Size>::__value;

      return __uninitialized_fill_n<__can_fill>::
 __uninit_fill_n(__first, __n, __x);
    }
# 340 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _InputIterator, typename _ForwardIterator,
    typename _Allocator>

    _ForwardIterator
    __uninitialized_copy_a(_InputIterator __first, _InputIterator __last,
      _ForwardIterator __result, _Allocator& __alloc)
    {
      _ForwardIterator __cur = __result;
      try
 {
   typedef __gnu_cxx::__alloc_traits<_Allocator> __traits;
   for (; __first != __last; ++__first, (void)++__cur)
     __traits::construct(__alloc, std::__addressof(*__cur), *__first);
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__result, __cur, __alloc);
   throw;
 }
    }

  template<typename _InputIterator, typename _ForwardIterator, typename _Tp>

    inline _ForwardIterator
    __uninitialized_copy_a(_InputIterator __first, _InputIterator __last,
      _ForwardIterator __result, allocator<_Tp>&)
    {




      return std::uninitialized_copy(__first, __last, __result);
    }

  template<typename _InputIterator, typename _ForwardIterator,
    typename _Allocator>

    inline _ForwardIterator
    __uninitialized_move_a(_InputIterator __first, _InputIterator __last,
      _ForwardIterator __result, _Allocator& __alloc)
    {
      return std::__uninitialized_copy_a(std::make_move_iterator(__first),
      std::make_move_iterator(__last),
      __result, __alloc);
    }

  template<typename _InputIterator, typename _ForwardIterator,
    typename _Allocator>

    inline _ForwardIterator
    __uninitialized_move_if_noexcept_a(_InputIterator __first,
           _InputIterator __last,
           _ForwardIterator __result,
           _Allocator& __alloc)
    {
      return std::__uninitialized_copy_a
 (std::__make_move_if_noexcept_iterator(__first),
  std::__make_move_if_noexcept_iterator(__last), __result, __alloc);
    }

  template<typename _ForwardIterator, typename _Tp, typename _Allocator>

    void
    __uninitialized_fill_a(_ForwardIterator __first, _ForwardIterator __last,
      const _Tp& __x, _Allocator& __alloc)
    {
      _ForwardIterator __cur = __first;
      try
 {
   typedef __gnu_cxx::__alloc_traits<_Allocator> __traits;
   for (; __cur != __last; ++__cur)
     __traits::construct(__alloc, std::__addressof(*__cur), __x);
 }
      catch(...)
 {
   std::_Destroy(__first, __cur, __alloc);
   throw;
 }
    }

  template<typename _ForwardIterator, typename _Tp, typename _Tp2>

    inline void
    __uninitialized_fill_a(_ForwardIterator __first, _ForwardIterator __last,
      const _Tp& __x, allocator<_Tp2>&)
    {




      std::uninitialized_fill(__first, __last, __x);
    }

  template<typename _ForwardIterator, typename _Size, typename _Tp,
    typename _Allocator>

    _ForwardIterator
    __uninitialized_fill_n_a(_ForwardIterator __first, _Size __n,
        const _Tp& __x, _Allocator& __alloc)
    {
      _ForwardIterator __cur = __first;
      try
 {
   typedef __gnu_cxx::__alloc_traits<_Allocator> __traits;
   for (; __n > 0; --__n, (void) ++__cur)
     __traits::construct(__alloc, std::__addressof(*__cur), __x);
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__first, __cur, __alloc);
   throw;
 }
    }

  template<typename _ForwardIterator, typename _Size, typename _Tp,
    typename _Tp2>

    inline _ForwardIterator
    __uninitialized_fill_n_a(_ForwardIterator __first, _Size __n,
        const _Tp& __x, allocator<_Tp2>&)
    {




      return std::uninitialized_fill_n(__first, __n, __x);
    }
# 480 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _InputIterator1, typename _InputIterator2,
    typename _ForwardIterator, typename _Allocator>
    inline _ForwardIterator
    __uninitialized_copy_move(_InputIterator1 __first1,
         _InputIterator1 __last1,
         _InputIterator2 __first2,
         _InputIterator2 __last2,
         _ForwardIterator __result,
         _Allocator& __alloc)
    {
      _ForwardIterator __mid = std::__uninitialized_copy_a(__first1, __last1,
          __result,
          __alloc);
      try
 {
   return std::__uninitialized_move_a(__first2, __last2, __mid, __alloc);
 }
      catch(...)
 {
   std::_Destroy(__result, __mid, __alloc);
   throw;
 }
    }





  template<typename _InputIterator1, typename _InputIterator2,
    typename _ForwardIterator, typename _Allocator>
    inline _ForwardIterator
    __uninitialized_move_copy(_InputIterator1 __first1,
         _InputIterator1 __last1,
         _InputIterator2 __first2,
         _InputIterator2 __last2,
         _ForwardIterator __result,
         _Allocator& __alloc)
    {
      _ForwardIterator __mid = std::__uninitialized_move_a(__first1, __last1,
          __result,
          __alloc);
      try
 {
   return std::__uninitialized_copy_a(__first2, __last2, __mid, __alloc);
 }
      catch(...)
 {
   std::_Destroy(__result, __mid, __alloc);
   throw;
 }
    }




  template<typename _ForwardIterator, typename _Tp, typename _InputIterator,
    typename _Allocator>
    inline _ForwardIterator
    __uninitialized_fill_move(_ForwardIterator __result, _ForwardIterator __mid,
         const _Tp& __x, _InputIterator __first,
         _InputIterator __last, _Allocator& __alloc)
    {
      std::__uninitialized_fill_a(__result, __mid, __x, __alloc);
      try
 {
   return std::__uninitialized_move_a(__first, __last, __mid, __alloc);
 }
      catch(...)
 {
   std::_Destroy(__result, __mid, __alloc);
   throw;
 }
    }




  template<typename _InputIterator, typename _ForwardIterator, typename _Tp,
    typename _Allocator>
    inline void
    __uninitialized_move_fill(_InputIterator __first1, _InputIterator __last1,
         _ForwardIterator __first2,
         _ForwardIterator __last2, const _Tp& __x,
         _Allocator& __alloc)
    {
      _ForwardIterator __mid2 = std::__uninitialized_move_a(__first1, __last1,
           __first2,
           __alloc);
      try
 {
   std::__uninitialized_fill_a(__mid2, __last2, __x, __alloc);
 }
      catch(...)
 {
   std::_Destroy(__first2, __mid2, __alloc);
   throw;
 }
    }
# 587 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<bool _TrivialValueType>
    struct __uninitialized_default_1
    {
      template<typename _ForwardIterator>
        static void
        __uninit_default(_ForwardIterator __first, _ForwardIterator __last)
        {
   _ForwardIterator __cur = __first;
   try
     {
       for (; __cur != __last; ++__cur)
  std::_Construct(std::__addressof(*__cur));
     }
   catch(...)
     {
       std::_Destroy(__first, __cur);
       throw;
     }
 }
    };

  template<>
    struct __uninitialized_default_1<true>
    {
      template<typename _ForwardIterator>
        static void
        __uninit_default(_ForwardIterator __first, _ForwardIterator __last)
        {
   if (__first == __last)
     return;

   typename iterator_traits<_ForwardIterator>::value_type* __val
     = std::__addressof(*__first);
   std::_Construct(__val);
   if (++__first != __last)
     std::fill(__first, __last, *__val);
 }
    };

  template<bool _TrivialValueType>
    struct __uninitialized_default_n_1
    {
      template<typename _ForwardIterator, typename _Size>

        static _ForwardIterator
        __uninit_default_n(_ForwardIterator __first, _Size __n)
        {
   _ForwardIterator __cur = __first;
   try
     {
       for (; __n > 0; --__n, (void) ++__cur)
  std::_Construct(std::__addressof(*__cur));
       return __cur;
     }
   catch(...)
     {
       std::_Destroy(__first, __cur);
       throw;
     }
 }
    };

  template<>
    struct __uninitialized_default_n_1<true>
    {
      template<typename _ForwardIterator, typename _Size>

        static _ForwardIterator
        __uninit_default_n(_ForwardIterator __first, _Size __n)
        {
   if (__n > 0)
     {
       typename iterator_traits<_ForwardIterator>::value_type* __val
  = std::__addressof(*__first);
       std::_Construct(__val);
       ++__first;
       __first = std::fill_n(__first, __n - 1, *__val);
     }
   return __first;
 }
    };



  template<typename _ForwardIterator>
    inline void
    __uninitialized_default(_ForwardIterator __first,
       _ForwardIterator __last)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;

      const bool __assignable = is_copy_assignable<_ValueType>::value;

      std::__uninitialized_default_1<__is_trivial(_ValueType)
         && __assignable>::
 __uninit_default(__first, __last);
    }



  template<typename _ForwardIterator, typename _Size>

    inline _ForwardIterator
    __uninitialized_default_n(_ForwardIterator __first, _Size __n)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;

      constexpr bool __can_fill
 = __and_<is_integral<_Size>, is_copy_assignable<_ValueType>>::value;

      return __uninitialized_default_n_1<__is_trivial(_ValueType)
      && __can_fill>::
 __uninit_default_n(__first, __n);
    }





  template<typename _ForwardIterator, typename _Allocator>
    void
    __uninitialized_default_a(_ForwardIterator __first,
         _ForwardIterator __last,
         _Allocator& __alloc)
    {
      _ForwardIterator __cur = __first;
      try
 {
   typedef __gnu_cxx::__alloc_traits<_Allocator> __traits;
   for (; __cur != __last; ++__cur)
     __traits::construct(__alloc, std::__addressof(*__cur));
 }
      catch(...)
 {
   std::_Destroy(__first, __cur, __alloc);
   throw;
 }
    }

  template<typename _ForwardIterator, typename _Tp>
    inline void
    __uninitialized_default_a(_ForwardIterator __first,
         _ForwardIterator __last,
         allocator<_Tp>&)
    { std::__uninitialized_default(__first, __last); }





  template<typename _ForwardIterator, typename _Size, typename _Allocator>
                         _ForwardIterator
    __uninitialized_default_n_a(_ForwardIterator __first, _Size __n,
    _Allocator& __alloc)
    {
      _ForwardIterator __cur = __first;
      try
 {
   typedef __gnu_cxx::__alloc_traits<_Allocator> __traits;
   for (; __n > 0; --__n, (void) ++__cur)
     __traits::construct(__alloc, std::__addressof(*__cur));
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__first, __cur, __alloc);
   throw;
 }
    }



  template<typename _ForwardIterator, typename _Size, typename _Tp>

    inline _ForwardIterator
    __uninitialized_default_n_a(_ForwardIterator __first, _Size __n,
    allocator<_Tp>&)
    { return std::__uninitialized_default_n(__first, __n); }

  template<bool _TrivialValueType>
    struct __uninitialized_default_novalue_1
    {
      template<typename _ForwardIterator>
 static void
 __uninit_default_novalue(_ForwardIterator __first,
     _ForwardIterator __last)
 {
   _ForwardIterator __cur = __first;
   try
     {
       for (; __cur != __last; ++__cur)
  std::_Construct_novalue(std::__addressof(*__cur));
     }
   catch(...)
     {
       std::_Destroy(__first, __cur);
       throw;
     }
 }
    };

  template<>
    struct __uninitialized_default_novalue_1<true>
    {
      template<typename _ForwardIterator>
        static void
        __uninit_default_novalue(_ForwardIterator __first,
     _ForwardIterator __last)
 {
 }
    };

  template<bool _TrivialValueType>
    struct __uninitialized_default_novalue_n_1
    {
      template<typename _ForwardIterator, typename _Size>
 static _ForwardIterator
 __uninit_default_novalue_n(_ForwardIterator __first, _Size __n)
 {
   _ForwardIterator __cur = __first;
   try
     {
       for (; __n > 0; --__n, (void) ++__cur)
  std::_Construct_novalue(std::__addressof(*__cur));
       return __cur;
     }
   catch(...)
     {
       std::_Destroy(__first, __cur);
       throw;
     }
 }
    };

  template<>
    struct __uninitialized_default_novalue_n_1<true>
    {
      template<typename _ForwardIterator, typename _Size>
 static _ForwardIterator
 __uninit_default_novalue_n(_ForwardIterator __first, _Size __n)
 { return std::next(__first, __n); }
    };



  template<typename _ForwardIterator>
    inline void
    __uninitialized_default_novalue(_ForwardIterator __first,
        _ForwardIterator __last)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;

      std::__uninitialized_default_novalue_1<
 is_trivially_default_constructible<_ValueType>::value>::
 __uninit_default_novalue(__first, __last);
    }



