// algorithm standard header
#pragma once
#ifndef _ALGORITHM_
#define _ALGORITHM_
#include <memory>

#pragma pack(push,8)
#pragma warning(push,3)
 #pragma warning(disable: 4244)
_STD_BEGIN

		// COMMON SORT PARAMETERS
const int _ISORT_MAX = 32;	// maximum size for insertion sort

		// TEMPLATE FUNCTION for_each
template<class _InIt,
	class _Fn1> inline
	_Fn1 for_each(_InIt _First, _InIt _Last, _Fn1 _Func)
	{	// perform function for each element
	for (; _First != _Last; ++_First)
		_Func(*_First);
	return (_Func);
	}

		// TEMPLATE FUNCTION find
template<class _InIt,
	class _Ty> inline
	_InIt find(_InIt _First, _InIt _Last, const _Ty& _Val)
	{	// find first matching _Val
	for (; _First != _Last; ++_First)
		if (*_First == _Val)
			break;
	return (_First);
	}

inline const char *find(const char *_First, const char *_Last, int _Val)
	{	// find first char that matches _Val
	_First = (const char *)::memchr(_First, _Val, _Last - _First);
	return (_First == 0 ? _Last : _First);
	}

inline const signed char *find(const signed char *_First,
	const signed char *_Last, int _Val)
	{	// find first signed char that matches _Val
	_First = (const signed char *)::memchr(_First, _Val,
		_Last - _First);
	return (_First == 0 ? _Last : _First);
	}

inline const unsigned char *find(const unsigned char *_First,
	const unsigned char *_Last, int _Val)
	{	// find first unsigned char that matches _Val
	_First = (const unsigned char *)::memchr(_First, _Val,
		_Last - _First);
	return (_First == 0 ? _Last : _First);
	}

		// TEMPLATE FUNCTION find_if
template<class _InIt,
	class _Pr> inline
	_InIt find_if(_InIt _First, _InIt _Last, _Pr _Pred)
	{	// find first satisfying _Pred
	for (; _First != _Last; ++_First)
		if (_Pred(*_First))
			break;
	return (_First);
	}

		// TEMPLATE FUNCTION adjacent_find
template<class _FwdIt> inline
	_FwdIt adjacent_find(_FwdIt _First, _FwdIt _Last)
	{	// find first matching successor
	for (_FwdIt _Firstb; (_Firstb = _First) != _Last && ++_First != _Last; )
		if (*_Firstb == *_First)
			return (_Firstb);
	return (_Last);
	}

		// TEMPLATE FUNCTION adjacent_find WITH PRED
template<class _FwdIt,
	class _Pr> inline
	_FwdIt adjacent_find(_FwdIt _First, _FwdIt _Last, _Pr _Pred)
	{	// find first satisfying _Pred with successor
	for (_FwdIt _Firstb; (_Firstb = _First) != _Last && ++_First != _Last; )
		if (_Pred(*_Firstb, *_First))
			return (_Firstb);
	return (_Last);
	}

 #if _HAS_PARTIAL_SPECIALIZATION
		// TEMPLATE FUNCTION count
template<class _InIt,
	class _Ty> inline
	typename iterator_traits<_InIt>::difference_type
		count(_InIt _First, _InIt _Last, const _Ty& _Val)
	{	// count elements that match _Val
	typename iterator_traits<_InIt>::difference_type _Count = 0;

	for (; _First != _Last; ++_First)
		if (*_First == _Val)
			++_Count;
	return (_Count);
	}

		// TEMPLATE FUNCTION count_if
template<class _InIt,
	class _Pr> inline
	typename iterator_traits<_InIt>::difference_type
		count_if(_InIt _First, _InIt _Last, _Pr _Pred)
	{	// count elements satisfying _Pred
	typename iterator_traits<_InIt>::difference_type _Count = 0;

	for (; _First != _Last; ++_First)
		if (_Pred(*_First))
			++_Count;
	return (_Count);
	}
 #else /* _HAS_PARTIAL_SPECIALIZATION */
		// TEMPLATE FUNCTION count
template<class _InIt,
	class _Ty> inline
	ptrdiff_t count(_InIt _First, _InIt _Last, const _Ty& _Val)
	{	// count elements that match _Val
	ptrdiff_t _Count = 0;

	for (; _First != _Last; ++_First)
		if (*_First == _Val)
			++_Count;
	return (_Count);
	}

		// TEMPLATE FUNCTION count_if
template<class _InIt,
	class _Pr> inline
	ptrdiff_t count_if(_InIt _First, _InIt _Last, _Pr _Pred)
	{	// count elements satisfying _Pred
	ptrdiff_t _Count = 0;

	for (; _First != _Last; ++_First)
		if (_Pred(*_First))
			++_Count;
	return (_Count);
	}
 #endif /* _HAS_PARTIAL_SPECIALIZATION */

		// TEMPLATE FUNCTION search
template<class _FwdIt1,
	class _FwdIt2,
	class _Diff1,
	class _Diff2> inline
	_FwdIt1 _Search(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Diff1 *, _Diff2 *)
	{	// find first [_First2, _Last2) match
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);
	_Diff2 _Count2 = 0;
	_Distance(_First2, _Last2, _Count2);

	for (; _Count2 <= _Count1; ++_First1, --_Count1)
		{	// room for match, try it
		_FwdIt1 _Mid1 = _First1;
		for (_FwdIt2 _Mid2 = _First2; ; ++_Mid1, ++_Mid2)
			if (_Mid2 == _Last2)
				return (_First1);
			else if (!(*_Mid1 == *_Mid2))
				break;
		}
	return (_Last1);
	}

template<class _FwdIt1,
	class _FwdIt2> inline
	_FwdIt1 search(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2)
	{	// find first [_First2, _Last2) match
	return (_Search(_First1, _Last1, _First2, _Last2,
		_Dist_type(_First1), _Dist_type(_First2)));
	}

		// TEMPLATE FUNCTION search WITH PRED
template<class _FwdIt1,
	class _FwdIt2,
	class _Diff1,
	class _Diff2,
	class _Pr> inline
	_FwdIt1 _Search(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Pr _Pred, _Diff1 *, _Diff2 *)
	{	// find first [_First2, _Last2) satisfying _Pred
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);
	_Diff2 _Count2 = 0;
	_Distance(_First2, _Last2, _Count2);

	for (; _Count2 <= _Count1; ++_First1, --_Count1)
		{	// room for match, try it
		_FwdIt1 _Mid1 = _First1;
		for (_FwdIt2 _Mid2 = _First2; ; ++_Mid1, ++_Mid2)
			if (_Mid2 == _Last2)
				return (_First1);
			else if (!_Pred(*_Mid1, *_Mid2))
				break;
		}
	return (_Last1);
	}

template<class _FwdIt1,
	class _FwdIt2,
	class _Pr> inline
	_FwdIt1 search(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Pr _Pred)
	{	// find first [_First2, _Last2) satisfying _Pred
	return (_Search(_First1, _Last1, _First2, _Last2, _Pred,
		_Dist_type(_First1), _Dist_type(_First2)));
	}

		// TEMPLATE FUNCTION search_n
template<class _FwdIt1,
	class _Diff2,
	class _Ty,
	class _Diff1> inline
	_FwdIt1 _Search_n(_FwdIt1 _First1, _FwdIt1 _Last1,
		_Diff2 _Count, const _Ty& _Val, _Diff1 *)
	{	// find first _Count * _Val match
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);

	for (; _Count <= _Count1; ++_First1, --_Count1)
		{	// room for match, try it
		_FwdIt1 _Mid1 = _First1;
		for (_Diff2 _Count2 = _Count; ; ++_Mid1, --_Count2)
			if (_Count2 == 0)
				return (_First1);
			else if (!(*_Mid1 == _Val))
				break;
		}
	return (_Last1);
	}

template<class _FwdIt1,
	class _Diff2,
	class _Ty> inline
	_FwdIt1 search_n(_FwdIt1 _First1, _FwdIt1 _Last1,
		_Diff2 _Count, const _Ty& _Val)
	{	// find first _Count * _Val match
	return (_Search_n(_First1, _Last1, _Count, _Val, _Dist_type(_First1)));
	}

		// TEMPLATE FUNCTION search_n WITH PRED
template<class _FwdIt1,
	class _Diff2,
	class _Ty,
	class _Diff1,
	class _Pr> inline
	_FwdIt1 _Search_n(_FwdIt1 _First1, _FwdIt1 _Last1,
		_Diff2 _Count, const _Ty& _Val, _Pr _Pred, _Diff1 *)
	{	// find first _Count * _Val satisfying _Pred
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);

	for (; _Count <= _Count1; ++_First1, --_Count1)
		{	// room for match, try it
		_FwdIt1 _Mid1 = _First1;
		for (_Diff2 _Count2 = _Count; ; ++_Mid1, --_Count2)
			if (_Count2 == 0)
				return (_First1);
			else if (!_Pred(*_Mid1, _Val))
				break;
		}
	return (_Last1);
	}

template<class _FwdIt1,
	class _Diff2,
	class _Ty,
	class _Pr> inline
	_FwdIt1 search_n(_FwdIt1 _First1, _FwdIt1 _Last1,
		_Diff2 _Count, const _Ty& _Val, _Pr _Pred)
	{	// find first _Count * _Val satisfying _Pred
	return (_Search_n(_First1, _Last1,
		_Count, _Val, _Pred, _Dist_type(_First1)));
	}

		// TEMPLATE FUNCTION find_end
template<class _FwdIt1,
	class _FwdIt2,
	class _Diff1,
	class _Diff2> inline
	_FwdIt1 _Find_end(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Diff1 *, _Diff2 *)
	{	// find last [_First2, _Last2) match
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);
	_Diff2 _Count2 = 0;
	_Distance(_First2, _Last2, _Count2);
	_FwdIt1 _Ans = _Last1;

	if (0 < _Count2)
		for (; _Count2 <= _Count1; ++_First1, --_Count1)
			{	// room for match, try it
			_FwdIt1 _Mid1 = _First1;
			for (_FwdIt2 _Mid2 = _First2; ; ++_Mid1)
				if (!(*_Mid1 == *_Mid2))
					break;
				else if (++_Mid2 == _Last2)
					{	// potential answer, save it
					_Ans = _First1;
					break;
					}
			}
	return (_Ans);
	}

template<class _FwdIt1,
	class _FwdIt2> inline
	_FwdIt1 find_end(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2)
	{	// find last [_First2, _Last2) match
	return (_Find_end(_First1, _Last1, _First2, _Last2,
		_Dist_type(_First1), _Dist_type(_First2)));
	}

		// TEMPLATE FUNCTION find_end WITH PRED
template<class _FwdIt1,
	class _FwdIt2,
	class _Diff1,
	class _Diff2,
	class _Pr> inline
	_FwdIt1 _Find_end(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Pr _Pred, _Diff1 *, _Diff2 *)
	{	// find last [_First2, _Last2) satisfying _Pred
	_Diff1 _Count1 = 0;
	_Distance(_First1, _Last1, _Count1);
	_Diff2 _Count2 = 0;
	_Distance(_First2, _Last2, _Count2);
	_FwdIt1 _Ans = _Last1;

	if (0 < _Count2)
		for (; _Count2 <= _Count1; ++_First1, --_Count1)
			{	// room for match, try it
			_FwdIt1 _Mid1 = _First1;
			for (_FwdIt2 _Mid2 = _First2; ; ++_Mid1)
				if (!_Pred(*_Mid1, *_Mid2))
					break;
				else if (++_Mid2 == _Last2)
					{	// potential answer, save it
					_Ans = _First1;
					break;
					}
			}
	return (_Ans);
	}

template<class _FwdIt1,
	class _FwdIt2,
	class _Pr> inline
	_FwdIt1 find_end(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Pr _Pred)
	{	// find last [_First2, _Last2) satisfying _Pred
	return (_Find_end(_First1, _Last1, _First2, _Last2, _Pred,
		_Dist_type(_First1), _Dist_type(_First2)));
	}

