include/numeric - platform/external/libcxx - Gitiles

 // -*- C++ -*-
 //===---------------------------- numeric ---------------------------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is dual licensed under the MIT and the University of Illinois Open
 // Source Licenses. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//

 #ifndef _LIBCPP_NUMERIC
 #define _LIBCPP_NUMERIC

 /*
     numeric synopsis

 namespace std
 {

 template <class InputIterator, class T>
     T
     accumulate(InputIterator first, InputIterator last, T init);

 template <class InputIterator, class T, class BinaryOperation>
     T
     accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);

 template<class InputIterator>
     typename iterator_traits<InputIterator>::value_type
     reduce(InputIterator first, InputIterator last);  // C++17

 template<class InputIterator, class T>
     T
     reduce(InputIterator first, InputIterator last, T init);  // C++17

 template<class InputIterator, class T, class BinaryOperation>
     T
     reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);  // C++17

 template <class InputIterator1, class InputIterator2, class T>
     T
     inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);

 template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
     T
     inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
                   T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);


 template<class InputIterator1, class InputIterator2, class T>
     T
     transform_reduce(InputIterator1 first1, InputIterator1 last1,
                      InputIterator2 first2, T init);  // C++17

 template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
     T
     transform_reduce(InputIterator1 first1, InputIterator1 last1,
                      InputIterator2 first2, T init,
                      BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);  // C++17

 template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
     T
     transform_reduce(InputIterator first, InputIterator last, T init,
                      BinaryOperation binary_op, UnaryOperation unary_op);  // C++17

 template <class InputIterator, class OutputIterator>
     OutputIterator
     partial_sum(InputIterator first, InputIterator last, OutputIterator result);

 template <class InputIterator, class OutputIterator, class BinaryOperation>
     OutputIterator
     partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);

 template<class InputIterator, class OutputIterator, class T>
     OutputIterator
     exclusive_scan(InputIterator first, InputIterator last,
                    OutputIterator result, T init); // C++17

 template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
     OutputIterator
     exclusive_scan(InputIterator first, InputIterator last,
                    OutputIterator result, T init, BinaryOperation binary_op); // C++17

 template<class InputIterator, class OutputIterator>
     OutputIterator
     inclusive_scan(InputIterator first, InputIterator last, OutputIterator result);  // C++17

 template<class InputIterator, class OutputIterator, class BinaryOperation>
     OutputIterator
     inclusive_scan(InputIterator first, InputIterator last,
                    OutputIterator result, BinaryOperation binary_op);  // C++17

 template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
     OutputIterator
     inclusive_scan(InputIterator first, InputIterator last,
                    OutputIterator result, BinaryOperation binary_op, T init);  // C++17

 template<class InputIterator, class OutputIterator, class T,
          class BinaryOperation, class UnaryOperation>
     OutputIterator
     transform_exclusive_scan(InputIterator first, InputIterator last,
                              OutputIterator result, T init,
                              BinaryOperation binary_op, UnaryOperation unary_op);  // C++17

 template<class InputIterator, class OutputIterator,
          class BinaryOperation, class UnaryOperation>
     OutputIterator
     transform_inclusive_scan(InputIterator first, InputIterator last,
                              OutputIterator result,
                              BinaryOperation binary_op, UnaryOperation unary_op);  // C++17

 template<class InputIterator, class OutputIterator,
          class BinaryOperation, class UnaryOperation, class T>
     OutputIterator
     transform_inclusive_scan(InputIterator first, InputIterator last,
                              OutputIterator result,
                              BinaryOperation binary_op, UnaryOperation unary_op,
                              T init);  // C++17

 template <class InputIterator, class OutputIterator>
     OutputIterator
     adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);

 template <class InputIterator, class OutputIterator, class BinaryOperation>
     OutputIterator
     adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);

 template <class ForwardIterator, class T>
     void iota(ForwardIterator first, ForwardIterator last, T value);

 template <class M, class N>
     constexpr common_type_t<M,N> gcd(M m, N n);    // C++17

 template <class M, class N>
     constexpr common_type_t<M,N> lcm(M m, N n);    // C++17