  template<typename _ForwardIterator, typename _Size>
    inline _ForwardIterator
    __uninitialized_default_novalue_n(_ForwardIterator __first, _Size __n)
    {
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType;

      return __uninitialized_default_novalue_n_1<
 is_trivially_default_constructible<_ValueType>::value>::
 __uninit_default_novalue_n(__first, __n);
    }

  template<typename _InputIterator, typename _Size,
    typename _ForwardIterator>
    _ForwardIterator
    __uninitialized_copy_n(_InputIterator __first, _Size __n,
      _ForwardIterator __result, input_iterator_tag)
    {
      _ForwardIterator __cur = __result;
      try
 {
   for (; __n > 0; --__n, (void) ++__first, ++__cur)
     std::_Construct(std::__addressof(*__cur), *__first);
   return __cur;
 }
      catch(...)
 {
   std::_Destroy(__result, __cur);
   throw;
 }
    }

  template<typename _RandomAccessIterator, typename _Size,
    typename _ForwardIterator>
    inline _ForwardIterator
    __uninitialized_copy_n(_RandomAccessIterator __first, _Size __n,
      _ForwardIterator __result,
      random_access_iterator_tag)
    { return std::uninitialized_copy(__first, __first + __n, __result); }

  template<typename _InputIterator, typename _Size,
    typename _ForwardIterator>
    pair<_InputIterator, _ForwardIterator>
    __uninitialized_copy_n_pair(_InputIterator __first, _Size __n,
      _ForwardIterator __result, input_iterator_tag)
    {
      _ForwardIterator __cur = __result;
      try
 {
   for (; __n > 0; --__n, (void) ++__first, ++__cur)
     std::_Construct(std::__addressof(*__cur), *__first);
   return {__first, __cur};
 }
      catch(...)
 {
   std::_Destroy(__result, __cur);
   throw;
 }
    }

  template<typename _RandomAccessIterator, typename _Size,
    typename _ForwardIterator>
    inline pair<_RandomAccessIterator, _ForwardIterator>
    __uninitialized_copy_n_pair(_RandomAccessIterator __first, _Size __n,
      _ForwardIterator __result,
      random_access_iterator_tag)
    {
      auto __second_res = uninitialized_copy(__first, __first + __n, __result);
      auto __first_res = std::next(__first, __n);
      return {__first_res, __second_res};
    }
# 933 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _InputIterator, typename _Size, typename _ForwardIterator>
    inline _ForwardIterator
    uninitialized_copy_n(_InputIterator __first, _Size __n,
    _ForwardIterator __result)
    { return std::__uninitialized_copy_n(__first, __n, __result,
      std::__iterator_category(__first)); }


  template<typename _InputIterator, typename _Size, typename _ForwardIterator>
    inline pair<_InputIterator, _ForwardIterator>
    __uninitialized_copy_n_pair(_InputIterator __first, _Size __n,
         _ForwardIterator __result)
    {
      return
 std::__uninitialized_copy_n_pair(__first, __n, __result,
      std::__iterator_category(__first));
    }
# 1053 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
  template<typename _Tp, typename _Up, typename _Allocator>

    inline void
    __relocate_object_a(_Tp* __restrict __dest, _Up* __restrict __orig,
   _Allocator& __alloc)
    noexcept(noexcept(std::allocator_traits<_Allocator>::construct(__alloc,
    __dest, std::move(*__orig)))
      && noexcept(std::allocator_traits<_Allocator>::destroy(
       __alloc, std::__addressof(*__orig))))
    {
      typedef std::allocator_traits<_Allocator> __traits;
      __traits::construct(__alloc, __dest, std::move(*__orig));
      __traits::destroy(__alloc, std::__addressof(*__orig));
    }



  template<typename _Tp, typename = void>
    struct __is_bitwise_relocatable
    : is_trivial<_Tp> { };

  template <typename _InputIterator, typename _ForwardIterator,
     typename _Allocator>

    inline _ForwardIterator
    __relocate_a_1(_InputIterator __first, _InputIterator __last,
     _ForwardIterator __result, _Allocator& __alloc)
    noexcept(noexcept(std::__relocate_object_a(std::addressof(*__result),
            std::addressof(*__first),
            __alloc)))
    {
      typedef typename iterator_traits<_InputIterator>::value_type
 _ValueType;
      typedef typename iterator_traits<_ForwardIterator>::value_type
 _ValueType2;
      static_assert(std::is_same<_ValueType, _ValueType2>::value,
   "relocation is only possible for values of the same type");
      _ForwardIterator __cur = __result;
      for (; __first != __last; ++__first, (void)++__cur)
 std::__relocate_object_a(std::__addressof(*__cur),
     std::__addressof(*__first), __alloc);
      return __cur;
    }

  template <typename _Tp, typename _Up>

    inline __enable_if_t<std::__is_bitwise_relocatable<_Tp>::value, _Tp*>
    __relocate_a_1(_Tp* __first, _Tp* __last,
     _Tp* __result,
     [[__maybe_unused__]] allocator<_Up>& __alloc) noexcept
    {
      ptrdiff_t __count = __last - __first;
      if (__count > 0)
 {
# 1117 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_uninitialized.h" 3
   __builtin_memmove(__result, __first, __count * sizeof(_Tp));
 }
      return __result + __count;
    }


  template <typename _InputIterator, typename _ForwardIterator,
     typename _Allocator>

    inline _ForwardIterator
    __relocate_a(_InputIterator __first, _InputIterator __last,
   _ForwardIterator __result, _Allocator& __alloc)
    noexcept(noexcept(__relocate_a_1(std::__niter_base(__first),
         std::__niter_base(__last),
         std::__niter_base(__result), __alloc)))
    {
      return std::__relocate_a_1(std::__niter_base(__first),
     std::__niter_base(__last),
     std::__niter_base(__result), __alloc);
    }







}
# 64 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 1 3
# 78 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{




  template<typename _Tp, typename _Alloc>
    struct _Vector_base
    {
      typedef typename __gnu_cxx::__alloc_traits<_Alloc>::template
 rebind<_Tp>::other _Tp_alloc_type;
      typedef typename __gnu_cxx::__alloc_traits<_Tp_alloc_type>::pointer
        pointer;

      struct _Vector_impl_data
      {
 pointer _M_start;
 pointer _M_finish;
 pointer _M_end_of_storage;


 _Vector_impl_data() noexcept
 : _M_start(), _M_finish(), _M_end_of_storage()
 { }



 _Vector_impl_data(_Vector_impl_data&& __x) noexcept
 : _M_start(__x._M_start), _M_finish(__x._M_finish),
   _M_end_of_storage(__x._M_end_of_storage)
 { __x._M_start = __x._M_finish = __x._M_end_of_storage = pointer(); }



 void
 _M_copy_data(_Vector_impl_data const& __x) noexcept
 {
   _M_start = __x._M_start;
   _M_finish = __x._M_finish;
   _M_end_of_storage = __x._M_end_of_storage;
 }


 void
 _M_swap_data(_Vector_impl_data& __x) noexcept
 {


   _Vector_impl_data __tmp;
   __tmp._M_copy_data(*this);
   _M_copy_data(__x);
   __x._M_copy_data(__tmp);
 }
      };

      struct _Vector_impl
 : public _Tp_alloc_type, public _Vector_impl_data
      {

 _Vector_impl() noexcept(is_nothrow_default_constructible<_Tp_alloc_type>::value)

 : _Tp_alloc_type()
 { }


 _Vector_impl(_Tp_alloc_type const& __a) noexcept
 : _Tp_alloc_type(__a)
 { }





 _Vector_impl(_Vector_impl&& __x) noexcept
 : _Tp_alloc_type(std::move(__x)), _Vector_impl_data(std::move(__x))
 { }


 _Vector_impl(_Tp_alloc_type&& __a) noexcept
 : _Tp_alloc_type(std::move(__a))
 { }


 _Vector_impl(_Tp_alloc_type&& __a, _Vector_impl&& __rv) noexcept
 : _Tp_alloc_type(std::move(__a)), _Vector_impl_data(std::move(__rv))
 { }
# 291 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      };

    public:
      typedef _Alloc allocator_type;


      _Tp_alloc_type&
      _M_get_Tp_allocator() noexcept
      { return this->_M_impl; }


      const _Tp_alloc_type&
      _M_get_Tp_allocator() const noexcept
      { return this->_M_impl; }


      allocator_type
      get_allocator() const noexcept
      { return allocator_type(_M_get_Tp_allocator()); }


      _Vector_base() = default;





      _Vector_base(const allocator_type& __a) noexcept
      : _M_impl(__a) { }




      _Vector_base(size_t __n)
      : _M_impl()
      { _M_create_storage(__n); }



      _Vector_base(size_t __n, const allocator_type& __a)
      : _M_impl(__a)
      { _M_create_storage(__n); }


      _Vector_base(_Vector_base&&) = default;




      _Vector_base(_Tp_alloc_type&& __a) noexcept
      : _M_impl(std::move(__a)) { }


      _Vector_base(_Vector_base&& __x, const allocator_type& __a)
      : _M_impl(__a)
      {
 if (__x.get_allocator() == __a)
   this->_M_impl._M_swap_data(__x._M_impl);
 else
   {
     size_t __n = __x._M_impl._M_finish - __x._M_impl._M_start;
     _M_create_storage(__n);
   }
      }



      _Vector_base(const allocator_type& __a, _Vector_base&& __x)
      : _M_impl(_Tp_alloc_type(__a), std::move(__x._M_impl))
      { }



      ~_Vector_base() noexcept
      {
 _M_deallocate(_M_impl._M_start,
        _M_impl._M_end_of_storage - _M_impl._M_start);
      }

    public:
      _Vector_impl _M_impl;


      pointer
      _M_allocate(size_t __n)
      {
 typedef __gnu_cxx::__alloc_traits<_Tp_alloc_type> _Tr;
 return __n != 0 ? _Tr::allocate(_M_impl, __n) : pointer();
      }


      void
      _M_deallocate(pointer __p, size_t __n)
      {
 typedef __gnu_cxx::__alloc_traits<_Tp_alloc_type> _Tr;
 if (__p)
   _Tr::deallocate(_M_impl, __p, __n);
      }

    protected:

      void
      _M_create_storage(size_t __n)
      {
 this->_M_impl._M_start = this->_M_allocate(__n);
 this->_M_impl._M_finish = this->_M_impl._M_start;
 this->_M_impl._M_end_of_storage = this->_M_impl._M_start + __n;
      }
    };
# 422 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
  template<typename _Tp, typename _Alloc = std::allocator<_Tp> >
    class vector : protected _Vector_base<_Tp, _Alloc>
    {
# 435 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      static_assert(is_same<typename remove_cv<_Tp>::type, _Tp>::value,
   "std::vector must have a non-const, non-volatile value_type");

      static_assert(is_same<typename _Alloc::value_type, _Tp>::value,
   "std::vector must have the same value_type as its allocator");



      typedef _Vector_base<_Tp, _Alloc> _Base;
      typedef typename _Base::_Tp_alloc_type _Tp_alloc_type;
      typedef __gnu_cxx::__alloc_traits<_Tp_alloc_type> _Alloc_traits;

    public:
      typedef _Tp value_type;
      typedef typename _Base::pointer pointer;
      typedef typename _Alloc_traits::const_pointer const_pointer;
      typedef typename _Alloc_traits::reference reference;
      typedef typename _Alloc_traits::const_reference const_reference;
      typedef __gnu_cxx::__normal_iterator<pointer, vector> iterator;
      typedef __gnu_cxx::__normal_iterator<const_pointer, vector>
      const_iterator;
      typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
      typedef std::reverse_iterator<iterator> reverse_iterator;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;
      typedef _Alloc allocator_type;

    private:

      static constexpr bool
      _S_nothrow_relocate(true_type)
      {
 return noexcept(std::__relocate_a(std::declval<pointer>(),
       std::declval<pointer>(),
       std::declval<pointer>(),
       std::declval<_Tp_alloc_type&>()));
      }

      static constexpr bool
      _S_nothrow_relocate(false_type)
      { return false; }

      static constexpr bool
      _S_use_relocate()
      {



 return _S_nothrow_relocate(__is_move_insertable<_Tp_alloc_type>{});
      }

      static pointer
      _S_do_relocate(pointer __first, pointer __last, pointer __result,
       _Tp_alloc_type& __alloc, true_type) noexcept
      {
 return std::__relocate_a(__first, __last, __result, __alloc);
      }

      static pointer
      _S_do_relocate(pointer, pointer, pointer __result,
       _Tp_alloc_type&, false_type) noexcept
      { return __result; }

      static pointer
      _S_relocate(pointer __first, pointer __last, pointer __result,
    _Tp_alloc_type& __alloc) noexcept
      {




 using __do_it = __bool_constant<_S_use_relocate()>;
 return _S_do_relocate(__first, __last, __result, __alloc, __do_it{});