		// TEMPLATE FUNCTION find_first_of
template<class _FwdIt1,
	class _FwdIt2> inline
	_FwdIt1 find_first_of(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2)
	{	// look for one of [_First2, _Last2) that matches element
	for (; _First1 != _Last1; ++_First1)
		for (_FwdIt2 _Mid2 = _First2; _Mid2 != _Last2; ++_Mid2)
			if (*_First1 == *_Mid2)
				return (_First1);
	return (_First1);
	}

		// TEMPLATE FUNCTION find_first_of WITH PRED
template<class _FwdIt1,
	class _FwdIt2,
	class _Pr> inline
	_FwdIt1 find_first_of(_FwdIt1 _First1, _FwdIt1 _Last1,
		_FwdIt2 _First2, _FwdIt2 _Last2, _Pr _Pred)
	{	// look for one of [_First2, _Last2) satisfying _Pred with element
	for (; _First1 != _Last1; ++_First1)
		for (_FwdIt2 _Mid2 = _First2; _Mid2 != _Last2; ++_Mid2)
			if (_Pred(*_First1, *_Mid2))
				return (_First1);
	return (_First1);
	}

		// TEMPLATE FUNCTION iter_swap
template<class _FwdIt1,
	class _FwdIt2> inline
	void iter_swap(_FwdIt1 _Left, _FwdIt2 _Right)
	{	// swap *_Left and *_Right
	std::swap(*_Left, *_Right);
	}

		// TEMPLATE FUNCTION swap_ranges
template<class _FwdIt1,
	class _FwdIt2> inline
	_FwdIt2 swap_ranges(_FwdIt1 _First1, _FwdIt1 _Last1, _FwdIt2 _First2)
	{	// swap [_First1, _Last1) with [_First2, ...)
	for (; _First1 != _Last1; ++_First1, ++_First2)
		std::iter_swap(_First1, _First2);
	return (_First2);
	}

		// TEMPLATE FUNCTION transform WITH UNARY OP
template<class _InIt,
	class _OutIt,
	class _Fn1> inline
	_OutIt transform(_InIt _First, _InIt _Last, _OutIt _Dest, _Fn1 _Func)
	{	// transform [_First, _Last) with _Func
	for (; _First != _Last; ++_First, ++_Dest)
		*_Dest = _Func(*_First);
	return (_Dest);
	}

		// TEMPLATE FUNCTION transform WITH BINARY OP
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Fn2> inline
	_OutIt transform(_InIt1 _First1, _InIt1 _Last1, _InIt2 _First2,
		_OutIt _Dest, _Fn2 _Func)
	{	// transform [_First1, _Last1) and [_First2, _Last2) with _Func
	for (; _First1 != _Last1; ++_First1, ++_First2, ++_Dest)
		*_Dest = _Func(*_First1, *_First2);
	return (_Dest);
	}

		// TEMPLATE FUNCTION replace
template<class _FwdIt,
	class _Ty> inline
	void replace(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Oldval, const _Ty& _Newval)
	{	// replace each matching _Oldval with _Newval
	for (; _First != _Last; ++_First)
		if (*_First == _Oldval)
			*_First = _Newval;
	}

		// TEMPLATE FUNCTION replace_if
template<class _FwdIt,
	class _Pr,
	class _Ty> inline
	void replace_if(_FwdIt _First, _FwdIt _Last, _Pr _Pred, const _Ty& _Val)
	{	// replace each satisfying _Pred with _Val
	for (; _First != _Last; ++_First)
		if (_Pred(*_First))
			*_First = _Val;
	}

		// TEMPLATE FUNCTION replace_copy
template<class _InIt,
	class _OutIt,
	class _Ty> inline
	_OutIt replace_copy(_InIt _First, _InIt _Last, _OutIt _Dest,
		const _Ty& _Oldval, const _Ty& _Newval)
	{	// copy replacing each matching _Oldval with _Newval
	for (; _First != _Last; ++_First, ++_Dest)
		*_Dest = *_First == _Oldval ? _Newval : *_First;
	return (_Dest);
	}

		// TEMPLATE FUNCTION replace_copy_if
template<class _InIt,
	class _OutIt,
	class _Pr,
	class _Ty> inline
	_OutIt replace_copy_if(_InIt _First, _InIt _Last, _OutIt _Dest,
		_Pr _Pred, const _Ty& _Val)
	{	// copy replacing each satisfying _Pred with _Val
	for (; _First != _Last; ++_First, ++_Dest)
		*_Dest = _Pred(*_First) ? _Val : *_First;
	return (_Dest);
	}

		// TEMPLATE FUNCTION generate
template<class _FwdIt,
	class _Fn0> inline
	void generate(_FwdIt _First, _FwdIt _Last, _Fn0 _Func)
	{	// replace [_First, _Last) with _Func()
	for (; _First != _Last; ++_First)
		*_First = _Func();
	}

		// TEMPLATE FUNCTION generate_n
template<class _OutIt,
	class _Diff,
	class _Fn0> inline
	void generate_n(_OutIt _Dest, _Diff _Count, _Fn0 _Func)
	{	// replace [_Dest, _Dest + _Count) with _Func()
	for (; 0 < _Count; --_Count, ++_Dest)
		*_Dest = _Func();
	}

		// TEMPLATE FUNCTION remove_copy
template<class _InIt,
	class _OutIt,
	class _Ty> inline
	_OutIt remove_copy(_InIt _First, _InIt _Last,
		_OutIt _Dest, const _Ty& _Val)
	{	// copy omitting each matching _Val
	for (; _First != _Last; ++_First)
		if (!(*_First == _Val))
			*_Dest++ = *_First;
	return (_Dest);
	}

		// TEMPLATE FUNCTION remove_copy_if
template<class _InIt,
	class _OutIt,
	class _Pr> inline
	_OutIt remove_copy_if(_InIt _First, _InIt _Last, _OutIt _Dest, _Pr _Pred)
	{	// copy omitting each element satisfying _Pred
	for (; _First != _Last; ++_First)
		if (!_Pred(*_First))
			*_Dest++ = *_First;
	return (_Dest);
	}

		// TEMPLATE FUNCTION remove
template<class _FwdIt,
	class _Ty> inline
	_FwdIt remove(_FwdIt _First, _FwdIt _Last, const _Ty& _Val)
	{	// remove each matching _Val
	_First = find(_First, _Last, _Val);
	if (_First == _Last)
		return (_First);	// empty sequence, all done
	else
		{	// nonempty sequence, worth doing
		_FwdIt _First1 = _First;
		return (std::remove_copy(++_First1, _Last, _First, _Val));
		}
	}

		// TEMPLATE FUNCTION remove_if
template<class _FwdIt,
	class _Pr> inline
	_FwdIt remove_if(_FwdIt _First, _FwdIt _Last, _Pr _Pred)
	{	// remove each satisfying _Pred
	_First = std::find_if(_First, _Last, _Pred);
	if (_First == _Last)
		return (_First);	// empty sequence, all done
	else
		{	// nonempty sequence, worth doing
		_FwdIt _First1 = _First;
		return (std::remove_copy_if(++_First1, _Last, _First, _Pred));
		}
	}

		// TEMPLATE FUNCTION unique
template<class _FwdIt> inline
	_FwdIt unique(_FwdIt _First, _FwdIt _Last)
	{	// remove each matching previous
	for (_FwdIt _Firstb; (_Firstb = _First) != _Last && ++_First != _Last; )
		if (*_Firstb == *_First)
			{	// copy down
			for (; ++_First != _Last; )
				if (!(*_Firstb == *_First))
					*++_Firstb = *_First;
			return (++_Firstb);
			}
	return (_Last);
	}

		// TEMPLATE FUNCTION unique WITH PRED
template<class _FwdIt,
	class _Pr> inline
	_FwdIt unique(_FwdIt _First, _FwdIt _Last, _Pr _Pred)
	{	// remove each satisfying _Pred with previous
	for (_FwdIt _Firstb; (_Firstb = _First) != _Last && ++_First != _Last; )
		if (_Pred(*_Firstb, *_First))
			{	// copy down
			for (; ++_First != _Last; )
				if (!_Pred(*_Firstb, *_First))
					*++_Firstb = *_First;
			return (++_Firstb);
			}
	return (_Last);
	}

		// TEMPLATE FUNCTION unique_copy
template<class _InIt,
	class _OutIt,
	class _Ty> inline
	_OutIt _Unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest, _Ty *)
	{	// copy compressing pairs that match, input iterators
	_Ty _Val = *_First;

	for (*_Dest++ = _Val; ++_First != _Last; )
		if (!(_Val == *_First))
			_Val = *_First, *_Dest++ = _Val;
	return (_Dest);
	}

template<class _InIt,
	class _OutIt> inline
	_OutIt _Unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest,
		input_iterator_tag)
	{	// copy compressing pairs that match, input iterators
	return (_Unique_copy(_First, _Last, _Dest, _Val_type(_First)));
	}

template<class _FwdIt,
	class _OutIt> inline
	_OutIt _Unique_copy(_FwdIt _First, _FwdIt _Last, _OutIt _Dest,
		forward_iterator_tag)
	{	// copy compressing pairs that match, forward iterators
	_FwdIt _Firstb = _First;
	for (*_Dest++ = *_Firstb; ++_First != _Last; )
		if (!(*_Firstb == *_First))
			_Firstb = _First, *_Dest++ = *_Firstb;
	return (_Dest);
	}

template<class _BidIt,
	class _OutIt> inline
	_OutIt _Unique_copy(_BidIt _First, _BidIt _Last, _OutIt _Dest,
		bidirectional_iterator_tag)
	{	// copy compressing pairs that match, bidirectional iterators
	return (_Unique_copy(_First, _Last, _Dest, forward_iterator_tag()));
	}

template<class _RanIt,
	class _OutIt> inline
	_OutIt _Unique_copy(_RanIt _First, _RanIt _Last, _OutIt _Dest,
		random_access_iterator_tag)
	{	// copy compressing pairs that match, random-access iterators
	return (_Unique_copy(_First, _Last, _Dest, forward_iterator_tag()));
	}

template<class _InIt,
	class _OutIt> inline
	_OutIt unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest)
	{	// copy compressing pairs that match
	return (_First == _Last ? _Dest :
		_Unique_copy(_First, _Last, _Dest, _Iter_cat(_First)));
	}

		// TEMPLATE FUNCTION unique_copy WITH PRED
template<class _InIt,
	class _OutIt,
	class _Ty,
	class _Pr> inline
	_OutIt _Unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest, _Pr _Pred,
		_Ty *)
	{	// copy compressing pairs satisfying _Pred, input iterators
	_Ty _Val = *_First;

	for (*_Dest++ = _Val; ++_First != _Last; )
		if (!_Pred(_Val, *_First))
			_Val = *_First, *_Dest++ = _Val;
	return (_Dest);
	}

template<class _InIt,
	class _OutIt,
	class _Pr> inline
	_OutIt _Unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest, _Pr _Pred,
		input_iterator_tag)
	{	// copy compressing pairs satisfying _Pred, input iterators
	return (_Unique_copy(_First, _Last, _Dest, _Pred, _Val_type(_First)));
	}

template<class _FwdIt,
	class _OutIt,
	class _Pr> inline
	_OutIt _Unique_copy(_FwdIt _First, _FwdIt _Last, _OutIt _Dest, _Pr _Pred,
		forward_iterator_tag)
	{	// copy compressing pairs satisfying _Pred, forward iterators
	_FwdIt _Firstb = _First;

	for (*_Dest++ = *_Firstb; ++_First != _Last; )
		if (!_Pred(*_Firstb, *_First))
			_Firstb = _First, *_Dest++ = *_Firstb;
	return (_Dest);
	}

template<class _BidIt,
	class _OutIt,
	class _Pr> inline
	_OutIt _Unique_copy(_BidIt _First, _BidIt _Last, _OutIt _Dest, _Pr _Pred,
		bidirectional_iterator_tag)
	{	// copy compressing pairs satisfying _Pred, bidirectional iterators
	return (_Unique_copy(_First, _Last, _Dest, _Pred,
		forward_iterator_tag()));
	}

template<class _RanIt,
	class _OutIt,
	class _Pr> inline
	_OutIt _Unique_copy(_RanIt _First, _RanIt _Last, _OutIt _Dest, _Pr _Pred,
		random_access_iterator_tag)
	{	// copy compressing pairs satisfying _Pred, random-access iterators
	return (_Unique_copy(_First, _Last, _Dest, _Pred,
		forward_iterator_tag()));
	}

template<class _InIt,
	class _OutIt,
	class _Pr> inline
	_OutIt unique_copy(_InIt _First, _InIt _Last, _OutIt _Dest, _Pr _Pred)
	{	// copy compressing pairs satisfying _Pred
	return (_First == _Last ? _Dest
		: _Unique_copy(_First, _Last, _Dest, _Pred, _Iter_cat(_First)));
	}

