// Algorithm implementation -*- C++ -*-

// Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.

/*
 *
 * 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.
 *
 *
 * Copyright (c) 1996
 * Silicon Graphics Computer Systems, Inc.
 *
 * 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.  Silicon Graphics makes no
 * representations about the suitability of this software for any
 * purpose.  It is provided "as is" without express or implied warranty.
 */

/** @file stl_algo.h
 *  This is an internal header file, included by other library headers.
 *  You should not attempt to use it directly.
 */

#ifndef _ALGO_H
#define _ALGO_H 1

#include <bits/stl_heap.h>
#include <bits/stl_tempbuf.h>  // for _Temporary_buffer
#include <cstdlib>             // for rand
#include <debug/debug.h>
#include <bits/concepts.h>

_GLIBCXX_BEGIN_NAMESPACE(std)

  template<InputIterator _InIter, typename _OutIter>
    requires HasStdMove<_InIter::reference>
          && OutputIterator<_OutIter, HasStdMove<_InIter::reference>::result_type>
    _OutIter move(_InIter __first, _InIter __last, _OutIter __result)
    {
      for (; __first != __last; ++__first, ++__result)
        *__result = std_move(*__first);
      return __result;
    }

  template<BidirectionalIterator _InIter, BidirectionalIterator _OutIter>
    requires HasStdMove<_InIter::reference>
          && OutputIterator<_OutIter, HasStdMove<_InIter::reference>::result_type>
    _OutIter move_backward(_InIter __first, _InIter __last, _OutIter __result)
    {
      while (__first != __last)
        *--__result = std_move(*--__last);
      return __result;
    }

  /**
   *  @brief Find the median of three values.
   *  @param  a  A value.
   *  @param  b  A value.
   *  @param  c  A value.
   *  @return One of @p a, @p b or @p c.
   *
   *  If @c {l,m,n} is some convolution of @p {a,b,c} such that @c l<=m<=n
   *  then the value returned will be @c m.
   *  This is an SGI extension.
   *  @ingroup SGIextensions
  */
  template<_GLIBCXX_REQ_PARM(LessThanComparable, _Tp)>
    inline const _Tp&
    __median(const _Tp& __a, const _Tp& __b, const _Tp& __c)
    {
      if (__a < __b)
        if (__b < __c)
          return __b;
        else if (__a < __c)
          return __c;
        else
          return __a;
      else if (__a < __c)
        return __a;
      else if (__b < __c)
        return __c;
      else
        return __b;
    }

  /**
   *  @brief Find the median of three values using a predicate for comparison.
   *  @param  a     A value.
   *  @param  b     A value.
   *  @param  c     A value.
   *  @param  comp  A binary predicate.
   *  @return One of @p a, @p b or @p c.
   *
   *  If @c {l,m,n} is some convolution of @p {a,b,c} such that @p comp(l,m)
   *  and @p comp(m,n) are both true then the value returned will be @c m.
   *  This is an SGI extension.
   *  @ingroup SGIextensions
  */
  template<typename _Tp, 
           _GLIBCXX_PARM_REQ(_Compare, BinaryPredicate<_Tp, _Tp>)>
    inline const _Tp&
    __median(const _Tp& __a, const _Tp& __b, const _Tp& __c, _Compare __comp)
    {
      if (__comp(__a, __b))
        if (__comp(__b, __c))
          return __b;
        else if (__comp(__a, __c))
          return __c;
        else
          return __a;
      else if (__comp(__a, __c))
        return __a;
      else if (__comp(__b, __c))
        return __c;
      else
        return __b;
    }

  /**
   *  @brief Apply a function to every element of a sequence.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  f      A unary function object.
   *  @return   @p f.
   *
   *  Applies the function object @p f to each element in the range
   *  @p [first,last).  @p f must not modify the order of the sequence.
   *  If @p f has a return value it is ignored.
  */
  template<InputIterator _Iter, Callable1<auto, _Iter::reference> _Function>
    requires CopyConstructible<_Function>
    _Function
    for_each(_Iter __first, _Iter __last, _Function __f)
    {
      __glibcxx_requires_valid_range(__first, __last);
      for ( ; __first != __last; ++__first)
        __f(*__first);
      return __f;
    }

  /**
   *  @brief Find the first occurrence of a value in a sequence.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  val    The value to find.
   *  @return   The first iterator @c i in the range @p [first,last)
   *  such that @c *i == @p val, or @p last if no such iterator exists.
  */
  template<InputIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
    inline _Iter
    find(_Iter __first, _Iter __last, const _Tp& __val)
    {
      while (__first != __last && !(*__first == __val))
        ++__first;
      return __first;
    }

  /**
   *  @brief Find the first element in a sequence for which a predicate is true.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  pred   A predicate.
   *  @return   The first iterator @c i in the range @p [first,last)
   *  such that @p pred(*i) is true, or @p last if no such iterator exists.
  */
  template<InputIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    requires CopyConstructible<_Pred>
    inline _Iter
    find_if(_Iter __first, _Iter __last, _Pred __pred)
    {
      while (__first != __last && !__pred(*__first))
        ++__first;
      return __first;
    }

  /**
   *  @brief Find the first occurrence of a value in a sequence.
   *
   *  This version of the algorithm is optimized for random access
   *  iterators.
   *
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  val    The value to find.
   *  @return   The first iterator @c i in the range @p [first,last)
   *  such that @c *i == @p val, or @p last if no such iterator exists.
  */
  template<RandomAccessIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
    _Iter
    find(_Iter __first, _Iter __last, const _Tp& __val)
    {
      _Iter::difference_type __trip_count = (__last - __first) >> 2;

      for ( ; __trip_count > 0 ; --__trip_count)
        {
          if (*__first == __val)
            return __first;
          ++__first;

          if (*__first == __val)
            return __first;
          ++__first;

          if (*__first == __val)
            return __first;
          ++__first;

          if (*__first == __val)
            return __first;
          ++__first;
        }

      switch (__last - __first)
        {
        case 3:
          if (*__first == __val)
            return __first;
          ++__first;
        case 2:
          if (*__first == __val)
            return __first;
          ++__first;
        case 1:
          if (*__first == __val)
            return __first;
          ++__first;
        case 0:
        default:
          return __last;
        }
    }