      }


    protected:
      using _Base::_M_allocate;
      using _Base::_M_deallocate;
      using _Base::_M_impl;
      using _Base::_M_get_Tp_allocator;

    public:







      vector() = default;
# 535 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      explicit

      vector(const allocator_type& __a) noexcept
      : _Base(__a) { }
# 549 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      explicit

      vector(size_type __n, const allocator_type& __a = allocator_type())
      : _Base(_S_check_init_len(__n, __a), __a)
      { _M_default_initialize(__n); }
# 564 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector(size_type __n, const value_type& __value,
      const allocator_type& __a = allocator_type())
      : _Base(_S_check_init_len(__n, __a), __a)
      { _M_fill_initialize(__n, __value); }
# 596 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector(const vector& __x)
      : _Base(__x.size(),
 _Alloc_traits::_S_select_on_copy(__x._M_get_Tp_allocator()))
      {
 this->_M_impl._M_finish =
   std::__uninitialized_copy_a(__x.begin(), __x.end(),
          this->_M_impl._M_start,
          _M_get_Tp_allocator());
      }
# 615 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector(vector&&) noexcept = default;



      vector(const vector& __x, const __type_identity_t<allocator_type>& __a)
      : _Base(__x.size(), __a)
      {
 this->_M_impl._M_finish =
   std::__uninitialized_copy_a(__x.begin(), __x.end(),
          this->_M_impl._M_start,
          _M_get_Tp_allocator());
      }

    private:

      vector(vector&& __rv, const allocator_type& __m, true_type) noexcept
      : _Base(__m, std::move(__rv))
      { }


      vector(vector&& __rv, const allocator_type& __m, false_type)
      : _Base(__m)
      {
 if (__rv.get_allocator() == __m)
   this->_M_impl._M_swap_data(__rv._M_impl);
 else if (!__rv.empty())
   {
     this->_M_create_storage(__rv.size());
     this->_M_impl._M_finish =
       std::__uninitialized_move_a(__rv.begin(), __rv.end(),
       this->_M_impl._M_start,
       _M_get_Tp_allocator());
     __rv.clear();
   }
      }

    public:


      vector(vector&& __rv, const __type_identity_t<allocator_type>& __m)
      noexcept( noexcept(
 vector(std::declval<vector&&>(), std::declval<const allocator_type&>(),
        std::declval<typename _Alloc_traits::is_always_equal>())) )
      : vector(std::move(__rv), __m, typename _Alloc_traits::is_always_equal{})
      { }
# 673 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector(initializer_list<value_type> __l,
      const allocator_type& __a = allocator_type())
      : _Base(__a)
      {
 _M_range_initialize(__l.begin(), __l.end(),
       random_access_iterator_tag());
      }
# 699 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 vector(_InputIterator __first, _InputIterator __last,
        const allocator_type& __a = allocator_type())
 : _Base(__a)
 {
   _M_range_initialize(__first, __last,
         std::__iterator_category(__first));
 }
# 728 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      ~vector() noexcept
      {
 std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
        _M_get_Tp_allocator());
                                      ;
      }
# 745 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector&
      operator=(const vector& __x);
# 760 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector&
      operator=(vector&& __x) noexcept(_Alloc_traits::_S_nothrow_move())
      {
 constexpr bool __move_storage =
   _Alloc_traits::_S_propagate_on_move_assign()
   || _Alloc_traits::_S_always_equal();
 _M_move_assign(std::move(__x), __bool_constant<__move_storage>());
 return *this;
      }
# 782 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      vector&
      operator=(initializer_list<value_type> __l)
      {
 this->_M_assign_aux(__l.begin(), __l.end(),
       random_access_iterator_tag());
 return *this;
      }
# 802 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      assign(size_type __n, const value_type& __val)
      { _M_fill_assign(__n, __val); }
# 819 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 void
 assign(_InputIterator __first, _InputIterator __last)
 { _M_assign_dispatch(__first, __last, __false_type()); }
# 849 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      assign(initializer_list<value_type> __l)
      {
 this->_M_assign_aux(__l.begin(), __l.end(),
       random_access_iterator_tag());
      }



      using _Base::get_allocator;
# 867 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator
      begin() noexcept
      { return iterator(this->_M_impl._M_start); }







      const_iterator
      begin() const noexcept
      { return const_iterator(this->_M_impl._M_start); }







      iterator
      end() noexcept
      { return iterator(this->_M_impl._M_finish); }







      const_iterator
      end() const noexcept
      { return const_iterator(this->_M_impl._M_finish); }







      reverse_iterator
      rbegin() noexcept
      { return reverse_iterator(end()); }







      const_reverse_iterator
      rbegin() const noexcept
      { return const_reverse_iterator(end()); }







      reverse_iterator
      rend() noexcept
      { return reverse_iterator(begin()); }







      const_reverse_iterator
      rend() const noexcept
      { return const_reverse_iterator(begin()); }







      [[__nodiscard__]]
      const_iterator
      cbegin() const noexcept
      { return const_iterator(this->_M_impl._M_start); }






      [[__nodiscard__]]
      const_iterator
      cend() const noexcept
      { return const_iterator(this->_M_impl._M_finish); }






      [[__nodiscard__]]
      const_reverse_iterator
      crbegin() const noexcept
      { return const_reverse_iterator(end()); }






      [[__nodiscard__]]
      const_reverse_iterator
      crend() const noexcept
      { return const_reverse_iterator(begin()); }





      size_type
      size() const noexcept
      { return size_type(this->_M_impl._M_finish - this->_M_impl._M_start); }



      size_type
      max_size() const noexcept
      { return _S_max_size(_M_get_Tp_allocator()); }
# 1007 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      resize(size_type __new_size)
      {
 if (__new_size > size())
   _M_default_append(__new_size - size());
 else if (__new_size < size())
   _M_erase_at_end(this->_M_impl._M_start + __new_size);
      }
# 1028 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      resize(size_type __new_size, const value_type& __x)
      {
 if (__new_size > size())
   _M_fill_insert(end(), __new_size - size(), __x);
 else if (__new_size < size())
   _M_erase_at_end(this->_M_impl._M_start + __new_size);
      }
# 1062 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      shrink_to_fit()
      { _M_shrink_to_fit(); }







      size_type
      capacity() const noexcept
      { return size_type(this->_M_impl._M_end_of_storage
    - this->_M_impl._M_start); }






      bool
      empty() const noexcept
      { return begin() == end(); }
# 1104 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      reserve(size_type __n);
# 1120 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      reference
      operator[](size_type __n) noexcept
      {
                                  ;
 return *(this->_M_impl._M_start + __n);
      }
# 1139 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      const_reference
      operator[](size_type __n) const noexcept
      {
                                  ;
 return *(this->_M_impl._M_start + __n);
      }

    protected:


      void
      _M_range_check(size_type __n) const
      {
 if (__n >= this->size())
   __throw_out_of_range_fmt(("vector::_M_range_check: __n " "(which is %zu) >= this->size() " "(which is %zu)"),


       __n, this->size());
      }

    public:
# 1172 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      reference
      at(size_type __n)
      {
 _M_range_check(__n);
 return (*this)[__n];
      }
# 1191 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      const_reference
      at(size_type __n) const
      {
 _M_range_check(__n);
 return (*this)[__n];
      }






      reference
      front() noexcept
      {
                              ;
 return *begin();
      }






      const_reference
      front() const noexcept
      {
                              ;
 return *begin();
      }






      reference
      back() noexcept
      {
                              ;
 return *(end() - 1);
      }






      const_reference
      back() const noexcept
      {
                              ;
 return *(end() - 1);
      }
# 1254 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      _Tp*
      data() noexcept
      { return _M_data_ptr(this->_M_impl._M_start); }


      const _Tp*
      data() const noexcept
      { return _M_data_ptr(this->_M_impl._M_start); }
# 1275 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      push_back(const value_type& __x)
      {
 if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
   {
                                   ;
     _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
         __x);
     ++this->_M_impl._M_finish;
                                   ;
   }
 else
   _M_realloc_insert(end(), __x);
      }



      void
      push_back(value_type&& __x)
      { emplace_back(std::move(__x)); }

      template<typename... _Args>




 void

 emplace_back(_Args&&... __args);
# 1316 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      pop_back() noexcept
      {
                              ;
 --this->_M_impl._M_finish;
 _Alloc_traits::destroy(this->_M_impl, this->_M_impl._M_finish);
                                 ;
      }
# 1338 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename... _Args>

 iterator
 emplace(const_iterator __position, _Args&&... __args)
 { return _M_emplace_aux(__position, std::forward<_Args>(__args)...); }
# 1356 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator
      insert(const_iterator __position, const value_type& __x);
# 1387 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator
      insert(const_iterator __position, value_type&& __x)
      { return _M_insert_rval(__position, std::move(__x)); }
# 1405 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator
      insert(const_iterator __position, initializer_list<value_type> __l)
      {
 auto __offset = __position - cbegin();
 _M_range_insert(begin() + __offset, __l.begin(), __l.end(),
   std::random_access_iterator_tag());
 return begin() + __offset;
      }
# 1431 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator
      insert(const_iterator __position, size_type __n, const value_type& __x)
      {
 difference_type __offset = __position - cbegin();
 _M_fill_insert(begin() + __offset, __n, __x);
 return begin() + __offset;
      }
# 1473 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 iterator
 insert(const_iterator __position, _InputIterator __first,
        _InputIterator __last)
 {
   difference_type __offset = __position - cbegin();
   _M_insert_dispatch(begin() + __offset,
        __first, __last, __false_type());
   return begin() + __offset;
 }
# 1527 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator

      erase(const_iterator __position)
      { return _M_erase(begin() + (__position - cbegin())); }
# 1555 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      iterator

      erase(const_iterator __first, const_iterator __last)
      {
 const auto __beg = begin();
 const auto __cbeg = cbegin();
 return _M_erase(__beg + (__first - __cbeg), __beg + (__last - __cbeg));
      }
# 1580 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      swap(vector& __x) noexcept
      {

 do { if (std::__is_constant_evaluated() && !bool(_Alloc_traits::propagate_on_container_swap::value || _M_get_Tp_allocator() == __x._M_get_Tp_allocator())) __builtin_unreachable(); } while (false);


 this->_M_impl._M_swap_data(__x._M_impl);
 _Alloc_traits::_S_on_swap(_M_get_Tp_allocator(),
      __x._M_get_Tp_allocator());
      }
# 1599 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      void
      clear() noexcept
      { _M_erase_at_end(this->_M_impl._M_start); }

    protected:




      template<typename _ForwardIterator>

 pointer
 _M_allocate_and_copy(size_type __n,
        _ForwardIterator __first, _ForwardIterator __last)
 {
   pointer __result = this->_M_allocate(__n);
   try
     {
       std::__uninitialized_copy_a(__first, __last, __result,
       _M_get_Tp_allocator());
       return __result;
     }
   catch(...)
     {
       _M_deallocate(__result, __n);
       throw;
     }
 }
# 1659 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename _InputIterator>

 void
 _M_range_initialize(_InputIterator __first, _InputIterator __last,
       std::input_iterator_tag)
 {
   try {
     for (; __first != __last; ++__first)

       emplace_back(*__first);