		// TEMPLATE FUNCTION reverse
template<class _BidIt> inline
	void _Reverse(_BidIt _First, _BidIt _Last, bidirectional_iterator_tag)
	{	// reverse elements in [_First, _Last), bidirectional iterators
	for (; _First != _Last && _First != --_Last; ++_First)
		std::iter_swap(_First, _Last);
	}

template<class _RanIt> inline
	void _Reverse(_RanIt _First, _RanIt _Last, random_access_iterator_tag)
	{	// reverse elements in [_First, _Last), random-access iterators
	for (; _First < _Last; ++_First)
		std::iter_swap(_First, --_Last);
	}

template<class _BidIt> inline
	void reverse(_BidIt _First, _BidIt _Last)
	{	// reverse elements in [_First, _Last)
	_Reverse(_First, _Last, _Iter_cat(_First));
	}

		// TEMPLATE FUNCTION reverse_copy
template<class _BidIt,
	class _OutIt> inline
	_OutIt reverse_copy(_BidIt _First, _BidIt _Last, _OutIt _Dest)
	{	// copy reversing elements in [_First, _Last)
	for (; _First != _Last; ++_Dest)
		*_Dest = *--_Last;
	return (_Dest);
	}

		// TEMPLATE FUNCTION rotate
template<class _FwdIt> inline
	void _Rotate(_FwdIt _First, _FwdIt _Mid, _FwdIt _Last,
		forward_iterator_tag)
	{	// rotate [_First, _Last), forward iterators
	for (_FwdIt _Next = _Mid; ; )
		{	// swap [_First, ...) into place
		std::iter_swap(_First, _Next);
		if (++_First == _Mid)
			if (++_Next == _Last)
				break;	// done, quit
			else
				_Mid = _Next;	// mark end of next interval
		else if (++_Next == _Last)
			_Next = _Mid;	// wrap to last end
		}
	}

template<class _BidIt> inline
	void _Rotate(_BidIt _First, _BidIt _Mid, _BidIt _Last,
		bidirectional_iterator_tag)
	{	// rotate [_First, _Last), bidirectional iterators
	std::reverse(_First, _Mid);
	std::reverse(_Mid, _Last);
	std::reverse(_First, _Last);
	}

template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Rotate(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Diff *, _Ty *)
	{	// rotate [_First, _Last), random-access iterators
	_Diff _Shift = _Mid - _First;
	_Diff _Count = _Last - _First;

	for (_Diff _Factor = _Shift; _Factor != 0; )
		{	// find subcycle count as GCD of shift count and length
		_Diff _Tmp = _Count % _Factor;
		_Count = _Factor, _Factor = _Tmp;
		}

	if (_Count < _Last - _First)
		for (; 0 < _Count; --_Count)
			{	// rotate each subcycle
			_RanIt _Hole = _First + _Count;
			_RanIt _Next = _Hole;
			_Ty _Holeval = *_Hole;
			_RanIt _Next1 = _Next + _Shift == _Last ? _First : _Next + _Shift;
			while (_Next1 != _Hole)
				{	// percolate elements back around subcycle
				*_Next = *_Next1;
				_Next = _Next1;
				_Next1 = _Shift < _Last - _Next1 ? _Next1 + _Shift
					: _First + (_Shift - (_Last - _Next1));
				}
			*_Next = _Holeval;
			}
	}

template<class _RanIt> inline
	void _Rotate(_RanIt _First, _RanIt _Mid, _RanIt _Last,
			random_access_iterator_tag)
	{	// rotate [_First, _Last), random-access iterators
	_Rotate(_First, _Mid, _Last, _Dist_type(_First), _Val_type(_First));
	}

template<class _FwdIt> inline
	void rotate(_FwdIt _First, _FwdIt _Mid, _FwdIt _Last)
	{	// rotate [_First, _Last)
	if (_First != _Mid && _Mid != _Last)
		_Rotate(_First, _Mid, _Last, _Iter_cat(_First));
	}

		// TEMPLATE FUNCTION rotate_copy
template<class _FwdIt,
	class _OutIt> inline
	_OutIt rotate_copy(_FwdIt _First, _FwdIt _Mid, _FwdIt _Last, _OutIt _Dest)
	{	// copy rotating [_First, _Last)
	_Dest = std::copy(_Mid, _Last, _Dest);
	return (std::copy(_First, _Mid, _Dest));
	}

		// TEMPLATE FUNCTION random_shuffle
template<class _RanIt,
	class _Diff> inline
	void _Random_shuffle(_RanIt _First, _RanIt _Last, _Diff *)
	{	// shuffle [_First, _Last)
	const int _RANDOM_BITS = 15;	// minimum random bits from rand()
	const int _RANDOM_MAX = (1U << _RANDOM_BITS) - 1;

	_RanIt _Next = _First;
	for (unsigned long _Index = 2; ++_Next != _Last; ++_Index)
		{	// assume unsigned long big enough for _Diff count
		unsigned long _Rm = _RANDOM_MAX;
		unsigned long _Rn = ::rand() & _RANDOM_MAX;
		for (; _Rm < _Index && _Rm != ~0UL;
			_Rm = _Rm << _RANDOM_BITS | _RANDOM_MAX)
			_Rn = _Rn << _RANDOM_BITS | _RANDOM_MAX;	// build random value

		std::iter_swap(_Next, _First + _Diff(_Rn % _Index));	// swap a pair
		}
	}

template<class _RanIt> inline
	void random_shuffle(_RanIt _First, _RanIt _Last)
	{	// shuffle [_First, _Last)
	if (_First != _Last)
		_Random_shuffle(_First, _Last, _Dist_type(_First));
	}

		// TEMPLATE FUNCTION random_shuffle WITH RANDOM FN
template<class _RanIt,
	class _Fn1,
	class _Diff> inline
	void _Random_shuffle(_RanIt _First, _RanIt _Last, _Fn1& _Func, _Diff *)
	{	// shuffle nonempty [_First, _Last) using random function _Func
	_RanIt _Next = _First;

	for (_Diff _Index = 2; ++_Next != _Last; ++_Index)
		std::iter_swap(_Next, _First + _Diff(_Func(_Index)));
	}

template<class _RanIt,
	class _Fn1> inline
	void random_shuffle(_RanIt _First, _RanIt _Last, _Fn1& _Func)
	{	// shuffle [_First, _Last) using random function _Func
	if (_First != _Last)
		_Random_shuffle(_First, _Last, _Func, _Dist_type(_First));
	}

		// TEMPLATE FUNCTION partition
template<class _BidIt,
	class _Pr> inline
	_BidIt partition(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// move elements satisfying _Pred to beginning of sequence
	for (; ; ++_First)
		{	// find any out-of-order pair
		for (; _First != _Last && _Pred(*_First); ++_First)
			;	// skip in-place elements at beginning
		if (_First == _Last)
			break;	// done

		for (; _First != --_Last && !_Pred(*_Last); )
			;	// skip in-place elements at end
		if (_First == _Last)
			break;	// done

		std::iter_swap(_First, _Last);	// swap out-of-place pair and loop
		}
	return (_First);
	}

		// TEMPLATE FUNCTION stable_partition
template<class _BidIt,
	class _Pr,
	class _Diff,
	class _Ty> inline
	_BidIt _Stable_partition(_BidIt _First, _BidIt _Last, _Pr _Pred,
		_Diff _Count, _Temp_iterator<_Ty>& _Tempbuf)
	{	// partition using _Pred, preserving order of equivalents
	if (_Count == 1)
		return (_Pred(*_First) ? _Last : _First);
	else if (_Count <= _Tempbuf._Maxlen())
		{	// temp buffer big enough, copy right partition out and back
		_BidIt _Next = _First;
		for (_Tempbuf._Init(); _First != _Last; ++_First)
			if (_Pred(*_First))
				*_Next++ = *_First;
			else
				*_Tempbuf++ = *_First;

		std::copy(_Tempbuf._First(), _Tempbuf._Last(), _Next);	// copy back
		return (_Next);
		}
	else
		{	// temp buffer not big enough, divide and conquer
		_BidIt _Mid = _First;
		std::advance(_Mid, _Count / 2);

		_BidIt _Left = _Stable_partition(_First, _Mid, _Pred,
			_Count / 2, _Tempbuf);	// form L1R1 in left half
		_BidIt _Right = _Stable_partition(_Mid, _Last, _Pred,
			_Count - _Count / 2, _Tempbuf);	// form L2R2 in right half

		_Diff _Count1 = 0;
		_Distance(_Left, _Mid, _Count1);
		_Diff _Count2 = 0;
		_Distance(_Mid, _Right, _Count2);

		return (_Buffered_rotate(_Left, _Mid, _Right,
			_Count1, _Count2, _Tempbuf));	// rotate L1R1L2R2 to L1L2R1R2
		}
	}

template<class _BidIt,
	class _Pr,
	class _Diff,
	class _Ty> inline
	_BidIt _Stable_partition(_BidIt _First, _BidIt _Last, _Pr _Pred,
		_Diff *, _Ty *)
	{	// partition preserving order of equivalents, using _Pred
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	_Temp_iterator<_Ty> _Tempbuf(_Count);
	return (_Stable_partition(_First, _Last, _Pred, _Count, _Tempbuf));
	}

template<class _BidIt,
	class _Pr> inline
	_BidIt stable_partition(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// partition preserving order of equivalents, using _Pred
	return (_First == _Last ? _First : _Stable_partition(_First, _Last, _Pred,
		_Dist_type(_First), _Val_type(_First)));
	}

		// TEMPLATE FUNCTION push_heap
template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Push_heap(_RanIt _First, _Diff _Hole,
		_Diff _Top, _Ty _Val)
	{	// percolate _Hole to _Top or where _Val belongs, using operator<
	for (_Diff _Idx = (_Hole - 1) / 2;
		_Top < _Hole && *(_First + _Idx) < _Val;
		_Idx = (_Hole - 1) / 2)
		{	// move _Hole up to parent
		*(_First + _Hole) = *(_First + _Idx);
		_Hole = _Idx;
		}

	*(_First + _Hole) = _Val;	// drop _Val into final hole
	}

template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Push_heap_0(_RanIt _First, _RanIt _Last, _Diff *, _Ty *)
	{	// push *(_Last - 1) onto heap at [_First, _Last - 1), using operator<
	_Diff _Count = _Last - _First;
	if (1 < _Count)
		_Push_heap(_First, --_Count, _Diff(0), _Ty(*(_Last - 1)));
	}

template<class _RanIt> inline
	void push_heap(_RanIt _First, _RanIt _Last)
	{	// push *(_Last - 1) onto heap at [_First, _Last - 1), using operator<
	_Push_heap_0(_First, _Last, _Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION push_heap WITH PRED
template<class _RanIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Push_heap(_RanIt _First, _Diff _Hole,
		_Diff _Top, _Ty _Val, _Pr _Pred)
	{	// percolate _Hole to _Top or where _Val belongs, using operator<
	for (_Diff _Idx = (_Hole - 1) / 2;
		_Top < _Hole && _Pred(*(_First + _Idx), _Val);
		_Idx = (_Hole - 1) / 2)
		{	// move _Hole up to parent
		*(_First + _Hole) = *(_First + _Idx);
		_Hole = _Idx;
		}