  /**
   *  @brief Find the first element in a sequence for which a predicate is true.
   *
   *  This version of the algorithm is optimized for random access
   *  iterators.
   *
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  pred   A predicate.
   *  @return   The first iterator @c i in the range @p [first,last)
   *  such that @p pred(*i) is true, or @p last if no such iterator exists.
  */
  template<RandomAccessIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _Iter
    find_if(_Iter __first, _Iter __last, _Pred __pred)
    {
      _Iter::difference_type __trip_count = (__last - __first) >> 2;

      for ( ; __trip_count > 0 ; --__trip_count)
        {
          if (__pred(*__first))
            return __first;
          ++__first;

          if (__pred(*__first))
            return __first;
          ++__first;

          if (__pred(*__first))
            return __first;
          ++__first;

          if (__pred(*__first))
            return __first;
          ++__first;
        }

      switch (__last - __first)
        {
        case 3:
          if (__pred(*__first))
            return __first;
          ++__first;
        case 2:
          if (__pred(*__first))
            return __first;
          ++__first;
        case 1:
          if (__pred(*__first))
            return __first;
          ++__first;
        case 0:
        default:
          return __last;
        }
    }

  /**
   *  @brief Find two adjacent values in a sequence that are equal.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @return   The first iterator @c i such that @c i and @c i+1 are both
   *  valid iterators in @p [first,last) and such that @c *i == @c *(i+1),
   *  or @p last if no such iterator exists.
  */
  template<ForwardIterator _Iter>
    requires EqualityComparable<_Iter::value_type>
    _Iter
    adjacent_find(_Iter __first, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);
      if (__first == __last)
        return __last;
      _Iter __next = __first;
      while(++__next != __last)
        {
          if (*__first == *__next)
            return __first;
          __first = __next;
        }
      return __last;
    }

  /**
   *  @brief Find two adjacent values in a sequence using a predicate.
   *  @param  first         A forward iterator.
   *  @param  last          A forward iterator.
   *  @param  binary_pred   A binary predicate.
   *  @return   The first iterator @c i such that @c i and @c i+1 are both
   *  valid iterators in @p [first,last) and such that
   *  @p binary_pred(*i,*(i+1)) is true, or @p last if no such iterator
   *  exists.
  */
  template<ForwardIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _Iter
    adjacent_find(_Iter __first, _Iter __last,
                  _Pred __binary_pred)
    {
      __glibcxx_requires_valid_range(__first, __last);
      if (__first == __last)
        return __last;
      _Iter __next = __first;
      while(++__next != __last)
        {
          if (__binary_pred(*__first, *__next))
            return __first;
          __first = __next;
        }
      return __last;
    }

  /**
   *  @brief Count the number of copies of a value in a sequence.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  value  The value to be counted.
   *  @return   The number of iterators @c i in the range @p [first,last)
   *  for which @c *i == @p value
  */
  template<InputIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
    _Iter::difference_type
    count(_Iter __first, _Iter __last, const _Tp& __value)
    {
      __glibcxx_requires_valid_range(__first, __last);
      _Iter::difference_type __n = 0;
      for ( ; __first != __last; ++__first)
        if (*__first == __value)
          ++__n;
      return __n;
    }

  /**
   *  @brief Count the elements of a sequence for which a predicate is true.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  pred   A predicate.
   *  @return   The number of iterators @c i in the range @p [first,last)
   *  for which @p pred(*i) is true.
  */
  template<InputIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    _Iter::difference_type
    count_if(_Iter __first, _Iter __last, _Pred __pred)
    {
      __glibcxx_requires_valid_range(__first, __last);

      _Iter::difference_type __n = 0;
      for ( ; __first != __last; ++__first)
        if (__pred(*__first))
          ++__n;
      return __n;
    }

  /**
   *  @brief Search a sequence for a matching sub-sequence.
   *  @param  first1  A forward iterator.
   *  @param  last1   A forward iterator.
   *  @param  first2  A forward iterator.
   *  @param  last2   A forward iterator.
   *  @return   The first iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that @c *(i+N) == @p *(first2+N)
   *  for each @c N in the range @p [0,last2-first2), or @p last1 if no
   *  such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2) and
   *  returns an iterator to the first element of the sub-sequence, or
   *  @p last1 if the sub-sequence is not found.
   *
   *  Because the sub-sequence must lie completely within the range
   *  @p [first1,last1) it must start at a position less than
   *  @p last1-(last2-first2) where @p last2-first2 is the length of the
   *  sub-sequence.
   *  This means that the returned iterator @c i will be in the range
   *  @p [first1,last1-(last2-first2))
  */
  template<ForwardIterator _Iter1, ForwardIterator _Iter2>
    requires HasEqualTo<_Iter1::value_type, _Iter2::value_type>
    _Iter1
    search(_Iter1 __first1, _Iter1 __last1,
           _Iter2 __first2, _Iter2 __last2)
    {
      __glibcxx_requires_valid_range(__first1, __last1);
      __glibcxx_requires_valid_range(__first2, __last2);
      // Test for empty ranges
      if (__first1 == __last1 || __first2 == __last2)
        return __first1;

      // Test for a pattern of length 1.
      _Iter2 __tmp(__first2);
      ++__tmp;
      if (__tmp == __last2)
        return std::find(__first1, __last1, _Iter2::value_type(*__first2));

      // General case.
      _Iter2 __p1, __p;
      __p1 = __first2; ++__p1;
      _Iter1 __current = __first1;

      while (__first1 != __last1)
        {
          __first1 = std::find(__first1, __last1, _Iter2::value_type(*__first2));
          if (__first1 == __last1)
            return __last1;

          __p = __p1;
          __current = __first1;
          if (++__current == __last1)
            return __last1;

          while (*__current == *__p)
            {
              if (++__p == __last2)
                return __first1;
              if (++__current == __last1)
                return __last1;
            }
          ++__first1;
        }
      return __first1;
    }

  /**
   *  @brief Search a sequence for a matching sub-sequence using a predicate.
   *  @param  first1     A forward iterator.
   *  @param  last1      A forward iterator.
   *  @param  first2     A forward iterator.
   *  @param  last2      A forward iterator.
   *  @param  predicate  A binary predicate.
   *  @return   The first iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that
   *  @p predicate(*(i+N),*(first2+N)) is true for each @c N in the range
   *  @p [0,last2-first2), or @p last1 if no such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2),
   *  using @p predicate to determine equality, and returns an iterator
   *  to the first element of the sub-sequence, or @p last1 if no such
   *  iterator exists.
   *
   *  @see search(_ForwardIter1, _ForwardIter1, _ForwardIter2, _ForwardIter2)
  */
  template<ForwardIterator _Iter1, ForwardIterator _Iter2,
           BinaryPredicate<auto, _Iter1::value_type,_Iter2::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _Iter1
    search(_Iter1 __first1, _Iter1 __last1,
           _Iter2 __first2, _Iter2 __last2,
           _Pred  __predicate)
    {
      __glibcxx_requires_valid_range(__first1, __last1);
      __glibcxx_requires_valid_range(__first2, __last2);