   } catch(...) {
     clear();
     throw;
   }
 }


      template<typename _ForwardIterator>

 void
 _M_range_initialize(_ForwardIterator __first, _ForwardIterator __last,
       std::forward_iterator_tag)
 {
   const size_type __n = std::distance(__first, __last);
   this->_M_impl._M_start
     = this->_M_allocate(_S_check_init_len(__n, _M_get_Tp_allocator()));
   this->_M_impl._M_end_of_storage = this->_M_impl._M_start + __n;
   this->_M_impl._M_finish =
     std::__uninitialized_copy_a(__first, __last,
     this->_M_impl._M_start,
     _M_get_Tp_allocator());
 }




      void
      _M_fill_initialize(size_type __n, const value_type& __value)
      {
 this->_M_impl._M_finish =
   std::__uninitialized_fill_n_a(this->_M_impl._M_start, __n, __value,
     _M_get_Tp_allocator());
      }




      void
      _M_default_initialize(size_type __n)
      {
 this->_M_impl._M_finish =
   std::__uninitialized_default_n_a(this->_M_impl._M_start, __n,
        _M_get_Tp_allocator());
      }
# 1725 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      template<typename _Integer>

 void
 _M_assign_dispatch(_Integer __n, _Integer __val, __true_type)
 { _M_fill_assign(__n, __val); }


      template<typename _InputIterator>

 void
 _M_assign_dispatch(_InputIterator __first, _InputIterator __last,
      __false_type)
 { _M_assign_aux(__first, __last, std::__iterator_category(__first)); }


      template<typename _InputIterator>

 void
 _M_assign_aux(_InputIterator __first, _InputIterator __last,
        std::input_iterator_tag);


      template<typename _ForwardIterator>

 void
 _M_assign_aux(_ForwardIterator __first, _ForwardIterator __last,
        std::forward_iterator_tag);




      void
      _M_fill_assign(size_type __n, const value_type& __val);







      template<typename _Integer>

 void
 _M_insert_dispatch(iterator __pos, _Integer __n, _Integer __val,
      __true_type)
 { _M_fill_insert(__pos, __n, __val); }


      template<typename _InputIterator>

 void
 _M_insert_dispatch(iterator __pos, _InputIterator __first,
      _InputIterator __last, __false_type)
 {
   _M_range_insert(__pos, __first, __last,
     std::__iterator_category(__first));
 }


      template<typename _InputIterator>

 void
 _M_range_insert(iterator __pos, _InputIterator __first,
   _InputIterator __last, std::input_iterator_tag);


      template<typename _ForwardIterator>

 void
 _M_range_insert(iterator __pos, _ForwardIterator __first,
   _ForwardIterator __last, std::forward_iterator_tag);




      void
      _M_fill_insert(iterator __pos, size_type __n, const value_type& __x);




      void
      _M_default_append(size_type __n);


      bool
      _M_shrink_to_fit();
# 1824 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
      struct _Temporary_value
      {
 template<typename... _Args>
                        explicit
   _Temporary_value(vector* __vec, _Args&&... __args) : _M_this(__vec)
   {
     _Alloc_traits::construct(_M_this->_M_impl, _M_ptr(),
         std::forward<_Args>(__args)...);
   }


 ~_Temporary_value()
 { _Alloc_traits::destroy(_M_this->_M_impl, _M_ptr()); }

                      value_type&
 _M_val() noexcept { return _M_storage._M_val; }

      private:
                      _Tp*
 _M_ptr() noexcept { return std::__addressof(_M_storage._M_val); }

 union _Storage
 {
   constexpr _Storage() : _M_byte() { }
                        ~_Storage() { }
   _Storage& operator=(const _Storage&) = delete;
   unsigned char _M_byte;
   _Tp _M_val;
 };

 vector* _M_this;
 _Storage _M_storage;
      };



      template<typename _Arg>

 void
 _M_insert_aux(iterator __position, _Arg&& __arg);

      template<typename... _Args>

 void
 _M_realloc_insert(iterator __position, _Args&&... __args);



      iterator
      _M_insert_rval(const_iterator __position, value_type&& __v);


      template<typename... _Args>

 iterator
 _M_emplace_aux(const_iterator __position, _Args&&... __args);



      iterator
      _M_emplace_aux(const_iterator __position, value_type&& __v)
      { return _M_insert_rval(__position, std::move(__v)); }




      size_type
      _M_check_len(size_type __n, const char* __s) const
      {
 if (max_size() - size() < __n)
   __throw_length_error((__s));

 const size_type __len = size() + (std::max)(size(), __n);
 return (__len < size() || __len > max_size()) ? max_size() : __len;
      }


      static size_type
      _S_check_init_len(size_type __n, const allocator_type& __a)
      {
 if (__n > _S_max_size(_Tp_alloc_type(__a)))
   __throw_length_error(
       ("cannot create std::vector larger than max_size()"));
 return __n;
      }

      static size_type
      _S_max_size(const _Tp_alloc_type& __a) noexcept
      {



 const size_t __diffmax
   = __gnu_cxx::__numeric_traits<ptrdiff_t>::__max / sizeof(_Tp);
 const size_t __allocmax = _Alloc_traits::max_size(__a);
 return (std::min)(__diffmax, __allocmax);
      }






      void
      _M_erase_at_end(pointer __pos) noexcept
      {
 if (size_type __n = this->_M_impl._M_finish - __pos)
   {
     std::_Destroy(__pos, this->_M_impl._M_finish,
     _M_get_Tp_allocator());
     this->_M_impl._M_finish = __pos;
                                       ;
   }
      }


      iterator
      _M_erase(iterator __position);


      iterator
      _M_erase(iterator __first, iterator __last);


    private:




      void
      _M_move_assign(vector&& __x, true_type) noexcept
      {
 vector __tmp(get_allocator());
 this->_M_impl._M_swap_data(__x._M_impl);
 __tmp._M_impl._M_swap_data(__x._M_impl);
 std::__alloc_on_move(_M_get_Tp_allocator(), __x._M_get_Tp_allocator());
      }




      void
      _M_move_assign(vector&& __x, false_type)
      {
 if (__x._M_get_Tp_allocator() == this->_M_get_Tp_allocator())
   _M_move_assign(std::move(__x), true_type());
 else
   {


     this->_M_assign_aux(std::make_move_iterator(__x.begin()),
           std::make_move_iterator(__x.end()),
    std::random_access_iterator_tag());
     __x.clear();
   }
      }


      template<typename _Up>

 _Up*
 _M_data_ptr(_Up* __ptr) const noexcept
 { return __ptr; }


      template<typename _Ptr>

 typename std::pointer_traits<_Ptr>::element_type*
 _M_data_ptr(_Ptr __ptr) const
 { return empty() ? nullptr : std::__to_address(__ptr); }
# 2010 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
    };
# 2032 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
  template<typename _Tp, typename _Alloc>

    inline bool
    operator==(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return (__x.size() == __y.size()
       && std::equal(__x.begin(), __x.end(), __y.begin())); }
# 2072 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
  template<typename _Tp, typename _Alloc>
    inline bool
    operator<(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return std::lexicographical_compare(__x.begin(), __x.end(),
       __y.begin(), __y.end()); }


  template<typename _Tp, typename _Alloc>
    inline bool
    operator!=(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return !(__x == __y); }


  template<typename _Tp, typename _Alloc>
    inline bool
    operator>(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return __y < __x; }


  template<typename _Tp, typename _Alloc>
    inline bool
    operator<=(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return !(__y < __x); }


  template<typename _Tp, typename _Alloc>
    inline bool
    operator>=(const vector<_Tp, _Alloc>& __x, const vector<_Tp, _Alloc>& __y)
    { return !(__x < __y); }



  template<typename _Tp, typename _Alloc>

    inline void
    swap(vector<_Tp, _Alloc>& __x, vector<_Tp, _Alloc>& __y)
    noexcept(noexcept(__x.swap(__y)))
    { __x.swap(__y); }
# 2128 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_vector.h" 3
}
# 65 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 2 3
# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 1 3
# 64 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
namespace std __attribute__ ((__visibility__ ("default")))
{


  typedef unsigned long _Bit_type;
  enum { _S_word_bit = int(8 * sizeof(_Bit_type)) };

  __attribute__((__nonnull__))

  void
  __fill_bvector_n(_Bit_type*, size_t, bool) noexcept;



  struct _Bit_reference
  {
    _Bit_type * _M_p;
    _Bit_type _M_mask;


    _Bit_reference(_Bit_type * __x, _Bit_type __y)
    : _M_p(__x), _M_mask(__y) { }


    _Bit_reference() noexcept : _M_p(0), _M_mask(0) { }


    _Bit_reference(const _Bit_reference&) = default;



    operator bool() const noexcept
    { return !!(*_M_p & _M_mask); }


    _Bit_reference&
    operator=(bool __x) noexcept
    {
      if (__x)
 *_M_p |= _M_mask;
      else
 *_M_p &= ~_M_mask;
      return *this;
    }


    _Bit_reference&
    operator=(const _Bit_reference& __x) noexcept
    { return *this = bool(__x); }


    bool
    operator==(const _Bit_reference& __x) const
    { return bool(*this) == bool(__x); }


    bool
    operator<(const _Bit_reference& __x) const
    { return !bool(*this) && bool(__x); }


    void
    flip() noexcept
    { *_M_p ^= _M_mask; }



    friend void
    swap(_Bit_reference __x, _Bit_reference __y) noexcept
    {
      bool __tmp = __x;
      __x = __y;
      __y = __tmp;
    }


    friend void
    swap(_Bit_reference __x, bool& __y) noexcept
    {
      bool __tmp = __x;
      __x = __y;
      __y = __tmp;
    }


    friend void
    swap(bool& __x, _Bit_reference __y) noexcept
    {
      bool __tmp = __x;
      __x = __y;
      __y = __tmp;
    }

  };


#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
  struct _Bit_iterator_base
  : public std::iterator<std::random_access_iterator_tag, bool>
  {
    _Bit_type * _M_p;
    unsigned int _M_offset;


    _Bit_iterator_base(_Bit_type * __x, unsigned int __y)
    : _M_p(__x), _M_offset(__y) { }


    void
    _M_bump_up()
    {
      if (_M_offset++ == int(_S_word_bit) - 1)
 {
   _M_offset = 0;
   ++_M_p;
 }
    }


    void
    _M_bump_down()
    {
      if (_M_offset-- == 0)
 {
   _M_offset = int(_S_word_bit) - 1;
   --_M_p;
 }
    }


    void
    _M_incr(ptrdiff_t __i)
    {
      difference_type __n = __i + _M_offset;
      _M_p += __n / int(_S_word_bit);
      __n = __n % int(_S_word_bit);
      if (__n < 0)
 {
   __n += int(_S_word_bit);
   --_M_p;
 }
      _M_offset = static_cast<unsigned int>(__n);
    }


    friend bool
    operator==(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    { return __x._M_p == __y._M_p && __x._M_offset == __y._M_offset; }
# 226 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
    friend bool
    operator<(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    {
      return __x._M_p < __y._M_p
     || (__x._M_p == __y._M_p && __x._M_offset < __y._M_offset);
    }


    friend bool
    operator!=(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    { return !(__x == __y); }


    friend bool
    operator>(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    { return __y < __x; }


    friend bool
    operator<=(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    { return !(__y < __x); }


    friend bool
    operator>=(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    { return !(__x < __y); }


    friend ptrdiff_t
    operator-(const _Bit_iterator_base& __x, const _Bit_iterator_base& __y)
    {
      return (int(_S_word_bit) * (__x._M_p - __y._M_p)
       + __x._M_offset - __y._M_offset);
    }
  };
#pragma GCC diagnostic pop

  struct _Bit_iterator : public _Bit_iterator_base
  {
    typedef _Bit_reference reference;



    typedef _Bit_reference* pointer;

    typedef _Bit_iterator iterator;


    _Bit_iterator() : _Bit_iterator_base(0, 0) { }


    _Bit_iterator(_Bit_type * __x, unsigned int __y)
    : _Bit_iterator_base(__x, __y) { }


    iterator
    _M_const_cast() const
    { return *this; }


    reference
    operator*() const
    { return reference(_M_p, 1UL << _M_offset); }


    iterator&
    operator++()
    {
      _M_bump_up();
      return *this;
    }


    iterator
    operator++(int)
    {
      iterator __tmp = *this;
      _M_bump_up();
      return __tmp;
    }


    iterator&
    operator--()
    {
      _M_bump_down();
      return *this;
    }


    iterator
    operator--(int)
    {
      iterator __tmp = *this;
      _M_bump_down();
      return __tmp;
    }


    iterator&
    operator+=(difference_type __i)
    {
      _M_incr(__i);
      return *this;
    }


    iterator&
    operator-=(difference_type __i)
    {
      *this += -__i;
      return *this;
    }


    reference
    operator[](difference_type __i) const
    { return *(*this + __i); }


    friend iterator
    operator+(const iterator& __x, difference_type __n)
    {
      iterator __tmp = __x;
      __tmp += __n;
      return __tmp;
    }


    friend iterator
    operator+(difference_type __n, const iterator& __x)
    { return __x + __n; }


    friend iterator
    operator-(const iterator& __x, difference_type __n)
    {
      iterator __tmp = __x;
      __tmp -= __n;
      return __tmp;
    }
  };

  struct _Bit_const_iterator : public _Bit_iterator_base
  {
    typedef bool reference;
    typedef bool const_reference;



    typedef const bool* pointer;

    typedef _Bit_const_iterator const_iterator;


    _Bit_const_iterator() : _Bit_iterator_base(0, 0) { }


    _Bit_const_iterator(_Bit_type * __x, unsigned int __y)
    : _Bit_iterator_base(__x, __y) { }


    _Bit_const_iterator(const _Bit_iterator& __x)
    : _Bit_iterator_base(__x._M_p, __x._M_offset) { }