	*(_First + _Hole) = _Val;	// drop _Val into final hole
	}

template<class _RanIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Push_heap_0(_RanIt _First, _RanIt _Last, _Pr _Pred, _Diff *, _Ty *)
	{	// push *(_Last - 1) onto heap at [_First, _Last - 1), using _Pred
	_Diff _Count = _Last - _First;
	if (1 < _Count)
		_Push_heap(_First, --_Count, _Diff(0), _Ty(*(_Last - 1)), _Pred);
	}

template<class _RanIt,
	class _Pr> inline
	void push_heap(_RanIt _First, _RanIt _Last, _Pr _Pred)
	{	// push *(_Last - 1) onto heap at [_First, _Last - 1), using _Pred
	_Push_heap_0(_First, _Last, _Pred,
		_Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION pop_heap
template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Adjust_heap(_RanIt _First, _Diff _Hole, _Diff _Bottom, _Ty _Val)
	{	// percolate _Hole to _Bottom, then push _Val, using operator<
	_Diff _Top = _Hole;
	_Diff _Idx = 2 * _Hole + 2;

	for (; _Idx < _Bottom; _Idx = 2 * _Idx + 2)
		{	// move _Hole down to larger child
		if (*(_First + _Idx) < *(_First + (_Idx - 1)))
			--_Idx;
		*(_First + _Hole) = *(_First + _Idx), _Hole = _Idx;
		}

	if (_Idx == _Bottom)
		{	// only child at bottom, move _Hole down to it
		*(_First + _Hole) = *(_First + (_Bottom - 1));
		_Hole = _Bottom - 1;
		}
	_Push_heap(_First, _Hole, _Top, _Val);
	}

template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Pop_heap(_RanIt _First, _RanIt _Last, _RanIt _Dest,
		_Ty _Val, _Diff *)
	{	// pop *_First to *_Dest and reheap, using operator<
	*_Dest = *_First;
	_Adjust_heap(_First, _Diff(0), _Diff(_Last - _First), _Val);
	}

template<class _RanIt,
	class _Ty> inline
	void _Pop_heap_0(_RanIt _First, _RanIt _Last, _Ty *)
	{	// pop *_First to *(_Last - 1) and reheap, using operator<
	_Pop_heap(_First, _Last - 1, _Last - 1,
		_Ty(*(_Last - 1)), _Dist_type(_First));
	}

template<class _RanIt> inline
	void pop_heap(_RanIt _First, _RanIt _Last)
	{	// pop *_First to *(_Last - 1) and reheap, using operator<
	if (1 < _Last - _First)
		_Pop_heap_0(_First, _Last, _Val_type(_First));
	}

		// TEMPLATE FUNCTION pop_heap WITH PRED
template<class _RanIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Adjust_heap(_RanIt _First, _Diff _Hole, _Diff _Bottom,
		_Ty _Val, _Pr _Pred)
	{	// percolate _Hole to _Bottom, then push _Val, using _Pred
	_Diff _Top = _Hole;
	_Diff _Idx = 2 * _Hole + 2;

	for (; _Idx < _Bottom; _Idx = 2 * _Idx + 2)
		{	// move _Hole down to larger child
		if (_Pred(*(_First + _Idx), *(_First + (_Idx - 1))))
			--_Idx;
		*(_First + _Hole) = *(_First + _Idx), _Hole = _Idx;
		}

	if (_Idx == _Bottom)
		{	// only child at bottom, move _Hole down to it
		*(_First + _Hole) = *(_First + (_Bottom - 1));
		_Hole = _Bottom - 1;
		}
	_Push_heap(_First, _Hole, _Top, _Val, _Pred);
	}

template<class _RanIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Pop_heap(_RanIt _First, _RanIt _Last, _RanIt _Dest,
		_Ty _Val, _Pr _Pred, _Diff *)
	{	// pop *_First to *_Dest and reheap, using _Pred
	*_Dest = *_First;
	_Adjust_heap(_First, _Diff(0), _Diff(_Last - _First), _Val, _Pred);
	}

template<class _RanIt,
	class _Ty,
	class _Pr> inline
	void _Pop_heap_0(_RanIt _First, _RanIt _Last, _Pr _Pred, _Ty *)
	{	// pop *_First to *(_Last - 1) and reheap, using _Pred
	_Pop_heap(_First, _Last - 1, _Last - 1,
		_Ty(*(_Last - 1)), _Pred, _Dist_type(_First));
	}

template<class _RanIt,
	class _Pr> inline
	void pop_heap(_RanIt _First, _RanIt _Last, _Pr _Pred)
	{	// pop *_First to *(_Last - 1) and reheap, using _Pred
	if (1 < _Last - _First)
		_Pop_heap_0(_First, _Last, _Pred, _Val_type(_First));
	}

		// TEMPLATE FUNCTION make_heap
template<class _RanIt,
	class _Diff,
	class _Ty> inline
	void _Make_heap(_RanIt _First, _RanIt _Last, _Diff *, _Ty *)
	{	// make nontrivial [_First, _Last) into a heap, using operator<
	_Diff _Bottom = _Last - _First;

	for (_Diff _Hole = _Bottom / 2; 0 < _Hole; )
		{	// reheap top half, bottom to top
		--_Hole;
		_Adjust_heap(_First, _Hole, _Bottom, _Ty(*(_First + _Hole)));
		}
	}

template<class _RanIt> inline
	void make_heap(_RanIt _First, _RanIt _Last)
	{	// make [_First, _Last) into a heap, using operator<
	if (1 < _Last - _First)
		_Make_heap(_First, _Last,
			_Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION make_heap WITH PRED
template<class _RanIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Make_heap(_RanIt _First, _RanIt _Last, _Pr _Pred, _Diff *, _Ty *)
	{	// make nontrivial [_First, _Last) into a heap, using _Pred
	_Diff _Bottom = _Last - _First;
	for (_Diff _Hole = _Bottom / 2; 0 < _Hole; )
		{	// reheap top half, bottom to top
		--_Hole;
		_Adjust_heap(_First, _Hole, _Bottom,
			_Ty(*(_First + _Hole)), _Pred);
		}
	}

template<class _RanIt,
	class _Pr> inline
	void make_heap(_RanIt _First, _RanIt _Last, _Pr _Pred)
	{	// make [_First, _Last) into a heap, using _Pred
	if (1 < _Last - _First)
		_Make_heap(_First, _Last, _Pred,
			_Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION sort_heap
template<class _RanIt> inline
	void sort_heap(_RanIt _First, _RanIt _Last)
	{	// order heap by repeatedly popping, using operator<
	for (; 1 < _Last - _First; --_Last)
		std::pop_heap(_First, _Last);
	}

		// TEMPLATE FUNCTION sort_heap WITH PRED
template<class _RanIt,
	class _Pr> inline
	void sort_heap(_RanIt _First, _RanIt _Last, _Pr _Pred)
	{	// order heap by repeatedly popping, using _Pred
	for (; 1 < _Last - _First; --_Last)
		std::pop_heap(_First, _Last, _Pred);
	}

		// TEMPLATE FUNCTION lower_bound
template<class _FwdIt,
	class _Ty,
	class _Diff> inline
	_FwdIt _Lower_bound(_FwdIt _First, _FwdIt _Last, const _Ty& _Val, _Diff *)
	{	// find first element not before _Val, using operator<
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);

	for (; 0 < _Count; )
		{	// divide and conquer, find half that contains answer
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (*_Mid < _Val)
			_First = ++_Mid, _Count -= _Count2 + 1;
		else
			_Count = _Count2;
		}
	return (_First);
	}

template<class _FwdIt,
	class _Ty> inline
	_FwdIt lower_bound(_FwdIt _First, _FwdIt _Last, const _Ty& _Val)
	{	// find first element not before _Val, using operator<
	return (_Lower_bound(_First, _Last, _Val, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION lower_bound WITH PRED
template<class _FwdIt,
	class _Ty,
	class _Diff,
	class _Pr> inline
	_FwdIt _Lower_bound(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred, _Diff *)
	{	// find first element not before _Val, using _Pred
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	for (; 0 < _Count; )
		{	// divide and conquer, find half that contains answer
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (_Pred(*_Mid, _Val))
			_First = ++_Mid, _Count -= _Count2 + 1;
		else
			_Count = _Count2;
		}
	return (_First);
	}

template<class _FwdIt,
	class _Ty,
	class _Pr> inline
	_FwdIt lower_bound(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred)
	{	// find first element not before _Val, using _Pred
	return (_Lower_bound(_First, _Last, _Val, _Pred, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION upper_bound
template<class _FwdIt,
	class _Ty,
	class _Diff> inline
	_FwdIt _Upper_bound(_FwdIt _First, _FwdIt _Last, const _Ty& _Val, _Diff *)
	{	// find first element that _Val is before, using operator<
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	for (; 0 < _Count; )
		{	// divide and conquer, find half that contains answer
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (!(_Val < *_Mid))
			_First = ++_Mid, _Count -= _Count2 + 1;
		else
			_Count = _Count2;
		}
	return (_First);
	}

template<class _FwdIt,
	class _Ty> inline
	_FwdIt upper_bound(_FwdIt _First, _FwdIt _Last, const _Ty& _Val)
	{	// find first element that _Val is before, using operator<
	return (_Upper_bound(_First, _Last, _Val, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION upper_bound WITH PRED
template<class _FwdIt,
	class _Ty,
	class _Diff,
	class _Pr> inline
	_FwdIt _Upper_bound(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred, _Diff *)
	{	// find first element that _Val is before, using _Pred
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	for (; 0 < _Count; )
		{	// divide and conquer, find half that contains answer
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (!_Pred(_Val, *_Mid))
			_First = ++_Mid, _Count -= _Count2 + 1;
		else
			_Count = _Count2;
		}
	return (_First);
	}

template<class _FwdIt,
	class _Ty,
	class _Pr> inline
	_FwdIt upper_bound(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred)
	{	// find first element that _Val is before, using _Pred
	return (_Upper_bound(_First, _Last, _Val, _Pred, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION equal_range
template<class _FwdIt,
	class _Ty,
	class _Diff> inline
	pair<_FwdIt, _FwdIt> _Equal_range(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Diff *)
	{	// find range equivalent to _Val, using operator<
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);

	for (; 0 < _Count; )
		{	// divide and conquer, check midpoint
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (*_Mid < _Val)
			{	// range begins above _Mid, loop
			_First = ++_Mid;
			_Count -= _Count2 + 1;
			}
		else if (_Val < *_Mid)
			_Count = _Count2;	// range in first half, loop
		else
			{	// range straddles mid, find each end and return
			_FwdIt _First2 = lower_bound(_First, _Mid, _Val);
			std::advance(_First, _Count);
			_FwdIt _Last2 = upper_bound(++_Mid, _First, _Val);
			return (pair<_FwdIt, _FwdIt>(_First2, _Last2));
			}
		}

	return (pair<_FwdIt, _FwdIt>(_First, _First));	// empty range
	}

template<class _FwdIt,
	class _Ty> inline
	pair<_FwdIt, _FwdIt> equal_range(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val)
	{	// find range equivalent to _Val, using operator<
	return (_Equal_range(_First, _Last, _Val, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION equal_range WITH PRED
template<class _FwdIt,
	class _Ty,
	class _Diff,
	class _Pr> inline
	pair<_FwdIt, _FwdIt> _Equal_range(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred, _Diff *)
	{	// find range equivalent to _Val, using _Pred
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);

	for (; 0 < _Count; )
		{	// divide and conquer, check midpoint
		_Diff _Count2 = _Count / 2;
		_FwdIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (_Pred(*_Mid, _Val))
			{	// range begins above _Mid, loop
			_First = ++_Mid;
			_Count -= _Count2 + 1;
			}
		else if (_Pred(_Val, *_Mid))
			_Count = _Count2;	// range in first half, loop
		else
			{	// range straddles _Mid, find each end and return
			_FwdIt _First2 = lower_bound(_First, _Mid, _Val, _Pred);
			std::advance(_First, _Count);
			_FwdIt _Last2 = upper_bound(++_Mid, _First, _Val, _Pred);
			return (pair<_FwdIt, _FwdIt>(_First2, _Last2));
			}
		}

	return (pair<_FwdIt, _FwdIt>(_First, _First));	// empty range
	}

template<class _FwdIt,
	class _Ty,
	class _Pr> inline
	pair<_FwdIt, _FwdIt> equal_range(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred)
	{	// find range equivalent to _Val, using _Pred
	return (_Equal_range(_First, _Last, _Val, _Pred, _Dist_type(_First)));
	}