 }  // std

 */

 #include <__config>
 #include <iterator>
 #include <limits> // for numeric_limits
 #include <functional>
 #include <version>

 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #pragma GCC system_header
 #endif

 _LIBCPP_PUSH_MACROS
 #include <__undef_macros>

 _LIBCPP_BEGIN_NAMESPACE_STD

 template <class _InputIterator, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
 {
     for (; __first != __last; ++__first)
         __init = __init + *__first;
     return __init;
 }

 template <class _InputIterator, class _Tp, class _BinaryOperation>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
 {
     for (; __first != __last; ++__first)
         __init = __binary_op(__init, *__first);
     return __init;
 }

 #if _LIBCPP_STD_VER > 14
 template <class _InputIterator, class _Tp, class _BinaryOp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
 {
     for (; __first != __last; ++__first)
         __init = __b(__init, *__first);
     return __init;
 }

 template <class _InputIterator, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
 {
     return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
 }

 template <class _InputIterator>
 inline _LIBCPP_INLINE_VISIBILITY
 typename iterator_traits<_InputIterator>::value_type
 reduce(_InputIterator __first, _InputIterator __last)
 {
     return _VSTD::reduce(__first, __last,
        typename iterator_traits<_InputIterator>::value_type{});
 }
 #endif

 template <class _InputIterator1, class _InputIterator2, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
 {
     for (; __first1 != __last1; ++__first1, (void) ++__first2)
         __init = __init + *__first1 * *__first2;
     return __init;
 }

 template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
               _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
 {
     for (; __first1 != __last1; ++__first1, (void) ++__first2)
         __init = __binary_op1(__init, __binary_op2(*__first1, *__first2));
     return __init;
 }

 #if _LIBCPP_STD_VER > 14
 template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 transform_reduce(_InputIterator __first, _InputIterator __last,
            _Tp __init,  _BinaryOp __b, _UnaryOp __u)
 {
     for (; __first != __last; ++__first)
         __init = __b(__init, __u(*__first));
     return __init;
 }

 template <class _InputIterator1, class _InputIterator2,
           class _Tp, class _BinaryOp1, class _BinaryOp2>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
                  _InputIterator2 __first2, _Tp __init,  _BinaryOp1 __b1, _BinaryOp2 __b2)
 {
     for (; __first1 != __last1; ++__first1, (void) ++__first2)
         __init = __b1(__init, __b2(*__first1, *__first2));
     return __init;
 }

 template <class _InputIterator1, class _InputIterator2, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _Tp
 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
                  _InputIterator2 __first2, _Tp __init)
 {
     return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
                                    _VSTD::plus<>(), _VSTD::multiplies<>());
 }
 #endif

 template <class _InputIterator, class _OutputIterator>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
 {
     if (__first != __last)
     {
         typename iterator_traits<_InputIterator>::value_type __t(*__first);
         *__result = __t;
         for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
         {
             __t = __t + *__first;
             *__result = __t;
         }
     }
     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
               _BinaryOperation __binary_op)
 {
     if (__first != __last)
     {
         typename iterator_traits<_InputIterator>::value_type __t(*__first);
         *__result = __t;
         for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
         {
             __t = __binary_op(__t, *__first);
             *__result = __t;
         }
     }
     return __result;
 }

 #if _LIBCPP_STD_VER > 14
 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 exclusive_scan(_InputIterator __first, _InputIterator __last,
                _OutputIterator __result, _Tp __init, _BinaryOp __b)
 {
     if (__first != __last)
     {
         _Tp __saved = __init;
         do
         {
             __init = __b(__init, *__first);
             *__result = __saved;
             __saved = __init;
             ++__result;
         } while (++__first != __last);
     }
     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 exclusive_scan(_InputIterator __first, _InputIterator __last,
                _OutputIterator __result, _Tp __init)
 {
     return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
 }