    _Bit_iterator
    _M_const_cast() const
    { return _Bit_iterator(_M_p, _M_offset); }


    const_reference
    operator*() const
    { return _Bit_reference(_M_p, 1UL << _M_offset); }


    const_iterator&
    operator++()
    {
      _M_bump_up();
      return *this;
    }


    const_iterator
    operator++(int)
    {
      const_iterator __tmp = *this;
      _M_bump_up();
      return __tmp;
    }


    const_iterator&
    operator--()
    {
      _M_bump_down();
      return *this;
    }


    const_iterator
    operator--(int)
    {
      const_iterator __tmp = *this;
      _M_bump_down();
      return __tmp;
    }


    const_iterator&
    operator+=(difference_type __i)
    {
      _M_incr(__i);
      return *this;
    }


    const_iterator&
    operator-=(difference_type __i)
    {
      *this += -__i;
      return *this;
    }


    const_reference
    operator[](difference_type __i) const
    { return *(*this + __i); }


    friend const_iterator
    operator+(const const_iterator& __x, difference_type __n)
    {
      const_iterator __tmp = __x;
      __tmp += __n;
      return __tmp;
    }


    friend const_iterator
    operator-(const const_iterator& __x, difference_type __n)
    {
      const_iterator __tmp = __x;
      __tmp -= __n;
      return __tmp;
    }


    friend const_iterator
    operator+(difference_type __n, const const_iterator& __x)
    { return __x + __n; }
  };

  template<typename _Alloc>
    struct _Bvector_base
    {
      typedef typename __gnu_cxx::__alloc_traits<_Alloc>::template
        rebind<_Bit_type>::other _Bit_alloc_type;
      typedef typename __gnu_cxx::__alloc_traits<_Bit_alloc_type>
 _Bit_alloc_traits;
      typedef typename _Bit_alloc_traits::pointer _Bit_pointer;

      struct _Bvector_impl_data
      {

 _Bit_iterator _M_start;
# 502 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
 _Bit_iterator _M_finish;
 _Bit_pointer _M_end_of_storage;


 _Bvector_impl_data() noexcept
 : _M_start(), _M_finish(), _M_end_of_storage()
 { }


 _Bvector_impl_data(const _Bvector_impl_data&) = default;

 _Bvector_impl_data&
 operator=(const _Bvector_impl_data&) = default;


 _Bvector_impl_data(_Bvector_impl_data&& __x) noexcept
 : _Bvector_impl_data(__x)
 { __x._M_reset(); }


 void
 _M_move_data(_Bvector_impl_data&& __x) noexcept
 {
   *this = __x;
   __x._M_reset();
 }



 void
 _M_reset() noexcept
 { *this = _Bvector_impl_data(); }


 void
 _M_swap_data(_Bvector_impl_data& __x) noexcept
 {


   std::swap(*this, __x);
 }
      };

      struct _Bvector_impl
 : public _Bit_alloc_type, public _Bvector_impl_data
      {

 _Bvector_impl() noexcept(is_nothrow_default_constructible<_Bit_alloc_type>::value)

 : _Bit_alloc_type()
 { }


 _Bvector_impl(const _Bit_alloc_type& __a) noexcept
 : _Bit_alloc_type(__a)
 { }





 _Bvector_impl(_Bvector_impl&& __x) noexcept
 : _Bit_alloc_type(std::move(__x)), _Bvector_impl_data(std::move(__x))
 { }


 _Bvector_impl(_Bit_alloc_type&& __a, _Bvector_impl&& __x) noexcept
 : _Bit_alloc_type(std::move(__a)), _Bvector_impl_data(std::move(__x))
 { }



 _Bit_type*
 _M_end_addr() const noexcept
 {
   if (this->_M_end_of_storage)
     return std::__addressof(this->_M_end_of_storage[-1]) + 1;
   return 0;
 }
      };

    public:
      typedef _Alloc allocator_type;


      _Bit_alloc_type&
      _M_get_Bit_allocator() noexcept
      { return this->_M_impl; }


      const _Bit_alloc_type&
      _M_get_Bit_allocator() const noexcept
      { return this->_M_impl; }


      allocator_type
      get_allocator() const noexcept
      { return allocator_type(_M_get_Bit_allocator()); }


      _Bvector_base() = default;





      _Bvector_base(const allocator_type& __a)
      : _M_impl(__a) { }


      _Bvector_base(_Bvector_base&&) = default;


      _Bvector_base(_Bvector_base&& __x, const allocator_type& __a) noexcept
      : _M_impl(_Bit_alloc_type(__a), std::move(__x._M_impl))
      { }



      ~_Bvector_base()
      { this->_M_deallocate(); }

    protected:
      _Bvector_impl _M_impl;


      _Bit_pointer
      _M_allocate(size_t __n)
      {
 _Bit_pointer __p = _Bit_alloc_traits::allocate(_M_impl, _S_nword(__n));
# 640 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
 return __p;
      }


      void
      _M_deallocate()
      {
 if (_M_impl._M_start._M_p)
   {
     const size_t __n = _M_impl._M_end_addr() - _M_impl._M_start._M_p;
     _Bit_alloc_traits::deallocate(_M_impl,
       _M_impl._M_end_of_storage - __n,
       __n);
     _M_impl._M_reset();
   }
      }



      void
      _M_move_data(_Bvector_base&& __x) noexcept
      { _M_impl._M_move_data(std::move(__x._M_impl)); }


      constexpr
      static size_t
      _S_nword(size_t __n)
      { return (__n + int(_S_word_bit) - 1) / int(_S_word_bit); }
    };
# 689 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
  template<typename _Alloc>
    class vector<bool, _Alloc> : protected _Bvector_base<_Alloc>
    {
      typedef _Bvector_base<_Alloc> _Base;
      typedef typename _Base::_Bit_pointer _Bit_pointer;
      typedef typename _Base::_Bit_alloc_traits _Bit_alloc_traits;


      friend struct std::hash<vector>;


    public:
      typedef bool value_type;
      typedef size_t size_type;
      typedef ptrdiff_t difference_type;
      typedef _Bit_reference reference;
      typedef bool const_reference;
      typedef _Bit_reference* pointer;
      typedef const bool* const_pointer;
      typedef _Bit_iterator iterator;
      typedef _Bit_const_iterator const_iterator;
      typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
      typedef std::reverse_iterator<iterator> reverse_iterator;
      typedef _Alloc allocator_type;


      allocator_type
      get_allocator() const
      { return _Base::get_allocator(); }

    protected:
      using _Base::_M_allocate;
      using _Base::_M_deallocate;
      using _Base::_S_nword;
      using _Base::_M_get_Bit_allocator;

    public:

      vector() = default;





      explicit
      vector(const allocator_type& __a)
      : _Base(__a) { }



      explicit
      vector(size_type __n, const allocator_type& __a = allocator_type())
      : vector(__n, false, __a)
      { }


      vector(size_type __n, const bool& __value,
      const allocator_type& __a = allocator_type())





      : _Base(__a)
      {
 _M_initialize(__n);
 _M_initialize_value(__value);
      }


      vector(const vector& __x)
      : _Base(_Bit_alloc_traits::_S_select_on_copy(__x._M_get_Bit_allocator()))
      {
 _M_initialize(__x.size());
 _M_copy_aligned(__x.begin(), __x.end(), begin());
      }


      vector(vector&&) = default;

    private:

      vector(vector&& __x, const allocator_type& __a, true_type) noexcept
      : _Base(std::move(__x), __a)
      { }


      vector(vector&& __x, const allocator_type& __a, false_type)
      : _Base(__a)
      {
 if (__x.get_allocator() == __a)
   this->_M_move_data(std::move(__x));
 else
   {
     _M_initialize(__x.size());
     _M_copy_aligned(__x.begin(), __x.end(), begin());
     __x.clear();
   }
      }

    public:

      vector(vector&& __x, const __type_identity_t<allocator_type>& __a)
      noexcept(_Bit_alloc_traits::_S_always_equal())
      : vector(std::move(__x), __a,
        typename _Bit_alloc_traits::is_always_equal{})
      { }


      vector(const vector& __x, const __type_identity_t<allocator_type>& __a)
      : _Base(__a)
      {
 _M_initialize(__x.size());
 _M_copy_aligned(__x.begin(), __x.end(), begin());
      }


      vector(initializer_list<bool> __l,
      const allocator_type& __a = allocator_type())
      : _Base(__a)
      {
 _M_initialize_range(__l.begin(), __l.end(),
       random_access_iterator_tag());
      }



      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 vector(_InputIterator __first, _InputIterator __last,
        const allocator_type& __a = allocator_type())
 : _Base(__a)
 {
   _M_initialize_range(__first, __last,
         std::__iterator_category(__first));
 }
# 839 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      ~vector() noexcept { }


      vector&
      operator=(const vector& __x)
      {
 if (&__x == this)
   return *this;

 if (_Bit_alloc_traits::_S_propagate_on_copy_assign())
   {
     if (this->_M_get_Bit_allocator() != __x._M_get_Bit_allocator())
       {
  this->_M_deallocate();
  std::__alloc_on_copy(_M_get_Bit_allocator(),
         __x._M_get_Bit_allocator());
  _M_initialize(__x.size());
       }
     else
       std::__alloc_on_copy(_M_get_Bit_allocator(),
       __x._M_get_Bit_allocator());
   }

 if (__x.size() > capacity())
   {
     this->_M_deallocate();
     _M_initialize(__x.size());
   }
 this->_M_impl._M_finish = _M_copy_aligned(__x.begin(), __x.end(),
        begin());
 return *this;
      }



      vector&
      operator=(vector&& __x) noexcept(_Bit_alloc_traits::_S_nothrow_move())
      {
 if (_Bit_alloc_traits::_S_propagate_on_move_assign()
     || this->_M_get_Bit_allocator() == __x._M_get_Bit_allocator())
   {
     this->_M_deallocate();
     this->_M_move_data(std::move(__x));
     std::__alloc_on_move(_M_get_Bit_allocator(),
     __x._M_get_Bit_allocator());
   }
 else
   {
     if (__x.size() > capacity())
       {
  this->_M_deallocate();
  _M_initialize(__x.size());
       }
     this->_M_impl._M_finish = _M_copy_aligned(__x.begin(), __x.end(),
            begin());
     __x.clear();
   }
 return *this;
      }


      vector&
      operator=(initializer_list<bool> __l)
      {
 this->assign(__l.begin(), __l.end());
 return *this;
      }







      void
      assign(size_type __n, const bool& __x)
      { _M_fill_assign(__n, __x); }


      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 void
 assign(_InputIterator __first, _InputIterator __last)
 { _M_assign_aux(__first, __last, std::__iterator_category(__first)); }
# 937 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      void
      assign(initializer_list<bool> __l)
      { _M_assign_aux(__l.begin(), __l.end(), random_access_iterator_tag()); }



      iterator
      begin() noexcept
      { return iterator(this->_M_impl._M_start._M_p, 0); }


      const_iterator
      begin() const noexcept
      { return const_iterator(this->_M_impl._M_start._M_p, 0); }


      iterator
      end() noexcept
      { return this->_M_impl._M_finish; }


      const_iterator
      end() const noexcept
      { return this->_M_impl._M_finish; }


      reverse_iterator
      rbegin() noexcept
      { return reverse_iterator(end()); }


      const_reverse_iterator
      rbegin() const noexcept
      { return const_reverse_iterator(end()); }


      reverse_iterator
      rend() noexcept
      { return reverse_iterator(begin()); }


      const_reverse_iterator
      rend() const noexcept
      { return const_reverse_iterator(begin()); }


      [[__nodiscard__]]
      const_iterator
      cbegin() const noexcept
      { return const_iterator(this->_M_impl._M_start._M_p, 0); }

      [[__nodiscard__]]
      const_iterator
      cend() const noexcept
      { return this->_M_impl._M_finish; }

      [[__nodiscard__]]
      const_reverse_iterator
      crbegin() const noexcept
      { return const_reverse_iterator(end()); }

      [[__nodiscard__]]
      const_reverse_iterator
      crend() const noexcept
      { return const_reverse_iterator(begin()); }



      size_type
      size() const noexcept
      { return size_type(end() - begin()); }


      size_type
      max_size() const noexcept
      {
 const size_type __isize =
   __gnu_cxx::__numeric_traits<difference_type>::__max
   - int(_S_word_bit) + 1;
 const size_type __asize
   = _Bit_alloc_traits::max_size(_M_get_Bit_allocator());
 return (__asize <= __isize / int(_S_word_bit)
  ? __asize * int(_S_word_bit) : __isize);
      }


      size_type
      capacity() const noexcept
      { return size_type(const_iterator(this->_M_impl._M_end_addr(), 0)
    - begin()); }


      bool
      empty() const noexcept
      { return begin() == end(); }


      reference
      operator[](size_type __n)
      { return begin()[__n]; }


      const_reference
      operator[](size_type __n) const
      { return begin()[__n]; }

    protected:

      void
      _M_range_check(size_type __n) const
      {
 if (__n >= this->size())
   __throw_out_of_range_fmt(("vector<bool>::_M_range_check: __n " "(which is %zu) >= this->size() " "(which is %zu)"),