		// TEMPLATE FUNCTION binary_search
template<class _FwdIt,
	class _Ty> inline
	bool binary_search(_FwdIt _First, _FwdIt _Last, const _Ty& _Val)
	{	// test if _Val equivalent to some element, using operator<
	_First = std::lower_bound(_First, _Last, _Val);
	return (_First != _Last && !(_Val < *_First));
	}

		// TEMPLATE FUNCTION binary_search WITH PRED
template<class _FwdIt,
	class _Ty,
	class _Pr> inline
	bool binary_search(_FwdIt _First, _FwdIt _Last,
		const _Ty& _Val, _Pr _Pred)
	{	// test if _Val equivalent to some element, using _Pred
	_First = std::lower_bound(_First, _Last, _Val, _Pred);
	return (_First != _Last && !_Pred(_Val, *_First));
	}

		// TEMPLATE FUNCTION merge
template<class _InIt1,
	class _InIt2,
	class _OutIt> inline
	_OutIt merge(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest)
	{	// copy merging ranges, both using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; ++_Dest)
		if (*_First2 < *_First1)
			*_Dest = *_First2, ++_First2;
		else
			*_Dest = *_First1, ++_First1;

	_Dest = std::copy(_First1, _Last1, _Dest);	// copy any tail
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION merge WITH PRED
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Pr> inline
	_OutIt merge(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest, _Pr _Pred)
	{	//  copy merging ranges, both using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; ++_Dest)
		if (_Pred(*_First2, *_First1))
			*_Dest = *_First2, ++_First2;
		else
			*_Dest = *_First1, ++_First1;

	_Dest = std::copy(_First1, _Last1, _Dest);	// copy any tail
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION inplace_merge
template<class _BidIt,
	class _Diff,
	class _Ty> inline
	_BidIt _Buffered_rotate(_BidIt _First, _BidIt _Mid, _BidIt _Last,
		_Diff _Count1, _Diff _Count2, _Temp_iterator<_Ty>& _Tempbuf)
	{	// rotate [_First, _Last) using temp buffer
	if (_Count1 <= _Count2 && _Count1 <= _Tempbuf._Maxlen())
		{	// buffer left partition, then copy parts
		std::copy(_First, _Mid, _Tempbuf._Init());
		std::copy(_Mid, _Last, _First);
		return (std::copy_backward(_Tempbuf._First(), _Tempbuf._Last(),
			_Last));
		}
	else if (_Count2 <= _Tempbuf._Maxlen())
		{	// buffer right partition, then copy parts
		std::copy(_Mid, _Last, _Tempbuf._Init());
		std::copy_backward(_First, _Mid, _Last);
		return (std::copy(_Tempbuf._First(), _Tempbuf._Last(), _First));
		}
	else
		{	// buffer too small, rotate in place
		std::rotate(_First, _Mid, _Last);
		std::advance(_First, _Count2);
		return (_First);
		}
	}

template<class _BidIt1,
	class _BidIt2,
	class _BidIt3> inline
	_BidIt3 _Merge_backward(_BidIt1 _First1, _BidIt1 _Last1,
		_BidIt2 _First2, _BidIt2 _Last2, _BidIt3 _Dest)
	{	// merge backwards to _Dest, using operator<
	for (; ; )
		if (_First1 == _Last1)
			return (std::copy_backward(_First2, _Last2, _Dest));
		else if (_First2 == _Last2)
			return (std::copy_backward(_First1, _Last1, _Dest));
		else if (*--_Last2 < *--_Last1)
			*--_Dest = *_Last1, ++_Last2;
		else
			*--_Dest = *_Last2, ++_Last1;
	}

template<class _BidIt,
	class _Diff,
	class _Ty> inline
	void _Buffered_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last,
		_Diff _Count1, _Diff _Count2,
			_Temp_iterator<_Ty>& _Tempbuf)
	{	// merge [_First, _Mid) with [_Mid, _Last), using operator<
	if (_Count1 + _Count2 == 2)
		{	// order two one-element partitions
		if (*_Mid < *_First)
			std::iter_swap(_First, _Mid);
		}
	else if (_Count1 <= _Count2 && _Count1 <= _Tempbuf._Maxlen())
		{	// buffer left partition, then merge
		std::copy(_First, _Mid, _Tempbuf._Init());
		std::merge(_Tempbuf._First(), _Tempbuf._Last(), _Mid, _Last, _First);
		}
	else if (_Count2 <= _Tempbuf._Maxlen())
		{	// buffer right partition, then merge
		std::copy(_Mid, _Last, _Tempbuf._Init());
		_Merge_backward(_First, _Mid,
			_Tempbuf._First(), _Tempbuf._Last(), _Last);
		}
	else
		{	// buffer too small, divide and conquer
		_BidIt _Firstn, _Lastn;
		_Diff _Count1n, _Count2n;

		if (_Count2 < _Count1)
			{	// left larger, cut it in half and partition right to match
			_Count1n = _Count1 / 2, _Count2n = 0;
			_Firstn = _First;
			std::advance(_Firstn, _Count1n);
			_Lastn = std::lower_bound(_Mid, _Last, *_Firstn);
			_Distance(_Mid, _Lastn, _Count2n);
			}
		else
			{	// right larger, cut it in half and partition left to match
			_Count1n = 0, _Count2n = _Count2 / 2;
			_Lastn = _Mid;
			std::advance(_Lastn, _Count2n);
			_Firstn = std::upper_bound(_First, _Mid, *_Lastn);
			_Distance(_First, _Firstn, _Count1n);
			}

		_BidIt _Midn = _Buffered_rotate(_Firstn, _Mid, _Lastn,
			_Count1 - _Count1n, _Count2n, _Tempbuf);	// rearrange middle
		_Buffered_merge(_First, _Firstn, _Midn,
			_Count1n, _Count2n, _Tempbuf);	// merge each new part
		_Buffered_merge(_Midn, _Lastn, _Last,
			_Count1 - _Count1n, _Count2 - _Count2n, _Tempbuf);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty> inline
	void _Inplace_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last,
		_Diff *, _Ty *)
	{	// merge [_First, _Mid) with [_Mid, _Last), using operator<
	_Diff _Count1 = 0;
	_Distance(_First, _Mid, _Count1);
	_Diff _Count2 = 0;
	_Distance(_Mid, _Last, _Count2);
	_Temp_iterator<_Ty> _Tempbuf(_Count1 < _Count2 ? _Count1 : _Count2);
	_Buffered_merge(_First, _Mid, _Last,
		_Count1, _Count2, _Tempbuf);
	}

template<class _BidIt> inline
	void inplace_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last)
	{	// merge [_First, _Mid) with [_Mid, _Last), using operator<
	if (_First != _Mid && _Mid != _Last)
		_Inplace_merge(_First, _Mid, _Last,
			_Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION inplace_merge WITH PRED
template<class _BidIt1,
	class _BidIt2,
	class _BidIt3,
	class _Pr> inline
	_BidIt3 _Merge_backward(_BidIt1 _First1, _BidIt1 _Last1,
		_BidIt2 _First2, _BidIt2 _Last2, _BidIt3 _Dest, _Pr _Pred)
	{	// merge backwards to _Dest, using _Pred
	for (; ; )
		if (_First1 == _Last1)
			return (std::copy_backward(_First2, _Last2, _Dest));
		else if (_First2 == _Last2)
			return (std::copy_backward(_First1, _Last1, _Dest));
		else if (_Pred(*--_Last2, *--_Last1))
			*--_Dest = *_Last1, ++_Last2;
		else
			*--_Dest = *_Last2, ++_Last1;
	}

template<class _BidIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Buffered_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last,
		_Diff _Count1, _Diff _Count2,
			_Temp_iterator<_Ty>& _Tempbuf, _Pr _Pred)
	{	// merge [_First, _Mid) with [_Mid, _Last), using _Pred
	if (_Count1 + _Count2 == 2)
		{	// order two one-element partitions
		if (_Pred(*_Mid, *_First))
			std::iter_swap(_First, _Mid);
		}
	else if (_Count1 <= _Count2 && _Count1 <= _Tempbuf._Maxlen())
		{	// buffer left partition, then merge
		std::copy(_First, _Mid, _Tempbuf._Init());
		std::merge(_Tempbuf._First(), _Tempbuf._Last(),
			_Mid, _Last, _First, _Pred);
		}
	else if (_Count2 <= _Tempbuf._Maxlen())
		{	// buffer right partition, then merge
		std::copy(_Mid, _Last, _Tempbuf._Init());
		_Merge_backward(_First, _Mid, _Tempbuf._First(), _Tempbuf._Last(),
			_Last, _Pred);
		}
	else
		{	// buffer too small, divide and conquer
		_BidIt _Firstn, _Lastn;
		_Diff _Count1n, _Count2n;
		if (_Count2 < _Count1)
			{	// left larger, cut it in half and partition right to match
			_Count1n = _Count1 / 2, _Count2n = 0;
			_Firstn = _First;
			std::advance(_Firstn, _Count1n);
			_Lastn = lower_bound(_Mid, _Last, *_Firstn, _Pred);
			_Distance(_Mid, _Lastn, _Count2n);
			}
		else
			{	// right larger, cut it in half and partition left to match
			_Count1n = 0, _Count2n = _Count2 / 2;
			_Lastn = _Mid;
			std::advance(_Lastn, _Count2n);
			_Firstn = upper_bound(_First, _Mid, *_Lastn, _Pred);
			_Distance(_First, _Firstn, _Count1n);
			}
		_BidIt _Midn = _Buffered_rotate(_Firstn, _Mid, _Lastn,
			_Count1 - _Count1n, _Count2n, _Tempbuf);	// rearrange middle
		_Buffered_merge(_First, _Firstn, _Midn,
			_Count1n, _Count2n, _Tempbuf, _Pred);	// merge each new part
		_Buffered_merge(_Midn, _Lastn, _Last,
			_Count1 - _Count1n, _Count2 - _Count2n, _Tempbuf, _Pred);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Inplace_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last, _Pr _Pred,
		_Diff *, _Ty *)
	{	// merge [_First, _Mid) with [_Mid, _Last), using _Pred
	_Diff _Count1 = 0;
	_Distance(_First, _Mid, _Count1);
	_Diff _Count2 = 0;
	_Distance(_Mid, _Last, _Count2);
	_Temp_iterator<_Ty> _Tempbuf(_Count1 < _Count2 ? _Count1 : _Count2);
	_Buffered_merge(_First, _Mid, _Last,
		_Count1, _Count2, _Tempbuf, _Pred);
	}

template<class _BidIt,
	class _Pr> inline
	void inplace_merge(_BidIt _First, _BidIt _Mid, _BidIt _Last, _Pr _Pred)
	{	// merge [_First, _Mid) with [_Mid, _Last), using _Pred
	if (_First != _Mid && _Mid != _Last)
		_Inplace_merge(_First, _Mid, _Last, _Pred,
			_Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION sort
template<class _BidIt> inline
	void _Insertion_sort(_BidIt _First, _BidIt _Last)
	{	// insertion sort [_First, _Last), using operator<
	if (_First != _Last)
		for (_BidIt _Next = _First; ++_Next != _Last; )
			if (*_Next < *_First)
				{	// found new earliest element, rotate to front
				_BidIt _Next1 = _Next;
				std::rotate(_First, _Next, ++_Next1);
				}
			else
				{	// look for insertion point after first
				_BidIt _Dest = _Next;
				for (_BidIt _Dest0 = _Dest; *_Next < *--_Dest0; )
					_Dest = _Dest0;
				if (_Dest != _Next)
					{	// rotate into place
					_BidIt _Next1 = _Next;
					std::rotate(_Dest, _Next, ++_Next1);
					}
				}
	}