      // Test for empty ranges
      if (__first1 == __last1 || __first2 == __last2)
        return __first1;

      // Test for a pattern of length 1.
      _Iter2 __tmp(__first2);
      ++__tmp;
      if (__tmp == __last2)
        {
          while (__first1 != __last1 && !__predicate(*__first1, *__first2))
            ++__first1;
          return __first1;
        }

      // General case.
      _Iter2 __p1, __p;
      __p1 = __first2; ++__p1;
      _Iter1 __current = __first1;

      while (__first1 != __last1)
        {
          while (__first1 != __last1)
            {
              if (__predicate(*__first1, *__first2))
                break;
              ++__first1;
            }
          while (__first1 != __last1 && !__predicate(*__first1, *__first2))
            ++__first1;
          if (__first1 == __last1)
            return __last1;

          __p = __p1;
          __current = __first1;
          if (++__current == __last1)
            return __last1;

          while (__predicate(*__current, *__p))
            {
              if (++__p == __last2)
                return __first1;
              if (++__current == __last1)
                return __last1;
            }
          ++__first1;
        }
      return __first1;
    }

  /**
   *  @brief Search a sequence for a number of consecutive values.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @param  count  The number of consecutive values.
   *  @param  val    The value to find.
   *  @return   The first iterator @c i in the range @p [first,last-count)
   *  such that @c *(i+N) == @p val for each @c N in the range @p [0,count),
   *  or @p last if no such iterator exists.
   *
   *  Searches the range @p [first,last) for @p count consecutive elements
   *  equal to @p val.
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
    _Iter
    search_n(_Iter __first, _Iter __last,
             _Iter::difference_type __count, const _Tp& __val)
    {
      if (__count <= 0)
        return __first;
      if (__count == 1)
	return std::find(__first, __last, __val);

      __first = std::find(__first, __last, __val);
      while (__first != __last)
	{
          _Iter::difference_type __n = __count;
	  _Iter __i = __first;
	  ++__i;
	  while (__i != __last && __n != 1 && *__i == __val)
	    {
	      ++__i;
	      --__n;
	    }
	  if (__n == 1)
	    return __first;
	  if (__i == __last)
	    return __last;
	  __first = std::find(++__i, __last, __val);
	}
      return __last;
    }

  /**
   *  @brief Search a sequence for a number of consecutive values.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @param  count  The number of consecutive values.
   *  @param  val    The value to find.
   *  @return   The first iterator @c i in the range @p [first,last-count)
   *  such that @c *(i+N) == @p val for each @c N in the range @p [0,count),
   *  or @p last if no such iterator exists.
   *
   *  Searches the range @p [first,last) for @p count consecutive elements
   *  equal to @p val.
  */
  template<RandomAccessIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
    _Iter
    search_n(_Iter __first, _Iter __last,
             _Iter::difference_type __count, const _Tp& __val)
    {
      if (__count <= 0)
        return __first;
      if (__count == 1)
	return std::find(__first, __last, __val);
      
      typedef _Iter::difference_type _DistanceType;

      _DistanceType __tailSize = __last - __first;
      const _DistanceType __pattSize = __count;

      if (__tailSize < __pattSize)
        return __last;

      const _DistanceType __skipOffset = __pattSize - 1;
      _Iter __lookAhead = __first + __skipOffset;
      __tailSize -= __pattSize;

      while (1) // the main loop...
	{
	  // __lookAhead here is always pointing to the last element of next 
	  // possible match.
	  while (!(*__lookAhead == __val)) // the skip loop...
	    {
	      if (__tailSize < __pattSize)
		return __last;  // Failure
	      __lookAhead += __pattSize;
	      __tailSize -= __pattSize;
	    }
	  _DistanceType __remainder = __skipOffset;
	  for (_Iter __backTrack = __lookAhead - 1; 
	       *__backTrack == __val; --__backTrack)
	    {
	      if (--__remainder == 0)
		return (__lookAhead - __skipOffset); // Success
	    }
	  if (__remainder > __tailSize)
	    return __last; // Failure
	  __lookAhead += __remainder;
	  __tailSize -= __remainder;
	}
    }

  /**
   *  @brief Search a sequence for a number of consecutive values using a
   *         predicate.
   *  @param  first        A forward iterator.
   *  @param  last         A forward iterator.
   *  @param  count        The number of consecutive values.
   *  @param  val          The value to find.
   *  @param  binary_pred  A binary predicate.
   *  @return   The first iterator @c i in the range @p [first,last-count)
   *  such that @p binary_pred(*(i+N),val) is true for each @c N in the
   *  range @p [0,count), or @p last if no such iterator exists.
   *
   *  Searches the range @p [first,last) for @p count consecutive elements
   *  for which the predicate returns true.
  */
  template<ForwardIterator _Iter, typename _Tp, 
           BinaryPredicate<auto, _Iter::value_type, _Tp> _Pred>
    requires CopyConstructible<_Pred>
    _Iter
    search_n(_Iter __first, _Iter __last,
             _Iter::difference_type __count, const _Tp& __val,
             _Pred __binary_pred)
    {
      if (__count <= 0)
        return __first;
      if (__count == 1)
        {
	  while (__first != __last && !__binary_pred(*__first, __val))
	    ++__first;
	  return __first;
        }

      while (__first != __last && !__binary_pred(*__first, __val))
        ++__first;

      while (__first != __last)
	{
          _Iter::difference_type __n = __count;
	  _Iter __i = __first;
	  ++__i;
	  while (__i != __last && __n != 1 && __binary_pred(*__i, __val))
	    {
	      ++__i;
	      --__n;
	    }
	  if (__n == 1)
	    return __first;
	  if (__i == __last)
	    return __last;
	  __first = ++__i;
	  while (__first != __last && !__binary_pred(*__first, __val))
	    ++__first;
	}
      return __last;
    }