 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
                                _OutputIterator __result, _BinaryOp __b,  _Tp __init)
 {
     for (; __first != __last; ++__first, (void) ++__result) {
         __init = __b(__init, *__first);
         *__result = __init;
         }
     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _BinaryOp>
 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
                                _OutputIterator __result, _BinaryOp __b)
 {
     if (__first != __last) {
         typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
         *__result++ = __init;
         if (++__first != __last)
             return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
         }

     return __result;
 }

 template <class _InputIterator, class _OutputIterator>
 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
                                _OutputIterator __result)
 {
     return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
 }

 template <class _InputIterator, class _OutputIterator, class _Tp,
           class _BinaryOp, class _UnaryOp>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
                            _OutputIterator __result, _Tp __init,
                            _BinaryOp __b, _UnaryOp __u)
 {
     if (__first != __last)
     {
         _Tp __saved = __init;
         do
         {
             __init = __b(__init, __u(*__first));
             *__result = __saved;
             __saved = __init;
             ++__result;
         } while (++__first != __last);
     }
     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
 _OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
                            _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
 {
     for (; __first != __last; ++__first, (void) ++__result) {
         __init = __b(__init, __u(*__first));
         *__result = __init;
         }

     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
 _OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
                                _OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
 {
     if (__first != __last) {
         typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
         *__result++ = __init;
         if (++__first != __last)
             return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
         }

     return __result;
 }
 #endif

 template <class _InputIterator, class _OutputIterator>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
 {
     if (__first != __last)
     {
         typename iterator_traits<_InputIterator>::value_type __t1(*__first);
         *__result = __t1;
         for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
         {
             typename iterator_traits<_InputIterator>::value_type __t2(*__first);
             *__result = __t2 - __t1;
             __t1 = _VSTD::move(__t2);
         }
     }
     return __result;
 }

 template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
 inline _LIBCPP_INLINE_VISIBILITY
 _OutputIterator
 adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
                       _BinaryOperation __binary_op)
 {
     if (__first != __last)
     {
         typename iterator_traits<_InputIterator>::value_type __t1(*__first);
         *__result = __t1;
         for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
         {
             typename iterator_traits<_InputIterator>::value_type __t2(*__first);
             *__result = __binary_op(__t2, __t1);
             __t1 = _VSTD::move(__t2);
         }
     }
     return __result;
 }

 template <class _ForwardIterator, class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY
 void
 iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
 {
     for (; __first != __last; ++__first, (void) ++__value_)
         *__first = __value_;
 }


 #if _LIBCPP_STD_VER > 14
 template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __abs;

 template <typename _Result, typename _Source>
 struct __abs<_Result, _Source, true> {
     _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
     _Result operator()(_Source __t) const noexcept
     {
     if (__t >= 0) return __t;
     if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
     return -__t;
     }
 };

 template <typename _Result, typename _Source>
 struct __abs<_Result, _Source, false> {
     _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
     _Result operator()(_Source __t) const noexcept { return __t; }
 };


 template<class _Tp>
 _LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
 _Tp __gcd(_Tp __m, _Tp __n)
 {
     static_assert((!is_signed<_Tp>::value), "");
     return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
 }


 template<class _Tp, class _Up>
 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
 common_type_t<_Tp,_Up>
 gcd(_Tp __m, _Up __n)
 {
     static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
     static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
     static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
     using _Rp = common_type_t<_Tp,_Up>;
     using _Wp = make_unsigned_t<_Rp>;
     return static_cast<_Rp>(_VSTD::__gcd(
         static_cast<_Wp>(__abs<_Rp, _Tp>()(__m)),
         static_cast<_Wp>(__abs<_Rp, _Up>()(__n))));
 }

 template<class _Tp, class _Up>
 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
 common_type_t<_Tp,_Up>
 lcm(_Tp __m, _Up __n)
 {
     static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
     static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
     static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
     if (__m == 0 || __n == 0)
         return 0;

     using _Rp = common_type_t<_Tp,_Up>;
     _Rp __val1 = __abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
     _Rp __val2 = __abs<_Rp, _Up>()(__n);
     _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
     return __val1 * __val2;
 }

 #endif /* _LIBCPP_STD_VER > 14 */

 _LIBCPP_END_NAMESPACE_STD

 _LIBCPP_POP_MACROS

 #endif  // _LIBCPP_NUMERIC
	// -- C++ --
	//===---------------------------- numeric ---------------------------------===//
	//
	// The LLVM Compiler Infrastructure
	//
	// This file is dual licensed under the MIT and the University of Illinois Open
	// Source Licenses. See LICENSE.TXT for details.
	//
	//===----------------------------------------------------------------------===//