template<class _RanIt> inline
	void _Med3(_RanIt _First, _RanIt _Mid, _RanIt _Last)
	{	// sort median of three elements to middle
	if (*_Mid < *_First)
		std::iter_swap(_Mid, _First);
	if (*_Last < *_Mid)
		std::iter_swap(_Last, _Mid);
	if (*_Mid < *_First)
		std::iter_swap(_Mid, _First);
	}

template<class _RanIt> inline
	void _Median(_RanIt _First, _RanIt _Mid, _RanIt _Last)
	{	// sort median element to middle
	if (40 < _Last - _First)
		{	// median of nine
		int _Step = (_Last - _First + 1) / 8;
		_Med3(_First, _First + _Step, _First + 2 * _Step);
		_Med3(_Mid - _Step, _Mid, _Mid + _Step);
		_Med3(_Last - 2 * _Step, _Last - _Step, _Last);
		_Med3(_First + _Step, _Mid, _Last - _Step);
		}
	else
		_Med3(_First, _Mid, _Last);
	}

template<class _RanIt> inline
	pair<_RanIt, _RanIt> _Unguarded_partition(_RanIt _First, _RanIt _Last)
	{	// partition [_First, _Last), using operator<
	_RanIt _Mid = _First + (_Last - _First) / 2;	// sort median to _Mid
	_Median(_First, _Mid, _Last - 1);
	_RanIt _Pfirst = _Mid;
	_RanIt _Plast = _Pfirst + 1;

	while (_First < _Pfirst
		&& !(*(_Pfirst - 1) < *_Pfirst)
		&& !(*_Pfirst < *(_Pfirst - 1)))
		--_Pfirst;
	while (_Plast < _Last
		&& !(*_Plast < *_Pfirst)
		&& !(*_Pfirst < *_Plast))
		++_Plast;

	_RanIt _Gfirst = _Plast;
	_RanIt _Glast = _Pfirst;

	for (; ; )
		{	// partition
		for (; _Gfirst < _Last; ++_Gfirst)
			if (*_Pfirst < *_Gfirst)
				;
			else if (*_Gfirst < *_Pfirst)
				break;
			else
				std::iter_swap(_Plast++, _Gfirst);
		for (; _First < _Glast; --_Glast)
			if (*(_Glast - 1) < *_Pfirst)
				;
			else if (*_Pfirst < *(_Glast - 1))
				break;
			else
				std::iter_swap(--_Pfirst, _Glast - 1);
		if (_Glast == _First && _Gfirst == _Last)
			return (pair<_RanIt, _RanIt>(_Pfirst, _Plast));

		if (_Glast == _First)
			{	// no room at bottom, rotate pivot upward
			if (_Plast != _Gfirst)
				std::iter_swap(_Pfirst, _Plast);
			++_Plast;
			std::iter_swap(_Pfirst++, _Gfirst++);
			}
		else if (_Gfirst == _Last)
			{	// no room at top, rotate pivot downward
			if (--_Glast != --_Pfirst)
				std::iter_swap(_Glast, _Pfirst);
			std::iter_swap(_Pfirst, --_Plast);
			}
		else
			std::iter_swap(_Gfirst++, --_Glast);
		}
	}

template<class _RanIt,
	class _Diff> inline
	void _Sort(_RanIt _First, _RanIt _Last, _Diff _Ideal)
	{	// order [_First, _Last), using operator<
	_Diff _Count;
	for (; _ISORT_MAX < (_Count = _Last - _First) && 0 < _Ideal; )
		{	// divide and conquer by quicksort
		pair<_RanIt, _RanIt> _Mid = _Unguarded_partition(_First, _Last);
		_Ideal /= 2, _Ideal += _Ideal / 2;	// allow 1.5 log2(N) divisions

		if (_Mid.first - _First < _Last - _Mid.second)	// loop on larger half
			_Sort(_First, _Mid.first, _Ideal), _First = _Mid.second;
		else
			_Sort(_Mid.second, _Last, _Ideal), _Last = _Mid.first;
		}

	if (_ISORT_MAX < _Count)
		{	// heap sort if too many divisions
		std::make_heap(_First, _Last);
		std::sort_heap(_First, _Last);
		}
	else if (1 < _Count)
		_Insertion_sort(_First, _Last);	// small, insertion sort
	}

template<class _RanIt> inline
	void sort(_RanIt _First, _RanIt _Last)
	{	// order [_First, _Last), using operator<
	_Sort(_First, _Last, _Last - _First);
	}

		// TEMPLATE FUNCTION sort WITH PRED
template<class _BidIt,
	class _Pr> inline
	void _Insertion_sort(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// insertion sort [_First, _Last), using _Pred
	if (_First != _Last)
		for (_BidIt _Next = _First; ++_Next != _Last; )
			if (_Pred(*_Next, *_First))
				{	// found new earliest element, rotate to front
				_BidIt _Next1 = _Next;
				std::rotate(_First, _Next, ++_Next1);
				}
			else
				{	// look for insertion point after first
				_BidIt _Dest = _Next;
				for (_BidIt _Dest0 = _Dest; _Pred(*_Next, *--_Dest0); )
					_Dest = _Dest0;
				if (_Dest != _Next)
					{	// rotate into place
					_BidIt _Next1 = _Next;
					std::rotate(_Dest, _Next, ++_Next1);
					}
				}
	}

template<class _RanIt,
	class _Pr> inline
	void _Med3(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Pr _Pred)
	{	// sort median of three elements to middle
	if (_Pred(*_Mid, *_First))
		std::iter_swap(_Mid, _First);
	if (_Pred(*_Last, *_Mid))
		std::iter_swap(_Last, _Mid);
	if (_Pred(*_Mid, *_First))
		std::iter_swap(_Mid, _First);
	}

template<class _RanIt,
	class _Pr> inline
	void _Median(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Pr _Pred)
	{	// sort median element to middle
	if (40 < _Last - _First)
		{	// median of nine
		int _Step = (_Last - _First + 1) / 8;
		_Med3(_First, _First + _Step, _First + 2 * _Step, _Pred);
		_Med3(_Mid - _Step, _Mid, _Mid + _Step, _Pred);
		_Med3(_Last - 2 * _Step, _Last - _Step, _Last, _Pred);
		_Med3(_First + _Step, _Mid, _Last - _Step, _Pred);
		}
	else
		_Med3(_First, _Mid, _Last, _Pred);
	}

template<class _RanIt,
	class _Pr> inline
	pair<_RanIt, _RanIt> _Unguarded_partition(_RanIt _First, _RanIt _Last,
		_Pr _Pred)
	{	// partition [_First, _Last), using _Pred
	_RanIt _Mid = _First + (_Last - _First) / 2;
	_Median(_First, _Mid, _Last - 1, _Pred);
	_RanIt _Pfirst = _Mid;
	_RanIt _Plast = _Pfirst + 1;

	while (_First < _Pfirst
		&& !_Pred(*(_Pfirst - 1), *_Pfirst)
		&& !_Pred(*_Pfirst, *(_Pfirst - 1)))
		--_Pfirst;
	while (_Plast < _Last
		&& !_Pred(*_Plast, *_Pfirst)
		&& !_Pred(*_Pfirst, *_Plast))
		++_Plast;

	_RanIt _Gfirst = _Plast;
	_RanIt _Glast = _Pfirst;

	for (; ; )
		{	// partition
		for (; _Gfirst < _Last; ++_Gfirst)
			if (_Pred(*_Pfirst, *_Gfirst))
				;
			else if (_Pred(*_Gfirst, *_Pfirst))
				break;
			else
				std::iter_swap(_Plast++, _Gfirst);
		for (; _First < _Glast; --_Glast)
			if (_Pred(*(_Glast - 1), *_Pfirst))
				;
			else if (_Pred(*_Pfirst, *(_Glast - 1)))
				break;
			else
				std::iter_swap(--_Pfirst, _Glast - 1);
		if (_Glast == _First && _Gfirst == _Last)
			return (pair<_RanIt, _RanIt>(_Pfirst, _Plast));

		if (_Glast == _First)
			{	// no room at bottom, rotate pivot upward
			if (_Plast != _Gfirst)
				std::iter_swap(_Pfirst, _Plast);
			++_Plast;
			std::iter_swap(_Pfirst++, _Gfirst++);
			}
		else if (_Gfirst == _Last)
			{	// no room at top, rotate pivot downward
			if (--_Glast != --_Pfirst)
				std::iter_swap(_Glast, _Pfirst);
			std::iter_swap(_Pfirst, --_Plast);
			}
		else
			std::iter_swap(_Gfirst++, --_Glast);
		}
	}

template<class _RanIt,
	class _Diff,
	class _Pr> inline
	void _Sort(_RanIt _First, _RanIt _Last, _Diff _Ideal, _Pr _Pred)
	{	// order [_First, _Last), using _Pred
	_Diff _Count;
	for (; _ISORT_MAX < (_Count = _Last - _First) && 0 < _Ideal; )
		{	// divide and conquer by quicksort
		pair<_RanIt, _RanIt> _Mid =
			_Unguarded_partition(_First, _Last, _Pred);
		_Ideal /= 2, _Ideal += _Ideal / 2;	// allow 1.5 log2(N) divisions

		if (_Mid.first - _First < _Last - _Mid.second)	// loop on larger half
			_Sort(_First, _Mid.first, _Ideal, _Pred), _First = _Mid.second;
		else
			_Sort(_Mid.second, _Last, _Ideal, _Pred), _Last = _Mid.first;
		}

	if (_ISORT_MAX < _Count)
		{	// heap sort if too many divisions
		std::make_heap(_First, _Last, _Pred);
		std::sort_heap(_First, _Last, _Pred);
		}
	else if (1 < _Count)
		_Insertion_sort(_First, _Last, _Pred);	// small, insertion sort
	}

template<class _RanIt,
	class _Pr> inline
	void sort(_RanIt _First, _RanIt _Last, _Pr _Pred)
	{	// order [_First, _Last), using _Pred
	_Sort(_First, _Last, _Last - _First, _Pred);
	}

		// TEMPLATE FUNCTION stable_sort
template<class _BidIt,
	class _OutIt,
	class _Diff> inline
	void _Chunked_merge(_BidIt _First, _BidIt _Last, _OutIt _Dest,
		_Diff _Chunk, _Diff _Count)
	{	// copy merging chunks, using operator<
	for (_Diff _Chunk2 = _Chunk * 2; _Chunk2 <= _Count; _Count -= _Chunk2)
		{	// copy merging pairs of adjacent chunks
		_BidIt _Mid1 = _First;
		std::advance(_Mid1, _Chunk);
		_BidIt _Mid2 = _Mid1;
		std::advance(_Mid2, _Chunk);

		_Dest = std::merge(_First, _Mid1, _Mid1, _Mid2, _Dest);
		_First = _Mid2;
		}

	if (_Count <= _Chunk)
		std::copy(_First, _Last, _Dest);	// copy partial last chunk
	else
		{	// copy merging whole and partial last chunk
		_BidIt _Mid = _First;
		std::advance(_Mid, _Chunk);

		std::merge(_First, _Mid, _Mid, _Last, _Dest);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty> inline
	void _Buffered_merge_sort(_BidIt _First, _BidIt _Last, _Diff _Count,
		_Temp_iterator<_Ty>& _Tempbuf)
	{	// sort using temp buffer for merges, using operator<
	_BidIt _Mid = _First;
	for (_Diff _Nleft = _Count; _ISORT_MAX <= _Nleft; _Nleft -= _ISORT_MAX)
		{	// sort chunks
		_BidIt _Midend = _Mid;
		std::advance(_Midend, (int)_ISORT_MAX);