       __n, this->size());
      }

    public:

      reference
      at(size_type __n)
      {
 _M_range_check(__n);
 return (*this)[__n];
      }


      const_reference
      at(size_type __n) const
      {
 _M_range_check(__n);
 return (*this)[__n];
      }


      void
      reserve(size_type __n)
      {
 if (__n > max_size())
   __throw_length_error(("vector::reserve"));
 if (capacity() < __n)
   _M_reallocate(__n);
      }


      reference
      front()
      { return *begin(); }


      const_reference
      front() const
      { return *begin(); }


      reference
      back()
      { return *(end() - 1); }


      const_reference
      back() const
      { return *(end() - 1); }


      void
      push_back(bool __x)
      {
 if (this->_M_impl._M_finish._M_p != this->_M_impl._M_end_addr())
   *this->_M_impl._M_finish++ = __x;
 else
   _M_insert_aux(end(), __x);
      }


      void
      swap(vector& __x) noexcept
      {

 do { if (std::__is_constant_evaluated() && !bool(_Bit_alloc_traits::propagate_on_container_swap::value || _M_get_Bit_allocator() == __x._M_get_Bit_allocator())) __builtin_unreachable(); } while (false);


 this->_M_impl._M_swap_data(__x._M_impl);
 _Bit_alloc_traits::_S_on_swap(_M_get_Bit_allocator(),
          __x._M_get_Bit_allocator());
      }



      static void
      swap(reference __x, reference __y) noexcept
      {
 bool __tmp = __x;
 __x = __y;
 __y = __tmp;
      }


      iterator

      insert(const_iterator __position, const bool& __x)



      {
 const difference_type __n = __position - begin();
 if (this->_M_impl._M_finish._M_p != this->_M_impl._M_end_addr()
     && __position == end())
   *this->_M_impl._M_finish++ = __x;
 else
   _M_insert_aux(__position._M_const_cast(), __x);
 return begin() + __n;
      }


      __attribute__ ((__deprecated__ ("use '" "insert(position, false)" "' instead")))
      iterator
      insert(const_iterator __position)
      { return this->insert(__position._M_const_cast(), false); }



      template<typename _InputIterator,
        typename = std::_RequireInputIter<_InputIterator>>

 iterator
 insert(const_iterator __position,
        _InputIterator __first, _InputIterator __last)
 {
   difference_type __offset = __position - cbegin();
   _M_insert_range(__position._M_const_cast(),
     __first, __last,
     std::__iterator_category(__first));
   return begin() + __offset;
 }
# 1187 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      iterator
      insert(const_iterator __position, size_type __n, const bool& __x)
      {
 difference_type __offset = __position - cbegin();
 _M_fill_insert(__position._M_const_cast(), __n, __x);
 return begin() + __offset;
      }
# 1202 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      iterator
      insert(const_iterator __p, initializer_list<bool> __l)
      { return this->insert(__p, __l.begin(), __l.end()); }



      void
      pop_back()
      { --this->_M_impl._M_finish; }


      iterator

      erase(const_iterator __position)



      { return _M_erase(__position._M_const_cast()); }


      iterator

      erase(const_iterator __first, const_iterator __last)



      { return _M_erase(__first._M_const_cast(), __last._M_const_cast()); }


      void
      resize(size_type __new_size, bool __x = bool())
      {
 if (__new_size < size())
   _M_erase_at_end(begin() + difference_type(__new_size));
 else
   insert(end(), __new_size - size(), __x);
      }



      void
      shrink_to_fit()
      { _M_shrink_to_fit(); }



      void
      flip() noexcept
      {
 _Bit_type * const __end = this->_M_impl._M_end_addr();
 for (_Bit_type * __p = this->_M_impl._M_start._M_p; __p != __end; ++__p)
   *__p = ~*__p;
      }


      void
      clear() noexcept
      { _M_erase_at_end(begin()); }


      template<typename... _Args>




 void

 emplace_back(_Args&&... __args)
 {
   push_back(bool(__args...));



 }

      template<typename... _Args>

 iterator
 emplace(const_iterator __pos, _Args&&... __args)
 { return insert(__pos, bool(__args...)); }


    protected:


      iterator
      _M_copy_aligned(const_iterator __first, const_iterator __last,
        iterator __result)
      {
 _Bit_type* __q = std::copy(__first._M_p, __last._M_p, __result._M_p);
 return std::copy(const_iterator(__last._M_p, 0), __last,
    iterator(__q, 0));
      }


      void
      _M_initialize(size_type __n)
      {
 if (__n)
   {
     _Bit_pointer __q = this->_M_allocate(__n);
     this->_M_impl._M_end_of_storage = __q + _S_nword(__n);
     iterator __start = iterator(std::__addressof(*__q), 0);
     this->_M_impl._M_start = __start;
     this->_M_impl._M_finish = __start + difference_type(__n);
   }
      }


      void
      _M_initialize_value(bool __x) noexcept
      {
 if (_Bit_type* __p = this->_M_impl._M_start._M_p)
   __fill_bvector_n(__p, this->_M_impl._M_end_addr() - __p, __x);
      }


      void
      _M_reallocate(size_type __n);



      bool
      _M_shrink_to_fit();
# 1347 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      template<typename _InputIterator>

 void
 _M_initialize_range(_InputIterator __first, _InputIterator __last,
       std::input_iterator_tag)
 {
   for (; __first != __last; ++__first)
     push_back(*__first);
 }

      template<typename _ForwardIterator>

 void
 _M_initialize_range(_ForwardIterator __first, _ForwardIterator __last,
       std::forward_iterator_tag)
 {
   const size_type __n = std::distance(__first, __last);
   _M_initialize(__n);
   std::copy(__first, __last, begin());
 }
# 1384 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      void
      _M_fill_assign(size_t __n, bool __x)
      {
 if (__n > size())
   {
     _M_initialize_value(__x);
     insert(end(), __n - size(), __x);
   }
 else
   {
     _M_erase_at_end(begin() + __n);
     _M_initialize_value(__x);
   }
      }

      template<typename _InputIterator>

 void
 _M_assign_aux(_InputIterator __first, _InputIterator __last,
        std::input_iterator_tag)
 {
   iterator __cur = begin();
   for (; __first != __last && __cur != end(); ++__cur, (void)++__first)
     *__cur = *__first;
   if (__first == __last)
     _M_erase_at_end(__cur);
   else
     insert(end(), __first, __last);
 }

      template<typename _ForwardIterator>

 void
 _M_assign_aux(_ForwardIterator __first, _ForwardIterator __last,
        std::forward_iterator_tag)
 {
   const size_type __len = std::distance(__first, __last);
   if (__len < size())
     _M_erase_at_end(std::copy(__first, __last, begin()));
   else
     {
       _ForwardIterator __mid = __first;
       std::advance(__mid, size());
       std::copy(__first, __mid, begin());
       insert(end(), __mid, __last);
     }
 }
# 1451 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
      void
      _M_fill_insert(iterator __position, size_type __n, bool __x);

      template<typename _InputIterator>

 void
 _M_insert_range(iterator __pos, _InputIterator __first,
   _InputIterator __last, std::input_iterator_tag)
 {
   for (; __first != __last; ++__first)
     {
       __pos = insert(__pos, *__first);
       ++__pos;
     }
 }

      template<typename _ForwardIterator>

 void
 _M_insert_range(iterator __position, _ForwardIterator __first,
   _ForwardIterator __last, std::forward_iterator_tag);


      void
      _M_insert_aux(iterator __position, bool __x);


      size_type
      _M_check_len(size_type __n, const char* __s) const
      {
 if (max_size() - size() < __n)
   __throw_length_error((__s));

 const size_type __len = size() + std::max(size(), __n);
 return (__len < size() || __len > max_size()) ? max_size() : __len;
      }


      void
      _M_erase_at_end(iterator __pos)
      { this->_M_impl._M_finish = __pos; }


      iterator
      _M_erase(iterator __pos);


      iterator
      _M_erase(iterator __first, iterator __last);

    protected:






      void data() = delete;



    };





  inline void
  __fill_bvector(_Bit_type* __v, unsigned int __first, unsigned int __last,
   bool __x) noexcept
  {
    const _Bit_type __fmask = ~0ul << __first;
    const _Bit_type __lmask = ~0ul >> (_S_word_bit - __last);
    const _Bit_type __mask = __fmask & __lmask;

    if (__x)
      *__v |= __mask;
    else
      *__v &= ~__mask;
  }


  __attribute__((__nonnull__))

  inline void
  __fill_bvector_n(_Bit_type* __p, size_t __n, bool __x) noexcept
  {
# 1546 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/stl_bvector.h" 3
    __builtin_memset(__p, __x ? ~0 : 0, __n * sizeof(_Bit_type));
  }



  inline void
  __fill_a1(std::_Bit_iterator __first,
     std::_Bit_iterator __last, const bool& __x)
  {
    if (__first._M_p != __last._M_p)
      {
 _Bit_type* __first_p = __first._M_p;
 if (__first._M_offset != 0)
   __fill_bvector(__first_p++, __first._M_offset, _S_word_bit, __x);

 __fill_bvector_n(__first_p, __last._M_p - __first_p, __x);

 if (__last._M_offset != 0)
   __fill_bvector(__last._M_p, 0, __last._M_offset, __x);
      }
    else if (__first._M_offset != __last._M_offset)
      __fill_bvector(__first._M_p, __first._M_offset, __last._M_offset, __x);
  }




  template<typename _Alloc>
    struct hash<std::vector<bool, _Alloc>>
    : public __hash_base<size_t, std::vector<bool, _Alloc>>
    {
      size_t
      operator()(const std::vector<bool, _Alloc>&) const noexcept;
    };



}
# 66 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 2 3




# 1 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/vector.tcc" 1 3
# 59 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/bits/vector.tcc" 3
namespace std __attribute__ ((__visibility__ ("default")))
{



  template<typename _Tp, typename _Alloc>

    void
    vector<_Tp, _Alloc>::
    reserve(size_type __n)
    {
      if (__n > this->max_size())
 __throw_length_error(("vector::reserve"));
      if (this->capacity() < __n)
 {
   const size_type __old_size = size();
   pointer __tmp;

   if (_S_use_relocate())
     {
       __tmp = this->_M_allocate(__n);
       _S_relocate(this->_M_impl._M_start, this->_M_impl._M_finish,
     __tmp, _M_get_Tp_allocator());
     }
   else

     {
       __tmp = _M_allocate_and_copy(__n,
  std::__make_move_if_noexcept_iterator(this->_M_impl._M_start),
  std::__make_move_if_noexcept_iterator(this->_M_impl._M_finish));
       std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
       _M_get_Tp_allocator());
     }
                                ;
   _M_deallocate(this->_M_impl._M_start,
   this->_M_impl._M_end_of_storage
   - this->_M_impl._M_start);
   this->_M_impl._M_start = __tmp;
   this->_M_impl._M_finish = __tmp + __old_size;
   this->_M_impl._M_end_of_storage = this->_M_impl._M_start + __n;
 }
    }


  template<typename _Tp, typename _Alloc>
    template<typename... _Args>




      void

      vector<_Tp, _Alloc>::
      emplace_back(_Args&&... __args)
      {
 if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
   {
                                   ;
     _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
         std::forward<_Args>(__args)...);
     ++this->_M_impl._M_finish;
                                   ;
   }
 else
   _M_realloc_insert(end(), std::forward<_Args>(__args)...);



      }


  template<typename _Tp, typename _Alloc>

    typename vector<_Tp, _Alloc>::iterator
    vector<_Tp, _Alloc>::

    insert(const_iterator __position, const value_type& __x)



    {
      const size_type __n = __position - begin();
      if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
 if (__position == end())
   {
                                   ;
     _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
         __x);
     ++this->_M_impl._M_finish;
                                   ;
   }
 else
   {

     const auto __pos = begin() + (__position - cbegin());


     _Temporary_value __x_copy(this, __x);
     _M_insert_aux(__pos, std::move(__x_copy._M_val()));