  /**
   *  @brief Search a sequence for a number of consecutive values using a
   *         predicate.
   *  @param  first        A forward iterator.
   *  @param  last         A forward iterator.
   *  @param  count        The number of consecutive values.
   *  @param  val          The value to find.
   *  @param  binary_pred  A binary predicate.
   *  @return   The first iterator @c i in the range @p [first,last-count)
   *  such that @p binary_pred(*(i+N),val) is true for each @c N in the
   *  range @p [0,count), or @p last if no such iterator exists.
   *
   *  Searches the range @p [first,last) for @p count consecutive elements
   *  for which the predicate returns true.
  */
  template<RandomAccessIterator _Iter, typename _Tp, 
           BinaryPredicate<auto, _Iter::value_type, _Tp> _Pred>
    requires CopyConstructible<_Pred>
    _Iter
    search_n(_Iter __first, _Iter __last,
             _Iter::difference_type __count, const _Tp& __val,
             _Pred __binary_pred)
    {
      if (__count <= 0)
        return __first;
      if (__count == 1)
        {
	  while (__first != __last && !__binary_pred(*__first, __val))
	    ++__first;
	  return __first;
        }
      
      typedef _Iter::difference_type _DistanceType;

      _DistanceType __tailSize = __last - __first;
      const _DistanceType __pattSize = __count;

      if (__tailSize < __pattSize)
        return __last;

      const _DistanceType __skipOffset = __pattSize - 1;
      _Iter __lookAhead = __first + __skipOffset;
      __tailSize -= __pattSize;

      while (1) // the main loop...
	{
	  // __lookAhead here is always pointing to the last element of next 
	  // possible match.
	  while (!__binary_pred(*__lookAhead, __val)) // the skip loop...
	    {
	      if (__tailSize < __pattSize)
		return __last;  // Failure
	      __lookAhead += __pattSize;
	      __tailSize -= __pattSize;
	    }
	  _DistanceType __remainder = __skipOffset;
	  for (_Iter __backTrack = __lookAhead - 1; 
	       __binary_pred(*__backTrack, __val); --__backTrack)
	    {
	      if (--__remainder == 0)
		return (__lookAhead - __skipOffset); // Success
	    }
	  if (__remainder > __tailSize)
	    return __last; // Failure
	  __lookAhead += __remainder;
	  __tailSize -= __remainder;
	}
    }

  /**
   *  @brief Perform an operation on a sequence.
   *  @param  first     An input iterator.
   *  @param  last      An input iterator.
   *  @param  result    An output iterator.
   *  @param  unary_op  A unary operator.
   *  @return   An output iterator equal to @p result+(last-first).
   *
   *  Applies the operator to each element in the input range and assigns
   *  the results to successive elements of the output sequence.
   *  Evaluates @p *(result+N)=unary_op(*(first+N)) for each @c N in the
   *  range @p [0,last-first).
   *
   *  @p unary_op must not alter its argument.
  */
  template<InputIterator _InIter, typename _OutIter,
           Callable1<auto, const _InIter::value_type&> _UnOp>
    requires OutputIterator<_OutIter, _UnOp::result_type>
          && CopyConstructible<_UnOp>
    _OutIter
    transform(_InIter __first, _InIter __last,
              _OutIter __result, _UnOp __unary_op)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first, ++__result)
        *__result = __unary_op(*__first);
      return __result;
    }

  /**
   *  @brief Perform an operation on corresponding elements of two sequences.
   *  @param  first1     An input iterator.
   *  @param  last1      An input iterator.
   *  @param  first2     An input iterator.
   *  @param  result     An output iterator.
   *  @param  binary_op  A binary operator.
   *  @return   An output iterator equal to @p result+(last-first).
   *
   *  Applies the operator to the corresponding elements in the two
   *  input ranges and assigns the results to successive elements of the
   *  output sequence.
   *  Evaluates @p *(result+N)=binary_op(*(first1+N),*(first2+N)) for each
   *  @c N in the range @p [0,last1-first1).
   *
   *  @p binary_op must not alter either of its arguments.
  */
  template<InputIterator _InIter1, InputIterator _InIter2,
           typename _OutIter,
           Callable2<auto, 
                     const _InIter1::value_type&, 
                     const _InIter2::value_type&> _BinOp>
    requires OutputIterator<_OutIter, _BinOp::result_type>
          && CopyConstructible<_BinOp>
    _OutIter
    transform(_InIter1 __first1, _InIter1 __last1,
              _InIter2 __first2, _OutIter __result,
              _BinOp __binary_op)
    {
      __glibcxx_requires_valid_range(__first1, __last1);

      for ( ; __first1 != __last1; ++__first1, ++__first2, ++__result)
        *__result = __binary_op(*__first1, *__first2);
      return __result;
    }

  /**
   *  @brief Replace each occurrence of one value in a sequence with another
   *         value.
   *  @param  first      A forward iterator.
   *  @param  last       A forward iterator.
   *  @param  old_value  The value to be replaced.
   *  @param  new_value  The replacement value.
   *  @return   replace() returns no value.
   *
   *  For each iterator @c i in the range @p [first,last) if @c *i ==
   *  @p old_value then the assignment @c *i = @p new_value is performed.
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasEqualTo<_Iter::value_type, _Tp>
          && OutputIterator<_Iter, const _Tp&>
    void
    replace(_Iter __first, _Iter __last,
            const _Tp& __old_value, const _Tp& __new_value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first)
        if (*__first == __old_value)
          *__first = __new_value;
    }

  /**
   *  @brief Replace each value in a sequence for which a predicate returns
   *         true with another value.
   *  @param  first      A forward iterator.
   *  @param  last       A forward iterator.
   *  @param  pred       A predicate.
   *  @param  new_value  The replacement value.
   *  @return   replace_if() returns no value.
   *
   *  For each iterator @c i in the range @p [first,last) if @p pred(*i)
   *  is true then the assignment @c *i = @p new_value is performed.
  */
  template<ForwardIterator _Iter, Predicate<auto, _Iter::value_type> _Pred,
           typename _Tp>
    requires OutputIterator<_Iter, const _Tp&>
          && CopyConstructible<_Pred>
    void
    replace_if(_Iter __first, _Iter __last,
               _Pred __pred, const _Tp& __new_value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first)
        if (__pred(*__first))
          *__first = __new_value;
    }

  /**
   *  @brief Copy a sequence, replacing each element of one value with another
   *         value.
   *  @param  first      An input iterator.
   *  @param  last       An input iterator.
   *  @param  result     An output iterator.
   *  @param  old_value  The value to be replaced.
   *  @param  new_value  The replacement value.
   *  @return   The end of the output sequence, @p result+(last-first).
   *
   *  Copies each element in the input range @p [first,last) to the
   *  output range @p [result,result+(last-first)) replacing elements
   *  equal to @p old_value with @p new_value.
  */
  template<InputIterator _InIter, typename _OutIter, typename _Tp>
    requires OutputIterator<_OutIter, _InIter::reference>
          && OutputIterator<_OutIter, const _Tp&>
          && HasEqualTo<_InIter::value_type, _Tp>
    _OutIter
    replace_copy(_InIter __first, _InIter __last,
                 _OutIter __result,
                 const _Tp& __old_value, const _Tp& __new_value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first, ++__result)
	if (*__first == __old_value)
	  *__result = __new_value;
	else
	  *__result = *__first;
      return __result;
    }