		_Insertion_sort(_Mid, _Midend);
		_Mid = _Midend;
		}
	_Insertion_sort(_Mid, _Last);	// sort partial last chunk

	for (_Diff _Chunk = _ISORT_MAX; _Chunk < _Count; _Chunk *= 2)
		{	// merge adjacent pairs of chunks to and from temp buffer
		_Chunked_merge(_First, _Last, _Tempbuf._Init(),
			_Chunk, _Count);
		_Chunked_merge(_Tempbuf._First(), _Tempbuf._Last(), _First,
			_Chunk *= 2, _Count);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty> inline
	void _Stable_sort(_BidIt _First, _BidIt _Last, _Diff _Count,
		_Temp_iterator<_Ty>& _Tempbuf)
	{	//  sort preserving order of equivalents, using operator<
	if (_Count <= _ISORT_MAX)
		_Insertion_sort(_First, _Last);	// small, insertion sort
	else
		{	// sort halves and merge
		_Diff _Count2 = (_Count + 1) / 2;
		_BidIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (_Count2 <= _Tempbuf._Maxlen())
			{	// temp buffer big enough, sort each half using buffer
			_Buffered_merge_sort(_First, _Mid, _Count2, _Tempbuf);
			_Buffered_merge_sort(_Mid, _Last, _Count - _Count2, _Tempbuf);
			}
		else
			{	// temp buffer not big enough, divide and conquer
			_Stable_sort(_First, _Mid, _Count2, _Tempbuf);
			_Stable_sort(_Mid, _Last, _Count - _Count2, _Tempbuf);
			}

		_Buffered_merge(_First, _Mid, _Last,
			_Count2, _Count - _Count2, _Tempbuf);	// merge sorted halves
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty> inline
	void _Stable_sort(_BidIt _First, _BidIt _Last, _Diff *, _Ty *)
	{	// sort preserving order of equivalents, using operator<
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	_Temp_iterator<_Ty> _Tempbuf(_Count);
	_Stable_sort(_First, _Last, _Count, _Tempbuf);
	}

template<class _BidIt> inline
	void stable_sort(_BidIt _First, _BidIt _Last)
	{	// sort preserving order of equivalents, using operator<
	if (_First != _Last)
		_Stable_sort(_First, _Last, _Dist_type(_First), _Val_type(_First));
	}

		// TEMPLATE FUNCTION stable_sort WITH PRED
template<class _BidIt,
	class _OutIt,
	class _Diff,
	class _Pr> inline
	void _Chunked_merge(_BidIt _First, _BidIt _Last, _OutIt _Dest,
		_Diff _Chunk, _Diff _Count, _Pr _Pred)
	{	// copy merging chunks, using _Pred
	for (_Diff _Chunk2 = _Chunk * 2; _Chunk2 <= _Count; _Count -= _Chunk2)
		{	// copy merging pairs of adjacent chunks
		_BidIt _Mid1 = _First;
		std::advance(_Mid1, _Chunk);
		_BidIt _Mid2 = _Mid1;
		std::advance(_Mid2, _Chunk);

		_Dest = std::merge(_First, _Mid1, _Mid1, _Mid2, _Dest, _Pred);
		_First = _Mid2;
		}

	if (_Count <= _Chunk)
		std::copy(_First, _Last, _Dest);	// copy partial last chunk
	else
		{	// copy merging whole and partial last chunk
		_BidIt _Mid1 = _First;
		std::advance(_Mid1, _Chunk);

		std::merge(_First, _Mid1, _Mid1, _Last, _Dest, _Pred);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Buffered_merge_sort(_BidIt _First, _BidIt _Last, _Diff _Count,
		_Temp_iterator<_Ty>& _Tempbuf, _Pr _Pred)
	{	// sort using temp buffer for merges, using _Pred
	_BidIt _Mid = _First;
	for (_Diff _Nleft = _Count; _ISORT_MAX <= _Nleft; _Nleft -= _ISORT_MAX)
		{	// sort chunks
		_BidIt _Midn = _Mid;
		std::advance(_Midn, (int)_ISORT_MAX);

		_Insertion_sort(_Mid, _Midn, _Pred);
		_Mid = _Midn;
		}
	_Insertion_sort(_Mid, _Last, _Pred);	// sort partial last chunk

	for (_Diff _Chunk = _ISORT_MAX; _Chunk < _Count; _Chunk *= 2)
		{	// merge adjacent pairs of chunks to and from temp buffer
		_Chunked_merge(_First, _Last, _Tempbuf._Init(),
			_Chunk, _Count, _Pred);
		_Chunked_merge(_Tempbuf._First(), _Tempbuf._Last(), _First,
			_Chunk *= 2, _Count, _Pred);
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Stable_sort(_BidIt _First, _BidIt _Last, _Diff _Count,
		_Temp_iterator<_Ty>& _Tempbuf, _Pr _Pred)
	{	// sort preserving order of equivalents, using _Pred
	if (_Count <= _ISORT_MAX)
		_Insertion_sort(_First, _Last, _Pred);	// small, insertion sort
	else
		{	// sort halves and merge
		_Diff _Count2 = (_Count + 1) / 2;
		_BidIt _Mid = _First;
		std::advance(_Mid, _Count2);

		if (_Count2 <= _Tempbuf._Maxlen())
			{	// temp buffer big enough, sort each half using buffer
			_Buffered_merge_sort(_First, _Mid, _Count2, _Tempbuf, _Pred);
			_Buffered_merge_sort(_Mid, _Last, _Count - _Count2,
				_Tempbuf, _Pred);
			}
		else
			{	// temp buffer not big enough, divide and conquer
			_Stable_sort(_First, _Mid, _Count2, _Tempbuf, _Pred);
			_Stable_sort(_Mid, _Last, _Count - _Count2, _Tempbuf, _Pred);
			}

		_Buffered_merge(_First, _Mid, _Last,
			_Count2, _Count - _Count2, _Tempbuf, _Pred);	// merge halves
		}
	}

template<class _BidIt,
	class _Diff,
	class _Ty,
	class _Pr> inline
	void _Stable_sort(_BidIt _First, _BidIt _Last, _Diff *, _Ty *, _Pr _Pred)
	{	// sort preserving order of equivalents, using _Pred
	_Diff _Count = 0;
	_Distance(_First, _Last, _Count);
	_Temp_iterator<_Ty> _Tempbuf(_Count);
	_Stable_sort(_First, _Last, _Count, _Tempbuf, _Pred);
	}

template<class _BidIt,
	class _Pr> inline
	void stable_sort(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// sort preserving order of equivalents, using _Pred
	if (_First != _Last)
		_Stable_sort(_First, _Last,
			_Dist_type(_First), _Val_type(_First), _Pred);
	}

		// TEMPLATE FUNCTION partial_sort
template<class _RanIt,
	class _Ty> inline
	void _Partial_sort(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Ty *)
	{	// order [First, _Last) up to _Mid, using operator<
	std::make_heap(_First, _Mid);

	for (_RanIt _Next = _Mid; _Next < _Last; ++_Next)
		if (*_Next < *_First)
			_Pop_heap(_First, _Mid, _Next, _Ty(*_Next),
				_Dist_type(_First));	// replace top with new largest
	std::sort_heap(_First, _Mid);
	}

template<class _RanIt> inline
	void partial_sort(_RanIt _First, _RanIt _Mid, _RanIt _Last)
	{	// order [First, _Last) up to _Mid, using operator<
	_Partial_sort(_First, _Mid, _Last, _Val_type(_First));
	}

		// TEMPLATE FUNCTION partial_sort WITH PRED
template<class _RanIt,
	class _Ty,
	class _Pr> inline
	void _Partial_sort(_RanIt _First, _RanIt _Mid, _RanIt _Last,
		_Pr _Pred, _Ty *)
	{	// order [First, _Last) up to _Mid, using _Pred
	std::make_heap(_First, _Mid, _Pred);

	for (_RanIt _Next = _Mid; _Next < _Last; ++_Next)
		if (_Pred(*_Next, *_First))
			_Pop_heap(_First, _Mid, _Next, _Ty(*_Next), _Pred,
				_Dist_type(_First));	// replace top with new largest
	std::sort_heap(_First, _Mid, _Pred);
	}

template<class _RanIt,
	class _Pr> inline
	void partial_sort(_RanIt _First, _RanIt _Mid, _RanIt _Last, _Pr _Pred)
	{	// order [First, _Last) up to _Mid, using _Pred
	_Partial_sort(_First, _Mid, _Last, _Pred, _Val_type(_First));
	}

		// TEMPLATE FUNCTION partial_sort_copy
template<class _InIt,
	class _RanIt,
	class _Diff,
	class _Ty> inline
	_RanIt _Partial_sort_copy(_InIt _First1, _InIt _Last1,
		_RanIt _First2, _RanIt _Last2, _Diff *, _Ty *)
	{	// copy [First1, _Last1) into [_First2, _Last2), using operator<
	_RanIt _Mid2 = _First2;
	for (; _First1 != _Last1 && _Mid2 != _Last2; ++_First1, ++_Mid2)
		*_Mid2 = *_First1;	// copy min(_Last1 - _First1, _Last2 - _First2)
	std::make_heap(_First2, _Mid2);

	for (; _First1 != _Last1; ++_First1)
		if (*_First1 < *_First2)
			_Adjust_heap(_First2, _Diff(0), _Diff(_Mid2 - _First2),
				_Ty(*_First1));	// replace top with new largest

	std::sort_heap(_First2, _Mid2);
	return (_Mid2);
	}

template<class _InIt,
	class _RanIt> inline
	_RanIt partial_sort_copy(_InIt _First1, _InIt _Last1,
		_RanIt _First2, _RanIt _Last2)
	{	// copy [First1, _Last1) into [_First2, _Last2), using operator<
	return (_First1 == _Last1 || _First2 == _Last2 ? _First2
		: _Partial_sort_copy(_First1, _Last1, _First2, _Last2,
			_Dist_type(_First2), _Val_type(_First1)));
	}

		// TEMPLATE FUNCTION partial_sort_copy WITH PRED
template<class _InIt,
	class _RanIt,
	class _Diff,
	class _Ty, class _Pr> inline
	_RanIt _Partial_sort_copy(_InIt _First1, _InIt _Last1,
		_RanIt _First2, _RanIt _Last2, _Pr _Pred, _Diff *, _Ty *)
	{	// copy [First1, _Last1) into [_First2, _Last2) using _Pred
	_RanIt _Mid2 = _First2;
	for (; _First1 != _Last1 && _Mid2 != _Last2; ++_First1, ++_Mid2)
		*_Mid2 = *_First1;	// copy min(_Last1 - _First1, _Last2 - _First2)
	std::make_heap(_First2, _Mid2, _Pred);

	for (; _First1 != _Last1; ++_First1)
		if (_Pred(*_First1, *_First2))
			_Adjust_heap(_First2, _Diff(0), _Diff(_Mid2 - _First2),
				_Ty(*_First1), _Pred);	// replace top with new largest

	std::sort_heap(_First2, _Mid2, _Pred);
	return (_Mid2);
	}

template<class _InIt,
	class _RanIt,
	class _Pr> inline
	_RanIt partial_sort_copy(_InIt _First1, _InIt _Last1,
		_RanIt _First2, _RanIt _Last2, _Pr _Pred)
	{	// copy [First1, _Last1) into [_First2, _Last2) using _Pred
	return (_First1 == _Last1 || _First2 == _Last2 ? _First2
		: _Partial_sort_copy(_First1, _Last1, _First2, _Last2, _Pred,
			_Dist_type(_First2), _Val_type(_First1)));
	}

		// TEMPLATE FUNCTION nth_element
template<class _RanIt> inline
	void nth_element(_RanIt _First, _RanIt _Nth, _RanIt _Last)
	{	// order Nth element, using operator<
	for (; _ISORT_MAX < _Last - _First; )
		{	// divide and conquer, ordering partition containing Nth
		pair<_RanIt, _RanIt> _Mid =
			_Unguarded_partition(_First, _Last);

		if (_Mid.second <= _Nth)
			_First = _Mid.second;
		else if (_Mid.first <= _Nth)
			return;	// Nth inside fat pivot, done
		else
			_Last = _Mid.first;
		}