	#ifndef _LIBCPP_NUMERIC
	#define _LIBCPP_NUMERIC

	/*
	numeric synopsis

	namespace std
	{

	template <class InputIterator, class T>
	T
	accumulate(InputIterator first, InputIterator last, T init);

	template <class InputIterator, class T, class BinaryOperation>
	T
	accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op);

	template<class InputIterator>
	typename iterator_traits<InputIterator>::value_type
	reduce(InputIterator first, InputIterator last); // C++17

	template<class InputIterator, class T>
	T
	reduce(InputIterator first, InputIterator last, T init); // C++17

	template<class InputIterator, class T, class BinaryOperation>
	T
	reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17

	template <class InputIterator1, class InputIterator2, class T>
	T
	inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init);

	template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
	T
	inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
	T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2);


	template<class InputIterator1, class InputIterator2, class T>
	T
	transform_reduce(InputIterator1 first1, InputIterator1 last1,
	InputIterator2 first2, T init); // C++17

	template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2>
	T
	transform_reduce(InputIterator1 first1, InputIterator1 last1,
	InputIterator2 first2, T init,
	BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); // C++17

	template<class InputIterator, class T, class BinaryOperation, class UnaryOperation>
	T
	transform_reduce(InputIterator first, InputIterator last, T init,
	BinaryOperation binary_op, UnaryOperation unary_op); // C++17

	template <class InputIterator, class OutputIterator>
	OutputIterator
	partial_sum(InputIterator first, InputIterator last, OutputIterator result);

	template <class InputIterator, class OutputIterator, class BinaryOperation>
	OutputIterator
	partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);

	template<class InputIterator, class OutputIterator, class T>
	OutputIterator
	exclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result, T init); // C++17

	template<class InputIterator, class OutputIterator, class T, class BinaryOperation>
	OutputIterator
	exclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result, T init, BinaryOperation binary_op); // C++17

	template<class InputIterator, class OutputIterator>
	OutputIterator
	inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17

	template<class InputIterator, class OutputIterator, class BinaryOperation>
	OutputIterator
	inclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result, BinaryOperation binary_op); // C++17

	template<class InputIterator, class OutputIterator, class BinaryOperation, class T>
	OutputIterator
	inclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result, BinaryOperation binary_op, T init); // C++17

	template<class InputIterator, class OutputIterator, class T,
	class BinaryOperation, class UnaryOperation>
	OutputIterator
	transform_exclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result, T init,
	BinaryOperation binary_op, UnaryOperation unary_op); // C++17

	template<class InputIterator, class OutputIterator,
	class BinaryOperation, class UnaryOperation>
	OutputIterator
	transform_inclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result,
	BinaryOperation binary_op, UnaryOperation unary_op); // C++17

	template<class InputIterator, class OutputIterator,
	class BinaryOperation, class UnaryOperation, class T>
	OutputIterator
	transform_inclusive_scan(InputIterator first, InputIterator last,
	OutputIterator result,
	BinaryOperation binary_op, UnaryOperation unary_op,
	T init); // C++17

	template <class InputIterator, class OutputIterator>
	OutputIterator
	adjacent_difference(InputIterator first, InputIterator last, OutputIterator result);

	template <class InputIterator, class OutputIterator, class BinaryOperation>
	OutputIterator
	adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op);

	template <class ForwardIterator, class T>
	void iota(ForwardIterator first, ForwardIterator last, T value);

	template <class M, class N>
	constexpr common_type_t<M,N> gcd(M m, N n); // C++17

	template <class M, class N>
	constexpr common_type_t<M,N> lcm(M m, N n); // C++17

	} // std

	*/

	#include <__config>
	#include <iterator>
	#include <limits> // for numeric_limits
	#include <functional>
	#include <version>

	#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
	#pragma GCC system_header
	#endif