   }
      else

 _M_realloc_insert(begin() + (__position - cbegin()), __x);




      return iterator(this->_M_impl._M_start + __n);
    }

  template<typename _Tp, typename _Alloc>

    typename vector<_Tp, _Alloc>::iterator
    vector<_Tp, _Alloc>::
    _M_erase(iterator __position)
    {
      if (__position + 1 != end())
 std::move(__position + 1, end(), __position);
      --this->_M_impl._M_finish;
      _Alloc_traits::destroy(this->_M_impl, this->_M_impl._M_finish);
                                      ;
      return __position;
    }

  template<typename _Tp, typename _Alloc>

    typename vector<_Tp, _Alloc>::iterator
    vector<_Tp, _Alloc>::
    _M_erase(iterator __first, iterator __last)
    {
      if (__first != __last)
 {
   if (__last != end())
     std::move(__last, end(), __first);
   _M_erase_at_end(__first.base() + (end() - __last));
 }
      return __first;
    }

  template<typename _Tp, typename _Alloc>

    vector<_Tp, _Alloc>&
    vector<_Tp, _Alloc>::
    operator=(const vector<_Tp, _Alloc>& __x)
    {
      if (std::__addressof(__x) != this)
 {
                                ;

   if (_Alloc_traits::_S_propagate_on_copy_assign())
     {
       if (!_Alloc_traits::_S_always_equal()
           && _M_get_Tp_allocator() != __x._M_get_Tp_allocator())
         {

    this->clear();
    _M_deallocate(this->_M_impl._M_start,
    this->_M_impl._M_end_of_storage
    - this->_M_impl._M_start);
    this->_M_impl._M_start = nullptr;
    this->_M_impl._M_finish = nullptr;
    this->_M_impl._M_end_of_storage = nullptr;
  }
       std::__alloc_on_copy(_M_get_Tp_allocator(),
       __x._M_get_Tp_allocator());
     }

   const size_type __xlen = __x.size();
   if (__xlen > capacity())
     {
       pointer __tmp = _M_allocate_and_copy(__xlen, __x.begin(),
         __x.end());
       std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
       _M_get_Tp_allocator());
       _M_deallocate(this->_M_impl._M_start,
       this->_M_impl._M_end_of_storage
       - this->_M_impl._M_start);
       this->_M_impl._M_start = __tmp;
       this->_M_impl._M_end_of_storage = this->_M_impl._M_start + __xlen;
     }
   else if (size() >= __xlen)
     {
       std::_Destroy(std::copy(__x.begin(), __x.end(), begin()),
       end(), _M_get_Tp_allocator());
     }
   else
     {
       std::copy(__x._M_impl._M_start, __x._M_impl._M_start + size(),
   this->_M_impl._M_start);
       std::__uninitialized_copy_a(__x._M_impl._M_start + size(),
       __x._M_impl._M_finish,
       this->_M_impl._M_finish,
       _M_get_Tp_allocator());
     }
   this->_M_impl._M_finish = this->_M_impl._M_start + __xlen;
 }
      return *this;
    }

  template<typename _Tp, typename _Alloc>

    void
    vector<_Tp, _Alloc>::
    _M_fill_assign(size_t __n, const value_type& __val)
    {
      if (__n > capacity())
 {
   vector __tmp(__n, __val, _M_get_Tp_allocator());
   __tmp._M_impl._M_swap_data(this->_M_impl);
 }
      else if (__n > size())
 {
   std::fill(begin(), end(), __val);
   const size_type __add = __n - size();
                                     ;
   this->_M_impl._M_finish =
     std::__uninitialized_fill_n_a(this->_M_impl._M_finish,
       __add, __val, _M_get_Tp_allocator());
                                     ;
 }
      else
        _M_erase_at_end(std::fill_n(this->_M_impl._M_start, __n, __val));
    }

  template<typename _Tp, typename _Alloc>
    template<typename _InputIterator>

      void
      vector<_Tp, _Alloc>::
      _M_assign_aux(_InputIterator __first, _InputIterator __last,
      std::input_iterator_tag)
      {
 pointer __cur(this->_M_impl._M_start);
 for (; __first != __last && __cur != this->_M_impl._M_finish;
      ++__cur, (void)++__first)
   *__cur = *__first;
 if (__first == __last)
   _M_erase_at_end(__cur);
 else
   _M_range_insert(end(), __first, __last,
     std::__iterator_category(__first));
      }

  template<typename _Tp, typename _Alloc>
    template<typename _ForwardIterator>

      void
      vector<_Tp, _Alloc>::
      _M_assign_aux(_ForwardIterator __first, _ForwardIterator __last,
      std::forward_iterator_tag)
      {
 const size_type __len = std::distance(__first, __last);

 if (__len > capacity())
   {
     _S_check_init_len(__len, _M_get_Tp_allocator());
     pointer __tmp(_M_allocate_and_copy(__len, __first, __last));
     std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
     _M_get_Tp_allocator());
                                  ;
     _M_deallocate(this->_M_impl._M_start,
     this->_M_impl._M_end_of_storage
     - this->_M_impl._M_start);
     this->_M_impl._M_start = __tmp;
     this->_M_impl._M_finish = this->_M_impl._M_start + __len;
     this->_M_impl._M_end_of_storage = this->_M_impl._M_finish;
   }
 else if (size() >= __len)
   _M_erase_at_end(std::copy(__first, __last, this->_M_impl._M_start));
 else
   {
     _ForwardIterator __mid = __first;
     std::advance(__mid, size());
     std::copy(__first, __mid, this->_M_impl._M_start);
     const size_type __attribute__((__unused__)) __n = __len - size();
                                     ;
     this->_M_impl._M_finish =
       std::__uninitialized_copy_a(__mid, __last,
       this->_M_impl._M_finish,
       _M_get_Tp_allocator());
                                     ;
   }
      }


  template<typename _Tp, typename _Alloc>

    auto
    vector<_Tp, _Alloc>::
    _M_insert_rval(const_iterator __position, value_type&& __v) -> iterator
    {
      const auto __n = __position - cbegin();
      if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
 if (__position == cend())
   {
                                   ;
     _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
         std::move(__v));
     ++this->_M_impl._M_finish;
                                   ;
   }
 else
   _M_insert_aux(begin() + __n, std::move(__v));
      else
 _M_realloc_insert(begin() + __n, std::move(__v));

      return iterator(this->_M_impl._M_start + __n);
    }

  template<typename _Tp, typename _Alloc>
    template<typename... _Args>

      auto
      vector<_Tp, _Alloc>::
      _M_emplace_aux(const_iterator __position, _Args&&... __args)
      -> iterator
      {
 const auto __n = __position - cbegin();
 if (this->_M_impl._M_finish != this->_M_impl._M_end_of_storage)
   if (__position == cend())
     {
                                     ;
       _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
           std::forward<_Args>(__args)...);
       ++this->_M_impl._M_finish;
                                     ;
     }
   else
     {



       _Temporary_value __tmp(this, std::forward<_Args>(__args)...);
       _M_insert_aux(begin() + __n, std::move(__tmp._M_val()));
     }
 else
   _M_realloc_insert(begin() + __n, std::forward<_Args>(__args)...);

 return iterator(this->_M_impl._M_start + __n);
      }

  template<typename _Tp, typename _Alloc>
    template<typename _Arg>

      void
      vector<_Tp, _Alloc>::
      _M_insert_aux(iterator __position, _Arg&& __arg)






    {
                                    ;
      _Alloc_traits::construct(this->_M_impl, this->_M_impl._M_finish,
          std::move(*(this->_M_impl._M_finish - 1)));
      ++this->_M_impl._M_finish;
                                    ;



      std::move_backward(__position.base(), this->_M_impl._M_finish - 2, this->_M_impl._M_finish - 1);





      *__position = std::forward<_Arg>(__arg);

    }


  template<typename _Tp, typename _Alloc>
    template<typename... _Args>

      void
      vector<_Tp, _Alloc>::
      _M_realloc_insert(iterator __position, _Args&&... __args)






    {
      const size_type __len =
 _M_check_len(size_type(1), "vector::_M_realloc_insert");
      pointer __old_start = this->_M_impl._M_start;
      pointer __old_finish = this->_M_impl._M_finish;
      const size_type __elems_before = __position - begin();
      pointer __new_start(this->_M_allocate(__len));
      pointer __new_finish(__new_start);
      try
 {





   _Alloc_traits::construct(this->_M_impl,
       __new_start + __elems_before,

       std::forward<_Args>(__args)...);



   __new_finish = pointer();


   if (_S_use_relocate())
     {
       __new_finish = _S_relocate(__old_start, __position.base(),
      __new_start, _M_get_Tp_allocator());

       ++__new_finish;

       __new_finish = _S_relocate(__position.base(), __old_finish,
      __new_finish, _M_get_Tp_allocator());
     }
   else

     {
       __new_finish
  = std::__uninitialized_move_if_noexcept_a
  (__old_start, __position.base(),
   __new_start, _M_get_Tp_allocator());

       ++__new_finish;

       __new_finish
  = std::__uninitialized_move_if_noexcept_a
  (__position.base(), __old_finish,
   __new_finish, _M_get_Tp_allocator());
     }
 }
      catch(...)
 {
   if (!__new_finish)
     _Alloc_traits::destroy(this->_M_impl,
       __new_start + __elems_before);
   else
     std::_Destroy(__new_start, __new_finish, _M_get_Tp_allocator());
   _M_deallocate(__new_start, __len);
   throw;
 }

      if (!_S_use_relocate())

 std::_Destroy(__old_start, __old_finish, _M_get_Tp_allocator());
                                   ;
      _M_deallocate(__old_start,
      this->_M_impl._M_end_of_storage - __old_start);
      this->_M_impl._M_start = __new_start;
      this->_M_impl._M_finish = __new_finish;
      this->_M_impl._M_end_of_storage = __new_start + __len;
    }

  template<typename _Tp, typename _Alloc>

    void
    vector<_Tp, _Alloc>::
    _M_fill_insert(iterator __position, size_type __n, const value_type& __x)
    {
      if (__n != 0)
 {
   if (size_type(this->_M_impl._M_end_of_storage
   - this->_M_impl._M_finish) >= __n)
     {



       _Temporary_value __tmp(this, __x);
       value_type& __x_copy = __tmp._M_val();

       const size_type __elems_after = end() - __position;
       pointer __old_finish(this->_M_impl._M_finish);
       if (__elems_after > __n)
  {
                                    ;
    std::__uninitialized_move_a(this->_M_impl._M_finish - __n,
           this->_M_impl._M_finish,
           this->_M_impl._M_finish,
           _M_get_Tp_allocator());
    this->_M_impl._M_finish += __n;
                                    ;
    std::move_backward(__position.base(), __old_finish - __n, __old_finish);

    std::fill(__position.base(), __position.base() + __n,
       __x_copy);
  }
       else
  {
                                    ;
    this->_M_impl._M_finish =
      std::__uninitialized_fill_n_a(this->_M_impl._M_finish,
        __n - __elems_after,
        __x_copy,
        _M_get_Tp_allocator());
                                                    ;
    std::__uninitialized_move_a(__position.base(), __old_finish,
           this->_M_impl._M_finish,
           _M_get_Tp_allocator());
    this->_M_impl._M_finish += __elems_after;
                                              ;
    std::fill(__position.base(), __old_finish, __x_copy);
  }
     }
   else
     {
       const size_type __len =
  _M_check_len(__n, "vector::_M_fill_insert");
       const size_type __elems_before = __position - begin();
       pointer __new_start(this->_M_allocate(__len));
       pointer __new_finish(__new_start);
       try
  {

    std::__uninitialized_fill_n_a(__new_start + __elems_before,
      __n, __x,
      _M_get_Tp_allocator());
    __new_finish = pointer();

    __new_finish
      = std::__uninitialized_move_if_noexcept_a
      (this->_M_impl._M_start, __position.base(),
       __new_start, _M_get_Tp_allocator());