  /**
   *  @brief Copy a sequence, replacing each value for which a predicate
   *         returns true with another value.
   *  @param  first      An input iterator.
   *  @param  last       An input iterator.
   *  @param  result     An output iterator.
   *  @param  pred       A predicate.
   *  @param  new_value  The replacement value.
   *  @return   The end of the output sequence, @p result+(last-first).
   *
   *  Copies each element in the range @p [first,last) to the range
   *  @p [result,result+(last-first)) replacing elements for which
   *  @p pred returns true with @p new_value.
  */
  template<InputIterator _InIter, typename _OutIter,
           Predicate<auto, _InIter::value_type> _Pred,
           typename _Tp>
    requires OutputIterator<_OutIter, _InIter::reference>
          && OutputIterator<_OutIter, const _Tp&>
    _OutIter
    replace_copy_if(_InIter __first, _InIter __last,
                    _OutIter __result,
                    _Pred __pred, const _Tp& __new_value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first, ++__result)
	if (__pred(*__first))
	  *__result = __new_value;
	else
	  *__result = *__first;
      return __result;
    }

  /**
   *  @brief Assign the result of a function object to each value in a
   *         sequence.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @param  gen    A function object taking no arguments.
   *  @return   generate() returns no value.
   *
   *  Performs the assignment @c *i = @p gen() for each @c i in the range
   *  @p [first,last).
  */
  template<ForwardIterator _Iter, Callable0 _Generator>
    requires OutputIterator<_Iter, _Generator::result_type>
          && CopyConstructible<_Generator>
    void
    generate(_Iter __first, _Iter __last,
             _Generator __gen)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first)
        *__first = __gen();
    }

  /**
   *  @brief Assign the result of a function object to each value in a
   *         sequence.
   *  @param  first  A forward iterator.
   *  @param  n      The length of the sequence.
   *  @param  gen    A function object taking no arguments.
   *  @return   The end of the sequence, @p first+n
   *
   *  Performs the assignment @c *i = @p gen() for each @c i in the range
   *  @p [first,first+n).
  */
  template<typename _Iter, IntegralLike _Size, Callable0 _Generator>
    requires OutputIterator<_Iter, _Generator::result_type>
          && CopyConstructible<_Generator>
    _Iter
    generate_n(_Iter __first, _Size __n, _Generator __gen)
    {
      for ( ; __n > 0; --__n, ++__first)
        *__first = __gen();
      return __first;
    }

  /**
   *  @brief Copy a sequence, removing elements of a given value.
   *  @param  first   An input iterator.
   *  @param  last    An input iterator.
   *  @param  result  An output iterator.
   *  @param  value   The value to be removed.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) not equal to @p value
   *  to the range beginning at @p result.
   *  remove_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
  */
  template<InputIterator _InIter, 
           OutputIterator<auto, _InIter::reference> _OutIter,
           typename _Tp>
    requires HasEqualTo<_InIter::value_type, _Tp>
    _OutIter
    remove_copy(_InIter __first, _InIter __last,
                _OutIter __result, const _Tp& __value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first)
        if (!(*__first == __value))
          {
            *__result = *__first;
            ++__result;
          }
      return __result;
    }

  /**
   *  @brief Copy a sequence, removing elements for which a predicate is true.
   *  @param  first   An input iterator.
   *  @param  last    An input iterator.
   *  @param  result  An output iterator.
   *  @param  pred    A predicate.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) for which
   *  @p pred returns true to the range beginning at @p result.
   *
   *  remove_copy_if() is stable, so the relative order of elements that are
   *  copied is unchanged.
  */
  template<InputIterator _InIter, 
           OutputIterator<auto, _InIter::reference>  _OutIter,
           Predicate<auto, _InIter::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _OutIter
    remove_copy_if(_InIter __first, _InIter __last,
                   _OutIter __result, _Pred __pred)
    {
      __glibcxx_requires_valid_range(__first, __last);

      for ( ; __first != __last; ++__first)
        if (!__pred(*__first))
          {
            *__result = *__first;
            ++__result;
          }
      return __result;
    }

  /**
   *  @brief Remove elements from a sequence.
   *  @param  first  An input iterator.
   *  @param  last   An input iterator.
   *  @param  value  The value to be removed.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  All elements equal to @p value are removed from the range
   *  @p [first,last).
   *
   *  remove() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires OutputIterator<_Iter, _Iter::reference>         
          && HasEqualTo<_Iter::value_type, _Tp>
    _Iter
    remove(_Iter __first, _Iter __last, const _Tp& __value)
    {
      __glibcxx_requires_valid_range(__first, __last);

      __first = std::find(__first, __last, __value);
      _Iter __i = __first;
      return __first == __last ? __first
                               : std::remove_copy(++__i, __last,
                                                  __first, __value);
    }

  /**
   *  @brief Remove elements from a sequence using a predicate.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @param  pred   A predicate.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  All elements for which @p pred returns true are removed from the range
   *  @p [first,last).
   *
   *  remove_if() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<ForwardIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    requires OutputIterator<_Iter, _Iter::reference>
          && CopyConstructible<_Pred>
    _Iter
    remove_if(_Iter __first, _Iter __last,
              _Pred __pred)
    {
      __glibcxx_requires_valid_range(__first, __last);

      __first = std::find_if(__first, __last, __pred);
      _Iter __i = __first;
      return __first == __last ? __first
                               : std::remove_copy_if(++__i, __last,
                                                     __first, __pred);
    }

  /**
   *  @brief Copy a sequence, removing consecutive duplicate values.
   *  @param  first   An input iterator.
   *  @param  last    An input iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements that compare equal.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 538. 241 again: Does unique_copy() require CopyConstructible and 
   *  Assignable?
   *  @endif
  */
  template<ForwardIterator _InIter, typename _OutIter>
    requires OutputIterator<_OutIter, _InIter::reference>
          && EqualityComparable<_InIter::value_type>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result)
    {
      if (__first == __last) return __result;      

      _InIter __next = __first;
      *__result = *__first;
      while (++__next != __last)
	if (!(*__first == *__next))
	  {
	    __first = __next;
	    *++__result = *__first;
	  }
      return ++__result;
    }