	_LIBCPP_PUSH_MACROS
	#include <__undef_macros>

	_LIBCPP_BEGIN_NAMESPACE_STD

	template <class _InputIterator, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	accumulate(_InputIterator __first, _InputIterator __last, _Tp __init)
	{
	for (; __first != __last; ++__first)
	__init = __init + *__first;
	return __init;
	}

	template <class _InputIterator, class _Tp, class _BinaryOperation>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op)
	{
	for (; __first != __last; ++__first)
	__init = __binary_op(__init, *__first);
	return __init;
	}

	#if _LIBCPP_STD_VER > 14
	template <class _InputIterator, class _Tp, class _BinaryOp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b)
	{
	for (; __first != __last; ++__first)
	__init = __b(__init, *__first);
	return __init;
	}

	template <class _InputIterator, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	reduce(_InputIterator __first, _InputIterator __last, _Tp __init)
	{
	return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>());
	}

	template <class _InputIterator>
	inline _LIBCPP_INLINE_VISIBILITY
	typename iterator_traits<_InputIterator>::value_type
	reduce(_InputIterator __first, _InputIterator __last)
	{
	return _VSTD::reduce(__first, __last,
	typename iterator_traits<_InputIterator>::value_type{});
	}
	#endif

	template <class _InputIterator1, class _InputIterator2, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init)
	{
	for (; __first1 != __last1; ++__first1, (void) ++__first2)
	__init = __init + __first1 *__first2;
	return __init;
	}

	template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2,
	_Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2)
	{
	for (; __first1 != __last1; ++__first1, (void) ++__first2)
	__init = __binary_op1(__init, __binary_op2(__first1, __first2));
	return __init;
	}

	#if _LIBCPP_STD_VER > 14
	template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	transform_reduce(_InputIterator __first, _InputIterator __last,
	_Tp __init, _BinaryOp __b, _UnaryOp __u)
	{
	for (; __first != __last; ++__first)
	__init = __b(__init, __u(*__first));
	return __init;
	}

	template <class _InputIterator1, class _InputIterator2,
	class _Tp, class _BinaryOp1, class _BinaryOp2>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
	_InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2)
	{
	for (; __first1 != __last1; ++__first1, (void) ++__first2)
	__init = __b1(__init, __b2(__first1, __first2));
	return __init;
	}

	template <class _InputIterator1, class _InputIterator2, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	_Tp
	transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1,
	_InputIterator2 __first2, _Tp __init)
	{
	return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init),
	_VSTD::plus<>(), _VSTD::multiplies<>());
	}
	#endif

	template <class _InputIterator, class _OutputIterator>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
	{
	if (__first != __last)
	{
	typename iterator_traits<_InputIterator>::value_type __t(*__first);
	*__result = __t;
	for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
	{
	__t = __t + *__first;
	*__result = __t;
	}
	}
	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
	_BinaryOperation __binary_op)
	{
	if (__first != __last)
	{
	typename iterator_traits<_InputIterator>::value_type __t(*__first);
	*__result = __t;
	for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
	{
	__t = __binary_op(__t, *__first);
	*__result = __t;
	}
	}
	return __result;
	}

	#if _LIBCPP_STD_VER > 14
	template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	exclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _Tp __init, _BinaryOp __b)
	{
	if (__first != __last)
	{
	_Tp __saved = __init;
	do
	{
	__init = __b(__init, *__first);
	*__result = __saved;
	__saved = __init;
	++__result;
	} while (++__first != __last);
	}
	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	exclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _Tp __init)
	{
	return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>());
	}

	template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp>
	_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _BinaryOp __b, _Tp __init)
	{
	for (; __first != __last; ++__first, (void) ++__result) {
	__init = __b(__init, *__first);
	*__result = __init;
	}
	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _BinaryOp>
	_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _BinaryOp __b)
	{
	if (__first != __last) {
	typename std::iterator_traits<_InputIterator>::value_type __init = *__first;
	*__result++ = __init;
	if (++__first != __last)
	return _VSTD::inclusive_scan(__first, __last, __result, __b, __init);
	}

	return __result;
	}

	template <class _InputIterator, class _OutputIterator>
	_OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result)
	{
	return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>());
	}

	template <class _InputIterator, class _OutputIterator, class _Tp,
	class _BinaryOp, class _UnaryOp>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	transform_exclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _Tp __init,
	_BinaryOp __b, _UnaryOp __u)
	{
	if (__first != __last)
	{
	_Tp __saved = __init;
	do
	{
	__init = __b(__init, __u(*__first));
	*__result = __saved;
	__saved = __init;
	++__result;
	} while (++__first != __last);
	}
	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp>
	_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init)
	{
	for (; __first != __last; ++__first, (void) ++__result) {
	__init = __b(__init, __u(*__first));
	*__result = __init;
	}