	_Insertion_sort(_First, _Last);	// sort any remainder
	}

		// TEMPLATE FUNCTION nth_element WITH PRED
template<class _RanIt,
	class _Pr> inline
	void nth_element(_RanIt _First, _RanIt _Nth, _RanIt _Last, _Pr _Pred)
	{	// order Nth element, using _Pred
	for (; _ISORT_MAX < _Last - _First; )
		{	// divide and conquer, ordering partition containing Nth
		pair<_RanIt, _RanIt> _Mid =
			_Unguarded_partition(_First, _Last, _Pred);

		if (_Mid.second <= _Nth)
			_First = _Mid.second;
		else if (_Mid.first <= _Nth)
			return;	// Nth inside fat pivot, done
		else
			_Last = _Mid.first;
		}

	_Insertion_sort(_First, _Last, _Pred);	// sort any remainder
	}

		// TEMPLATE FUNCTION includes
template<class _InIt1,
	class _InIt2> inline
	bool includes(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2)
	{	// test if all [_First1, _Last1) in [_First2, _Last2), using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (*_First2 < *_First1)
			return (false);
		else if (*_First1 < *_First2)
			++_First1;
		else
			++_First1, ++_First2;
	return (_First2 == _Last2);
	}

		// TEMPLATE FUNCTION includes WITH PRED
template<class _InIt1,
	class _InIt2,
	class _Pr> inline
	bool includes(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _Pr _Pred)
	{	// test if set [_First1, _Last1) in [_First2, _Last2), using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (_Pred(*_First2, *_First1))
			return (false);
		else if (_Pred(*_First1, *_First2))
			++_First1;
		else
			++_First1, ++_First2;
	return (_First2 == _Last2);
	}

		// TEMPLATE FUNCTION set_union
template<class _InIt1,
	class _InIt2,
	class _OutIt> inline
	_OutIt set_union(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest)
	{	// OR sets [_First1, _Last1) and [_First2, _Last2), using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (*_First1 < *_First2)
			*_Dest++ = *_First1, ++_First1;
		else if (*_First2 < *_First1)
			*_Dest++ = *_First2, ++_First2;
		else
			*_Dest++ = *_First1, ++_First1, ++_First2;
	_Dest = std::copy(_First1, _Last1, _Dest);
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION set_union WITH PRED
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Pr> inline
	_OutIt set_union(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest, _Pr _Pred)
	{	// OR sets [_First1, _Last1) and [_First2, _Last2), using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (_Pred(*_First1, *_First2))
			*_Dest++ = *_First1, ++_First1;
		else if (_Pred(*_First2, *_First1))
			*_Dest++ = *_First2, ++_First2;
		else
			*_Dest++ = *_First1, ++_First1, ++_First2;
	_Dest = std::copy(_First1, _Last1, _Dest);
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION set_intersection
template<class _InIt1,
	class _InIt2,
	class _OutIt> inline
	_OutIt set_intersection(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest)
	{	// AND sets [_First1, _Last1) and [_First2, _Last2), using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (*_First1 < *_First2)
			++_First1;
		else if (*_First2 < *_First1)
			++_First2;
		else
			*_Dest++ = *_First1++, ++_First2;
	return (_Dest);
	}

		// TEMPLATE FUNCTION set_intersection WITH PRED
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Pr> inline
	_OutIt set_intersection(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest, _Pr _Pred)
	{	// AND sets [_First1, _Last1) and [_First2, _Last2), using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (_Pred(*_First1, *_First2))
			++_First1;
		else if (_Pred(*_First2, *_First1))
			++_First2;
		else
			*_Dest++ = *_First1++, ++_First2;
	return (_Dest);
	}

		// TEMPLATE FUNCTION set_difference
template<class _InIt1,
	class _InIt2,
	class _OutIt> inline
	_OutIt set_difference(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2,	_OutIt _Dest)
	{	// take set [_First2, _Last2) from [_First1, _Last1), using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (*_First1 < *_First2)
			*_Dest++ = *_First1, ++_First1;
		else if (*_First2 < *_First1)
			++_First2;
		else
			++_First1, ++_First2;
	return (std::copy(_First1, _Last1, _Dest));
	}

		// TEMPLATE FUNCTION set_difference WITH PRED
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Pr> inline
	_OutIt set_difference(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest, _Pr _Pred)
	{	//  take set [_First2, _Last2) from [_First1, _Last1), using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (_Pred(*_First1, *_First2))
			*_Dest++ = *_First1, ++_First1;
		else if (_Pred(*_First2, *_First1))
			++_First2;
		else
			++_First1, ++_First2;
	return (std::copy(_First1, _Last1, _Dest));
	}

		// TEMPLATE FUNCTION set_symmetric_difference
template<class _InIt1,
	class _InIt2,
	class _OutIt> inline
	_OutIt set_symmetric_difference(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest)
	{	// XOR sets [_First1, _Last1) and [_First2, _Last2), using operator<
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (*_First1 < *_First2)
			*_Dest++ = *_First1, ++_First1;
		else if (*_First2 < *_First1)
			*_Dest++ = *_First2, ++_First2;
		else
			++_First1, ++_First2;
	_Dest = std::copy(_First1, _Last1, _Dest);
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION set_symmetric_difference WITH PRED
template<class _InIt1,
	class _InIt2,
	class _OutIt,
	class _Pr> inline
	_OutIt set_symmetric_difference(_InIt1 _First1, _InIt1 _Last1,
		_InIt2 _First2, _InIt2 _Last2, _OutIt _Dest, _Pr _Pred)
	{	// XOR sets [_First1, _Last1) and [_First2, _Last2), using _Pred
	for (; _First1 != _Last1 && _First2 != _Last2; )
		if (_Pred(*_First1, *_First2))
			*_Dest++ = *_First1, ++_First1;
		else if (_Pred(*_First2, *_First1))
			*_Dest++ = *_First2, ++_First2;
		else
			++_First1, ++_First2;
	_Dest = std::copy(_First1, _Last1, _Dest);
	return (std::copy(_First2, _Last2, _Dest));
	}

		// TEMPLATE FUNCTION max_element
template<class _FwdIt> inline
	_FwdIt max_element(_FwdIt _First, _FwdIt _Last)
	{	// find largest element, using operator<
	_FwdIt _Found = _First;
	if (_First != _Last)
		for (; ++_First != _Last; )
			if (*_Found < *_First)
				_Found = _First;
	return (_Found);
	}

		// TEMPLATE FUNCTION max_element WITH PRED
template<class _FwdIt,
	class _Pr> inline
	_FwdIt max_element(_FwdIt _First, _FwdIt _Last, _Pr _Pred)
	{	// find largest element, using _Pred
	_FwdIt _Found = _First;
	if (_First != _Last)
		for (; ++_First != _Last; )
			if (_Pred(*_Found, *_First))
				_Found = _First;
	return (_Found);
	}

		// TEMPLATE FUNCTION min_element
template<class _FwdIt> inline
	_FwdIt min_element(_FwdIt _First, _FwdIt _Last)
	{	// find smallest element, using operator<
	_FwdIt _Found = _First;
	if (_First != _Last)
		for (; ++_First != _Last; )
			if (*_First < *_Found)
				_Found = _First;
	return (_Found);
	}

		// TEMPLATE FUNCTION min_element WITH PRED
template<class _FwdIt,
	class _Pr> inline
	_FwdIt min_element(_FwdIt _First, _FwdIt _Last, _Pr _Pred)
	{	// find smallest element, using _Pred
	_FwdIt _Found = _First;
	if (_First != _Last)
		for (; ++_First != _Last; )
			if (_Pred(*_First, *_Found))
				_Found = _First;
	return (_Found);
	}

		// TEMPLATE FUNCTION next_permutation
template<class _BidIt> inline
	bool next_permutation(_BidIt _First, _BidIt _Last)
	{	// permute and test for pure ascending, using operator<
	_BidIt _Next = _Last;
	if (_First == _Last || _First == --_Next)
		return (false);

	for (; ; )
		{	// find rightmost element smaller than successor
		_BidIt _Next1 = _Next;
		if (*--_Next < *_Next1)
			{	// swap with rightmost element that's smaller, flip suffix
			_BidIt _Mid = _Last;
			for (; !(*_Next < *--_Mid); )
				;
			std::iter_swap(_Next, _Mid);
			std::reverse(_Next1, _Last);
			return (true);
			}

		if (_Next == _First)
			{	// pure descending, flip all
			std::reverse(_First, _Last);
			return (false);
			}
		}
	}

		// TEMPLATE FUNCTION next_permutation WITH PRED
template<class _BidIt,
	class _Pr> inline
	bool next_permutation(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// permute and test for pure ascending, using _Pred
	_BidIt _Next = _Last;
	if (_First == _Last || _First == --_Next)
		return (false);

	for (; ; )
		{	// find rightmost element smaller than successor
		_BidIt _Next1 = _Next;
		if (_Pred(*--_Next, *_Next1))
			{	// swap with rightmost element that's smaller, flip suffix
			_BidIt _Mid = _Last;
			for (; !_Pred(*_Next, *--_Mid); )
				;
			std::iter_swap(_Next, _Mid);
			std::reverse(_Next1, _Last);
			return (true);
			}

		if (_Next == _First)
			{	// pure descending, flip all
			std::reverse(_First, _Last);
			return (false);
			}
		}
	}

		// TEMPLATE FUNCTION prev_permutation
template<class _BidIt> inline
	bool prev_permutation(_BidIt _First, _BidIt _Last)
	{	// reverse permute and test for pure descending, using operator<
	_BidIt _Next = _Last;
	if (_First == _Last || _First == --_Next)
		return (false);
	for (; ; )
		{	// find rightmost element not smaller than successor
		_BidIt _Next1 = _Next;
		if (!(*--_Next < *_Next1))
			{	// swap with rightmost element that's not smaller, flip suffix
			_BidIt _Mid = _Last;
			for (; *_Next < *--_Mid; )
				;
			std::iter_swap(_Next, _Mid);
			std::reverse(_Next1, _Last);
			return (true);
			}

		if (_Next == _First)
			{	// pure ascending, flip all
			std::reverse(_First, _Last);
			return (false);
			}
		}
	}

		// TEMPLATE FUNCTION prev_permutation WITH PRED
template<class _BidIt,
	class _Pr> inline
	bool prev_permutation(_BidIt _First, _BidIt _Last, _Pr _Pred)
	{	// reverse permute and test for pure descending, using _Pred
	_BidIt _Next = _Last;
	if (_First == _Last || _First == --_Next)
		return (false);

	for (; ; )
		{	// find rightmost element not smaller than successor
		_BidIt _Next1 = _Next;
		if (!_Pred(*--_Next, *_Next1))
			{	// swap with rightmost element that's not smaller, flip suffix
			_BidIt _Mid = _Last;
			for (; _Pred(*_Next, *--_Mid); )
				;
			std::iter_swap(_Next, _Mid);
			std::reverse(_Next1, _Last);
			return (true);
			}

		if (_Next == _First)
			{	// pure ascending, flip all
			std::reverse(_First, _Last);
			return (false);
			}
		}
	}
_STD_END
  #pragma warning(default: 4244)
#pragma warning(pop)
#pragma pack(pop)

#endif /* _ALGORITHM_ */

/*
* Copyright (c) 1992-2001 by P.J. Plauger.  ALL RIGHTS RESERVED.
 * Consult your license regarding permissions and restrictions.
 */

/*
 * This file is derived from software bearing the following
 * restrictions:
 *
 * Copyright (c) 1994
 * Hewlett-Packard Company
 *
 * Permission to use, copy, modify, distribute and sell this
 * software and its documentation for any purpose is hereby
 * granted without fee, provided that the above copyright notice
 * appear in all copies and that both that copyright notice and
 * this permission notice appear in supporting documentation.
 * Hewlett-Packard Company makes no representations about the
 * suitability of this software for any purpose. It is provided
 * "as is" without express or implied warranty.
 V3.10:0009 */