  /**
   *  @brief Copy a sequence, removing consecutive duplicate values.
   *  @param  first   An input iterator.
   *  @param  last    An input iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements that compare equal.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 538. 241 again: Does unique_copy() require CopyConstructible and 
   *  Assignable?
   *  @endif
  */
  template<InputIterator _InIter, typename _OutIter>
    requires OutputIterator<_OutIter, const _InIter::value_type&>
          && EqualityComparable<_InIter::value_type>
          && CopyAssignable<_InIter::value_type>
          && CopyConstructible<_InIter::value_type>
          && !ForwardIterator<_InIter>
          && !ForwardIterator<_OutIter>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result)
    {
      if (__first == __last) return __result;      

      _InIter::value_type __value = *__first;
      *__result = __value;
      while (++__first != __last)
        if (!(__value == *__first))
          {
            __value = *__first;
            *++__result = __value;
          }
      return ++__result;
    }

  /**
   *  @brief Copy a sequence, removing consecutive duplicate values.
   *  @param  first   An input iterator.
   *  @param  last    An input iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements that compare equal.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 538. 241 again: Does unique_copy() require CopyConstructible and 
   *  Assignable?
   *  @endif
  */
  template<InputIterator _InIter, ForwardIterator _OutIter>
    requires OutputIterator<_OutIter, _InIter::reference>
          && HasEqualTo<_OutIter::value_type, _InIter::value_type>
          && !ForwardIterator<_InIter>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result)
    {
      if (__first == __last) return __result;      

      *__result = *__first;
      while (++__first != __last)
        if (!(*__result == *__first))
          *++__result = *__first;
      return ++__result;
    }

  /**
   *  @brief Copy a sequence, removing consecutive values using a predicate.
   *  @param  first        An input iterator.
   *  @param  last         An input iterator.
   *  @param  result       An output iterator.
   *  @param  binary_pred  A binary predicate.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements for which @p binary_pred returns
   *  true.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  @endif
  */
  template<ForwardIterator _InIter, 
           OutputIterator<auto, _InIter::reference> _OutIter,
	   BinaryPredicate<auto, _InIter::value_type, 
                           _InIter::value_type> _BinaryPred>
    requires CopyConstructible<_BinaryPred>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result,
                _BinaryPred __binary_pred)
    {
      if (__first == __last) return __result;      

      _InIter __next = __first;
      *__result = *__first;
      while (++__next != __last)
	if (!__binary_pred(*__first, *__next))
	  {
	    __first = __next;
	    *++__result = *__first;
	  }
      return ++__result;
    }

  /**
   *  @brief Copy a sequence, removing consecutive values using a predicate.
   *  @param  first        An input iterator.
   *  @param  last         An input iterator.
   *  @param  result       An output iterator.
   *  @param  binary_pred  A binary predicate.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements for which @p binary_pred returns
   *  true.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  @endif
  */
  template<InputIterator _InIter, typename _OutIter,
           BinaryPredicate<auto, _InIter::value_type, _InIter::value_type> _Pred>
    requires OutputIterator<_OutIter, const _InIter::value_type&>
          && CopyAssignable<_InIter::value_type>
          && CopyConstructible<_InIter::value_type>
          && CopyConstructible<_Pred>
          && !ForwardIterator<_InIter>
          && !ForwardIterator<_OutIter>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result,
                _Pred __binary_pred)
    {
      if (__first == __last) return __result;      

      _InIter::value_type __value = *__first;
      *__result = __value;
      while (++__first != __last)
        if (!__binary_pred(__value, *__first))
          {
            __value = *__first;
            *++__result = __value;
          }
      return ++__result;
    }

  /**
   *  @brief Copy a sequence, removing consecutive values using a predicate.
   *  @param  first        An input iterator.
   *  @param  last         An input iterator.
   *  @param  result       An output iterator.
   *  @param  binary_pred  A binary predicate.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies each element in the range @p [first,last) to the range
   *  beginning at @p result, except that only the first element is copied
   *  from groups of consecutive elements for which @p binary_pred returns
   *  true.
   *  unique_copy() is stable, so the relative order of elements that are
   *  copied is unchanged.
   *
   *  @if maint
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS
   *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
   *  @endif
  */
  template<InputIterator _InIter, ForwardIterator _OutIter,
           BinaryPredicate<auto, _OutIter::value_type, 
                           _InIter::value_type> _Pred>
    requires OutputIterator<_OutIter, _InIter::reference>
          && CopyConstructible<_Pred>
          && !ForwardIterator<_InIter>
    _OutIter
    unique_copy(_InIter __first, _InIter __last,
                _OutIter __result,
                _Pred __binary_pred)
    {
      if (__first == __last) return __result;      

      *__result = *__first;
      while (++__first != __last)
	if (!__binary_pred(*__result, *__first))
	  *++__result = *__first;
      return ++__result;
    }

  /**
   *  @brief Remove consecutive duplicate values from a sequence.
   *  @param  first  A forward iterator.
   *  @param  last   A forward iterator.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Removes all but the first element from each group of consecutive
   *  values that compare equal.
   *  unique() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<ForwardIterator _Iter>
    requires OutputIterator<_Iter, _Iter::reference>
          && EqualityComparable<_Iter::value_type>
    _Iter
    unique(_Iter __first, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      // Skip the beginning, if already unique.
      __first = std::adjacent_find(__first, __last);
      if (__first == __last)
        return __last;

      // Do the real copy work.
      _Iter __dest = __first;
      ++__first;
      while (++__first != __last)
        if (!(*__dest == *__first))
          *++__dest = *__first;
      return ++__dest;
    }

  /**
   *  @brief Remove consecutive values from a sequence using a predicate.
   *  @param  first        A forward iterator.
   *  @param  last         A forward iterator.
   *  @param  binary_pred  A binary predicate.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Removes all but the first element from each group of consecutive
   *  values for which @p binary_pred returns true.
   *  unique() is stable, so the relative order of elements that are
   *  not removed is unchanged.
   *  Elements between the end of the resulting sequence and @p last
   *  are still present, but their value is unspecified.
  */
  template<ForwardIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Pred>
    requires OutputIterator<_Iter, _Iter::reference>
          && CopyConstructible<_Pred>
    _Iter
    unique(_Iter __first, _Iter __last,
           _Pred __binary_pred)
    {
      __glibcxx_requires_valid_range(__first, __last);

      // Skip the beginning, if already unique.
      __first = std::adjacent_find(__first, __last, __binary_pred);
      if (__first == __last)
        return __last;

      // Do the real copy work.
      _Iter __dest = __first;
      ++__first;
      while (++__first != __last)
        if (!__binary_pred(*__dest, *__first))
          *++__dest = *__first;
      return ++__dest;
    }