	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp>
	_OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last,
	_OutputIterator __result, _BinaryOp __b, _UnaryOp __u)
	{
	if (__first != __last) {
	typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first);
	*__result++ = __init;
	if (++__first != __last)
	return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init);
	}

	return __result;
	}
	#endif

	template <class _InputIterator, class _OutputIterator>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result)
	{
	if (__first != __last)
	{
	typename iterator_traits<_InputIterator>::value_type __t1(*__first);
	*__result = __t1;
	for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
	{
	typename iterator_traits<_InputIterator>::value_type __t2(*__first);
	*__result = __t2 - __t1;
	__t1 = _VSTD::move(__t2);
	}
	}
	return __result;
	}

	template <class _InputIterator, class _OutputIterator, class _BinaryOperation>
	inline _LIBCPP_INLINE_VISIBILITY
	_OutputIterator
	adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result,
	_BinaryOperation __binary_op)
	{
	if (__first != __last)
	{
	typename iterator_traits<_InputIterator>::value_type __t1(*__first);
	*__result = __t1;
	for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result)
	{
	typename iterator_traits<_InputIterator>::value_type __t2(*__first);
	*__result = __binary_op(__t2, __t1);
	__t1 = _VSTD::move(__t2);
	}
	}
	return __result;
	}

	template <class _ForwardIterator, class _Tp>
	inline _LIBCPP_INLINE_VISIBILITY
	void
	iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_)
	{
	for (; __first != __last; ++__first, (void) ++__value_)
	*__first = __value_;
	}


	#if _LIBCPP_STD_VER > 14
	template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __abs;

	template <typename _Result, typename _Source>
	struct __abs<_Result, _Source, true> {
	_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
	_Result operator()(_Source __t) const noexcept
	{
	if (__t >= 0) return __t;
	if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t);
	return -__t;
	}
	};

	template <typename _Result, typename _Source>
	struct __abs<_Result, _Source, false> {
	_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
	_Result operator()(_Source __t) const noexcept { return __t; }
	};


	template<class _Tp>
	_LIBCPP_CONSTEXPR _LIBCPP_HIDDEN
	_Tp __gcd(_Tp __m, _Tp __n)
	{
	static_assert((!is_signed<_Tp>::value), "");
	return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n);
	}


	template<class _Tp, class _Up>
	_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
	common_type_t<_Tp,_Up>
	gcd(_Tp __m, _Up __n)
	{
	static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types");
	static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" );
	static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" );
	using _Rp = common_type_t<_Tp,_Up>;
	using _Wp = make_unsigned_t<_Rp>;
	return static_cast<_Rp>(_VSTD::__gcd(
	static_cast<_Wp>(__abs<_Rp, _Tp>()(__m)),
	static_cast<_Wp>(__abs<_Rp, _Up>()(__n))));
	}

	template<class _Tp, class _Up>
	_LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY
	common_type_t<_Tp,_Up>
	lcm(_Tp __m, _Up __n)
	{
	static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types");
	static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" );
	static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" );
	if (__m == 0 \|\| __n == 0)
	return 0;

	using _Rp = common_type_t<_Tp,_Up>;
	_Rp __val1 = __abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n);
	_Rp __val2 = __abs<_Rp, _Up>()(__n);
	_LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm");
	return __val1 * __val2;
	}

	#endif /* _LIBCPP_STD_VER > 14 */

	_LIBCPP_END_NAMESPACE_STD

	_LIBCPP_POP_MACROS

	#endif // _LIBCPP_NUMERIC