// 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);
  }

    // 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);
  }


    // 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 preserving order of equivalents, using _Pred
  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 onto heap at [_First, _Last), using operator<
  _Diff _Count = _Last - _First;
  if (0 < _Count)
    _Push_heap(_First, _Count, _Diff(0), _Ty(*_Last));
  }

template<class _RanIt> inline
  void push_heap(_RanIt _First, _RanIt _Last)
  { // push *(_Last - 1) onto heap at [_First, _Last - 1), using operator<
  if (_First != _Last)
    _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 onto heap at [_First, _Last), using _Pred
  _Diff _Count = _Last - _First;
  if (0 < _Count)
    _Push_heap(_First, _Count, _Diff(0), _Ty(*_Last), _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
  if (_First != _Last)
    _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) 1992-2002 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.
 V3.13:0009 */