  /**
   *  @brief Reverse a sequence.
   *  @param  first  A bidirectional iterator.
   *  @param  last   A bidirectional iterator.
   *  @return   reverse() returns no value.
   *
   *  Reverses the order of the elements in the range @p [first,last),
   *  so that the first element becomes the last etc.
   *  For every @c i such that @p 0<=i<=(last-first)/2), @p reverse()
   *  swaps @p *(first+i) and @p *(last-(i+1))
  */
  template<BidirectionalIterator _Iter>
    requires HasSwap<_Iter::reference, _Iter::reference>
    void
    reverse(_Iter __first, _Iter __last)
    {
      while (true)
        if (__first == __last || __first == --__last)
          return;
        else
          {
            swap(*__first, *__last);
            ++__first;
          }
    }

  /**
   *  @brief Reverse a sequence.
   *  @param  first  A bidirectional iterator.
   *  @param  last   A bidirectional iterator.
   *  @return   reverse() returns no value.
   *
   *  Reverses the order of the elements in the range @p [first,last),
   *  so that the first element becomes the last etc.
   *  For every @c i such that @p 0<=i<=(last-first)/2), @p reverse()
   *  swaps @p *(first+i) and @p *(last-(i+1))
  */
  template<RandomAccessIterator _Iter>
    requires HasSwap<_Iter::reference, _Iter::reference>
    void
    reverse(_Iter __first, _Iter __last)
    {
      if (__first == __last)
        return;
      --__last;
      while (__first < __last)
        {
          swap(*__first, *__last);
          ++__first;
          --__last;
        }
    }

  /**
   *  @brief Copy a sequence, reversing its elements.
   *  @param  first   A bidirectional iterator.
   *  @param  last    A bidirectional iterator.
   *  @param  result  An output iterator.
   *  @return  An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements in the range @p [first,last) to the range
   *  @p [result,result+(last-first)) such that the order of the
   *  elements is reversed.
   *  For every @c i such that @p 0<=i<=(last-first), @p reverse_copy()
   *  performs the assignment @p *(result+(last-first)-i) = *(first+i).
   *  The ranges @p [first,last) and @p [result,result+(last-first))
   *  must not overlap.
  */
  template<BidirectionalIterator _InIter,
           OutputIterator<auto, _InIter::reference> _OutIter>
    _OutIter
    reverse_copy(_InIter __first, _InIter __last,
                 _OutIter __result)
    {
      __glibcxx_requires_valid_range(__first, __last);

      while (__first != __last)
        {
          --__last;
          *__result = *__last;
          ++__result;
        }
      return __result;
    }


  /**
   *  @if maint
   *  This is a helper function for the rotate algorithm specialized on RAIs.
   *  It returns the greatest common divisor of two integer values.
   *  @endif
  */
  template<typename _EuclideanRingElement>
    _EuclideanRingElement
    __gcd(_EuclideanRingElement __m, _EuclideanRingElement __n)
    {
      while (__n != 0)
        {
          _EuclideanRingElement __t = __m % __n;
          __m = __n;
          __n = __t;
        }
      return __m;
    }

  /**
   *  @brief Rotate the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Rotates the elements of the range @p [first,last) by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p first, the
   *  element at @p middle+1 is moved to @first+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  This effectively swaps the ranges @p [first,middle) and
   *  @p [middle,last).
   *
   *  Performs @p *(first+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<ForwardIterator _Iter>
    requires HasSwap<_Iter::reference, _Iter::reference>
    void
    rotate(_Iter __first, _Iter __middle,_Iter __last)
    {
      if (__first == __middle || __last  == __middle)
        return;

      _Iter __first2 = __middle;
      do
        {
          swap(*__first, *__first2);
          ++__first;
          ++__first2;
          if (__first == __middle)
            __middle = __first2;
        }
      while (__first2 != __last);

      __first2 = __middle;

      while (__first2 != __last)
        {
          swap(*__first, *__first2);
          ++__first;
          ++__first2;
          if (__first == __middle)
            __middle = __first2;
          else if (__first2 == __last)
            __first2 = __middle;
        }
    }

  /**
   *  @brief Rotate the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Rotates the elements of the range @p [first,last) by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p first, the
   *  element at @p middle+1 is moved to @first+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  This effectively swaps the ranges @p [first,middle) and
   *  @p [middle,last).
   *
   *  Performs @p *(first+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<BidirectionalIterator _Iter>
    requires HasSwap<_Iter::reference, _Iter::reference>
    void
    rotate(_Iter __first, _Iter __middle, _Iter __last)
    {
      if (__first == __middle || __last  == __middle)
        return;

      std::reverse(__first,  __middle);
      std::reverse(__middle, __last);

      while (__first != __middle && __middle != __last)
        {
          --__last;
          swap(*__first, *__last);
          ++__first;
        }

      if (__first == __middle)
        std::reverse(__middle, __last);
      else
        std::reverse(__first,  __middle);
    }

  /**
   *  @brief Rotate the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Rotates the elements of the range @p [first,last) by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p first, the
   *  element at @p middle+1 is moved to @first+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  This effectively swaps the ranges @p [first,middle) and
   *  @p [middle,last).
   *
   *  Performs @p *(first+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
    void
    rotate(_Iter __first, _Iter __middle, _Iter __last)
    {
      if (__first == __middle || __last  == __middle)
        return;

      typedef _Iter::difference_type _Distance;
      typedef _Iter::value_type      _ValueType;

      const _Distance __n = __last   - __first;
      const _Distance __k = __middle - __first;
      const _Distance __l = __n - __k;

      if (__k == __l)
        {
          std::swap_ranges(__first, __middle, __middle);
          return;
        }

      const _Distance __d = __gcd(__n, __k);

      for (_Distance __i = 0; __i < __d; __i++)
        {
          _ValueType __tmp(std_move(*__first));
          _Iter __p = __first;

          if (__k < __l)
            {
              for (_Distance __j = 0; __j < __l / __d; __j++)
                {
                  if (__p > __first + __l)
                    {
                      *__p = std_move(*(__p - __l));
                      __p -= __l;
                    }

                  *__p = std_move(*(__p + __k));
                  __p += __k;
                }
            }
          else
            {
              for (_Distance __j = 0; __j < __k / __d - 1; __j ++)
                {
                  if (__p < __last - __k)
                    {
                      *__p = std_move(*(__p + __k));
                      __p += __k;
                    }
                  *__p = std_move(* (__p - __l));
                  __p -= __l;
                }
            }