    __new_finish += __n;

    __new_finish
      = std::__uninitialized_move_if_noexcept_a
      (__position.base(), this->_M_impl._M_finish,
       __new_finish, _M_get_Tp_allocator());
  }
       catch(...)
  {
    if (!__new_finish)
      std::_Destroy(__new_start + __elems_before,
      __new_start + __elems_before + __n,
      _M_get_Tp_allocator());
    else
      std::_Destroy(__new_start, __new_finish,
      _M_get_Tp_allocator());
    _M_deallocate(__new_start, __len);
    throw;
  }
       std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
       _M_get_Tp_allocator());
                                    ;
       _M_deallocate(this->_M_impl._M_start,
       this->_M_impl._M_end_of_storage
       - this->_M_impl._M_start);
       this->_M_impl._M_start = __new_start;
       this->_M_impl._M_finish = __new_finish;
       this->_M_impl._M_end_of_storage = __new_start + __len;
     }
 }
    }


  template<typename _Tp, typename _Alloc>

    void
    vector<_Tp, _Alloc>::
    _M_default_append(size_type __n)
    {
      if (__n != 0)
 {
   const size_type __size = size();
   size_type __navail = size_type(this->_M_impl._M_end_of_storage
      - this->_M_impl._M_finish);

   if (__size > max_size() || __navail > max_size() - __size)
     __builtin_unreachable();

   if (__navail >= __n)
     {
                                       ;
       this->_M_impl._M_finish =
  std::__uninitialized_default_n_a(this->_M_impl._M_finish,
       __n, _M_get_Tp_allocator());
                                       ;
     }
   else
     {
       const size_type __len =
  _M_check_len(__n, "vector::_M_default_append");
       pointer __new_start(this->_M_allocate(__len));
       if (_S_use_relocate())
  {
    try
      {
        std::__uninitialized_default_n_a(__new_start + __size,
         __n, _M_get_Tp_allocator());
      }
    catch(...)
      {
        _M_deallocate(__new_start, __len);
        throw;
      }
    _S_relocate(this->_M_impl._M_start, this->_M_impl._M_finish,
         __new_start, _M_get_Tp_allocator());
  }
       else
  {
    pointer __destroy_from = pointer();
    try
      {
        std::__uninitialized_default_n_a(__new_start + __size,
         __n, _M_get_Tp_allocator());
        __destroy_from = __new_start + __size;
        std::__uninitialized_move_if_noexcept_a(
         this->_M_impl._M_start, this->_M_impl._M_finish,
         __new_start, _M_get_Tp_allocator());
      }
    catch(...)
      {
        if (__destroy_from)
   std::_Destroy(__destroy_from, __destroy_from + __n,
          _M_get_Tp_allocator());
        _M_deallocate(__new_start, __len);
        throw;
      }
    std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
    _M_get_Tp_allocator());
  }
                                    ;
       _M_deallocate(this->_M_impl._M_start,
       this->_M_impl._M_end_of_storage
       - this->_M_impl._M_start);
       this->_M_impl._M_start = __new_start;
       this->_M_impl._M_finish = __new_start + __size + __n;
       this->_M_impl._M_end_of_storage = __new_start + __len;
     }
 }
    }

  template<typename _Tp, typename _Alloc>

    bool
    vector<_Tp, _Alloc>::
    _M_shrink_to_fit()
    {
      if (capacity() == size())
 return false;
                                   ;
      return std::__shrink_to_fit_aux<vector>::_S_do_it(*this);
    }


  template<typename _Tp, typename _Alloc>
    template<typename _InputIterator>

      void
      vector<_Tp, _Alloc>::
      _M_range_insert(iterator __pos, _InputIterator __first,
        _InputIterator __last, std::input_iterator_tag)
      {
 if (__pos == end())
   {
     for (; __first != __last; ++__first)
       insert(end(), *__first);
   }
 else if (__first != __last)
   {
     vector __tmp(__first, __last, _M_get_Tp_allocator());
     insert(__pos,
     std::make_move_iterator(__tmp.begin()),
     std::make_move_iterator(__tmp.end()));
   }
      }

  template<typename _Tp, typename _Alloc>
    template<typename _ForwardIterator>

      void
      vector<_Tp, _Alloc>::
      _M_range_insert(iterator __position, _ForwardIterator __first,
        _ForwardIterator __last, std::forward_iterator_tag)
      {
 if (__first != __last)
   {
     const size_type __n = std::distance(__first, __last);
     if (size_type(this->_M_impl._M_end_of_storage
     - this->_M_impl._M_finish) >= __n)
       {
  const size_type __elems_after = end() - __position;
  pointer __old_finish(this->_M_impl._M_finish);
  if (__elems_after > __n)
    {
                                      ;
      std::__uninitialized_move_a(this->_M_impl._M_finish - __n,
      this->_M_impl._M_finish,
      this->_M_impl._M_finish,
      _M_get_Tp_allocator());
      this->_M_impl._M_finish += __n;
                                      ;
      std::move_backward(__position.base(), __old_finish - __n, __old_finish);

      std::copy(__first, __last, __position);
    }
  else
    {
      _ForwardIterator __mid = __first;
      std::advance(__mid, __elems_after);
                                      ;
      std::__uninitialized_copy_a(__mid, __last,
      this->_M_impl._M_finish,
      _M_get_Tp_allocator());
      this->_M_impl._M_finish += __n - __elems_after;
                                                      ;
      std::__uninitialized_move_a(__position.base(),
      __old_finish,
      this->_M_impl._M_finish,
      _M_get_Tp_allocator());
      this->_M_impl._M_finish += __elems_after;
                                                ;
      std::copy(__first, __mid, __position);
    }
       }
     else
       {
  const size_type __len =
    _M_check_len(__n, "vector::_M_range_insert");
  pointer __new_start(this->_M_allocate(__len));
  pointer __new_finish(__new_start);
  try
    {
      __new_finish
        = std::__uninitialized_move_if_noexcept_a
        (this->_M_impl._M_start, __position.base(),
         __new_start, _M_get_Tp_allocator());
      __new_finish
        = std::__uninitialized_copy_a(__first, __last,
          __new_finish,
          _M_get_Tp_allocator());
      __new_finish
        = std::__uninitialized_move_if_noexcept_a
        (__position.base(), this->_M_impl._M_finish,
         __new_finish, _M_get_Tp_allocator());
    }
  catch(...)
    {
      std::_Destroy(__new_start, __new_finish,
      _M_get_Tp_allocator());
      _M_deallocate(__new_start, __len);
      throw;
    }
  std::_Destroy(this->_M_impl._M_start, this->_M_impl._M_finish,
         _M_get_Tp_allocator());
                               ;
  _M_deallocate(this->_M_impl._M_start,
         this->_M_impl._M_end_of_storage
         - this->_M_impl._M_start);
  this->_M_impl._M_start = __new_start;
  this->_M_impl._M_finish = __new_finish;
  this->_M_impl._M_end_of_storage = __new_start + __len;
       }
   }
      }



  template<typename _Alloc>

    void
    vector<bool, _Alloc>::
    _M_reallocate(size_type __n)
    {
      _Bit_pointer __q = this->_M_allocate(__n);
      iterator __start(std::__addressof(*__q), 0);
      iterator __finish(_M_copy_aligned(begin(), end(), __start));
      this->_M_deallocate();
      this->_M_impl._M_start = __start;
      this->_M_impl._M_finish = __finish;
      this->_M_impl._M_end_of_storage = __q + _S_nword(__n);
    }

  template<typename _Alloc>

    void
    vector<bool, _Alloc>::
    _M_fill_insert(iterator __position, size_type __n, bool __x)
    {
      if (__n == 0)
 return;
      if (capacity() - size() >= __n)
 {
   std::copy_backward(__position, end(),
        this->_M_impl._M_finish + difference_type(__n));
   std::fill(__position, __position + difference_type(__n), __x);
   this->_M_impl._M_finish += difference_type(__n);
 }
      else
 {
   const size_type __len =
     _M_check_len(__n, "vector<bool>::_M_fill_insert");
   _Bit_pointer __q = this->_M_allocate(__len);
   iterator __start(std::__addressof(*__q), 0);
   iterator __i = _M_copy_aligned(begin(), __position, __start);
   std::fill(__i, __i + difference_type(__n), __x);
   iterator __finish = std::copy(__position, end(),
     __i + difference_type(__n));
   this->_M_deallocate();
   this->_M_impl._M_end_of_storage = __q + _S_nword(__len);
   this->_M_impl._M_start = __start;
   this->_M_impl._M_finish = __finish;
 }
    }

  template<typename _Alloc>
    template<typename _ForwardIterator>

      void
      vector<bool, _Alloc>::
      _M_insert_range(iterator __position, _ForwardIterator __first,
        _ForwardIterator __last, std::forward_iterator_tag)
      {
 if (__first != __last)
   {
     size_type __n = std::distance(__first, __last);
     if (capacity() - size() >= __n)
       {
  std::copy_backward(__position, end(),
       this->_M_impl._M_finish
       + difference_type(__n));
  std::copy(__first, __last, __position);
  this->_M_impl._M_finish += difference_type(__n);
       }
     else
       {
  const size_type __len =
    _M_check_len(__n, "vector<bool>::_M_insert_range");
  _Bit_pointer __q = this->_M_allocate(__len);
  iterator __start(std::__addressof(*__q), 0);
  iterator __i = _M_copy_aligned(begin(), __position, __start);
  __i = std::copy(__first, __last, __i);
  iterator __finish = std::copy(__position, end(), __i);
  this->_M_deallocate();
  this->_M_impl._M_end_of_storage = __q + _S_nword(__len);
  this->_M_impl._M_start = __start;
  this->_M_impl._M_finish = __finish;
       }
   }
      }

  template<typename _Alloc>

    void
    vector<bool, _Alloc>::
    _M_insert_aux(iterator __position, bool __x)
    {
      if (this->_M_impl._M_finish._M_p != this->_M_impl._M_end_addr())
 {
   std::copy_backward(__position, this->_M_impl._M_finish,
        this->_M_impl._M_finish + 1);
   *__position = __x;
   ++this->_M_impl._M_finish;
 }
      else
 {
   const size_type __len =
     _M_check_len(size_type(1), "vector<bool>::_M_insert_aux");
   _Bit_pointer __q = this->_M_allocate(__len);
   iterator __start(std::__addressof(*__q), 0);
   iterator __i = _M_copy_aligned(begin(), __position, __start);
   *__i++ = __x;
   iterator __finish = std::copy(__position, end(), __i);
   this->_M_deallocate();
   this->_M_impl._M_end_of_storage = __q + _S_nword(__len);
   this->_M_impl._M_start = __start;
   this->_M_impl._M_finish = __finish;
 }
    }

  template<typename _Alloc>

    typename vector<bool, _Alloc>::iterator
    vector<bool, _Alloc>::
    _M_erase(iterator __position)
    {
      if (__position + 1 != end())
        std::copy(__position + 1, end(), __position);
      --this->_M_impl._M_finish;
      return __position;
    }

  template<typename _Alloc>

    typename vector<bool, _Alloc>::iterator
    vector<bool, _Alloc>::
    _M_erase(iterator __first, iterator __last)
    {
      if (__first != __last)
 _M_erase_at_end(std::copy(__last, end(), __first));
      return __first;
    }


  template<typename _Alloc>

    bool
    vector<bool, _Alloc>::
    _M_shrink_to_fit()
    {
      if (capacity() - size() < int(_S_word_bit))
 return false;
      try
 {
   if (size_type __n = size())
     _M_reallocate(__n);
   else
     {
       this->_M_deallocate();
       this->_M_impl._M_reset();
     }
   return true;
 }
      catch(...)
 { return false; }
    }




}



namespace std __attribute__ ((__visibility__ ("default")))
{


  template<typename _Alloc>
    size_t
    hash<std::vector<bool, _Alloc>>::
    operator()(const std::vector<bool, _Alloc>& __b) const noexcept
    {
      size_t __hash = 0;
      const size_t __words = __b.size() / _S_word_bit;
      if (__words)
 {
   const size_t __clength = __words * sizeof(_Bit_type);
   __hash = std::_Hash_impl::hash(__b._M_impl._M_start._M_p, __clength);
 }

      const size_t __extrabits = __b.size() % _S_word_bit;
      if (__extrabits)
 {
   _Bit_type __hiword = *__b._M_impl._M_finish._M_p;
   __hiword &= ~((~static_cast<_Bit_type>(0)) << __extrabits);

   const size_t __clength
     = (__extrabits + 8 - 1) / 8;
   if (__words)
     __hash = std::_Hash_impl::hash(&__hiword, __clength, __hash);
   else
     __hash = std::_Hash_impl::hash(&__hiword, __clength);
 }

      return __hash;
    }


}
# 71 "/usr/bin/../lib/gcc/x86_64-linux-gnu/12/../../../../include/c++/12/vector" 2 3
# 4 "float16.cpp" 2

int main()
{
  const size_t count = 4;

  std::vector<_Float16> f16(count);
  std::vector<float> f32(count);

  for(size_t i = 0 ; i < count; ++i)
    f16[i] = static_cast<_Float16>(0.123) * static_cast<_Float16>(i);

  std::copy_n(f16.begin(), count, f32.begin());

  for(size_t i = 0; i < count; ++i)
    {
      std::cout << "loop f16=" << static_cast<float>(f16[i]) << " f32=" << f32[i] << std::endl;
    }

  _Float16 one_f16 = 0.123;
  float one_f32 = one_f16;
  std::cout << "one f32=" << one_f32 << std::endl;
  return 0;
}