          *__p = std_move(__tmp);
          ++__first;
        }
    }

  /**
   *  @brief Copy a sequence, rotating its elements.
   *  @param  first   A forward iterator.
   *  @param  middle  A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  result  An output iterator.
   *  @return   An iterator designating the end of the resulting sequence.
   *
   *  Copies the elements of the range @p [first,last) to the range
   *  beginning at @result, rotating the copied elements by @p (middle-first)
   *  positions so that the element at @p middle is moved to @p result, the
   *  element at @p middle+1 is moved to @result+1 and so on for each element
   *  in the range @p [first,last).
   *
   *  Performs @p *(result+(n+(last-middle))%(last-first))=*(first+n) for
   *  each @p n in the range @p [0,last-first).
  */
  template<ForwardIterator _InIter,
           OutputIterator<auto, _InIter::reference> _OutIter>
    _OutIter
    rotate_copy(_InIter __first, _InIter __middle,
                _InIter __last, _OutIter __result)
    {
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      return std::copy(__first, __middle,
                       std::copy(__middle, __last, __result));
    }

  /**
   *  @brief Randomly shuffle the elements of a sequence.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @return  Nothing.
   *
   *  Reorder the elements in the range @p [first,last) using a random
   *  distribution, so that every possible ordering of the sequence is
   *  equally likely.
  */
  template<RandomAccessIterator _Iter>
    requires HasSwap<_Iter::reference, _Iter::reference>
    inline void
    random_shuffle(_Iter __first, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first != __last)
        for (_Iter __i = __first + 1; __i != __last; ++__i) 
          {
            _Iter __other(__first + (std::rand() % (__i - __first) + 1));
            swap(*__i, *__other);
          }
    }

  /**
   *  @brief Shuffle the elements of a sequence using a random number
   *         generator.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  rand    The RNG functor or function.
   *  @return  Nothing.
   *
   *  Reorders the elements in the range @p [first,last) using @p rand to
   *  provide a random distribution. Calling @p rand(N) for a positive
   *  integer @p N should return a randomly chosen integer from the
   *  range [0,N).
  */
  template<RandomAccessIterator _Iter,
           Callable1<auto, _Iter::difference_type> _Rand>
    requires Convertible<_Rand::result_type, _Iter::difference_type>
          && HasSwap<_Iter::reference, _Iter::reference>
          && CopyConstructible<_Rand>
    void
    random_shuffle(_Iter __first, _Iter __last,
                   _Rand& __rand)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return;
      for (_Iter __i = __first + 1; __i != __last; ++__i)
        {
          _Iter __other(__first + __rand((__i - __first) + 1));
          swap(*__i, *__other);
        }
    }


  /**
   *  @brief Move elements for which a predicate is true to the beginning
   *         of a sequence.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  pred    A predicate functor.
   *  @return  An iterator @p middle such that @p pred(i) is true for each
   *  iterator @p i in the range @p [first,middle) and false for each @p i
   *  in the range @p [middle,last).
   *
   *  @p pred must not modify its operand. @p partition() does not preserve
   *  the relative ordering of elements in each group, use
   *  @p stable_partition() if this is needed.
  */
  template<ForwardIterator _Iter,
           Predicate<auto, _Iter::value_type> _Pred>
    requires HasSwap<_Iter::reference, _Iter::reference>
          && CopyConstructible<_Pred>
    _Iter
    partition(_Iter __first, _Iter __last,
              _Pred __pred)
    {
      if (__first == __last)
        return __first;

      while (__pred(*__first))
        if (++__first == __last)
          return __first;

      _Iter __next = __first;

      while (++__next != __last)
        if (__pred(*__next))
          {
            std::iter_swap(__first, __next);
            ++__first;
          }

      return __first;
    }

  /**
   *  @brief Move elements for which a predicate is true to the beginning
   *         of a sequence.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  pred    A predicate functor.
   *  @return  An iterator @p middle such that @p pred(i) is true for each
   *  iterator @p i in the range @p [first,middle) and false for each @p i
   *  in the range @p [middle,last).
   *
   *  @p pred must not modify its operand. @p partition() does not preserve
   *  the relative ordering of elements in each group, use
   *  @p stable_partition() if this is needed.
  */
  template<BidirectionalIterator _Iter,
           Predicate<auto, _Iter::value_type> _Pred>
    requires HasSwap<_Iter::reference, _Iter::reference>
          && CopyConstructible<_Pred>
    _Iter
    partition(_Iter __first, _Iter __last,
              _Pred __pred)
    {
      while (true)
        {
          while (true)
            if (__first == __last)
              return __first;
            else if (__pred(*__first))
              ++__first;
            else
              break;
          --__last;
          while (true)
            if (__first == __last)
              return __first;
            else if (!__pred(*__last))
              --__last;
            else
              break;
          std::iter_swap(__first, __last);
          ++__first;
        }
    }

  /**
   *  @if maint
   *  This is a helper function...
   *  @endif
  */
  template<ForwardIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    requires ShuffleIterator<_Iter>
    _Iter
    __inplace_stable_partition(_Iter __first,
                               _Iter __last,
                               _Pred __pred,
                               _Iter::difference_type __len)
    {
      if (__len == 1)
        return __pred(*__first) ? __last : __first;
      _Iter __middle = __first;
      std::advance(__middle, __len / 2);
      _Iter __begin = std::__inplace_stable_partition(__first, __middle,
                                                      __pred,
                                                      __len / 2);
      _Iter __end = std::__inplace_stable_partition(__middle, __last,
                                                    __pred,
                                                    __len - __len / 2);
      std::rotate(__begin, __middle, __end);
      std::advance(__begin, std::distance(__middle, __end));
      return __begin;
    }

  /**
   *  @if maint
   *  This is a helper function...
   *  @endif
  */
  template<ForwardIterator _Iter, typename _Pointer, 
           Predicate<auto, _Iter::value_type> _Pred>
    _Iter
    __stable_partition_adaptive(_Iter __first,
                                _Iter __last,
                                _Pred __pred,
                                _GLIBCXX_ITERATOR_TRAITS(ForwardIterator,
                                                         _Iter)::difference_type
                                  __len,
                                _Pointer __buffer,
                                _GLIBCXX_ITERATOR_TRAITS(ForwardIterator,
                                                         _Iter)::difference_type
                                  __buffer_size)
    {
      if (__len <= __buffer_size)
        {
          _Iter __result1 = __first;
          late_check {
            _Pointer __result2 = __buffer;
            for ( ; __first != __last ; ++__first)
              if (__pred(*__first))
                {
                  *__result1 = *__first;
                  ++__result1;
                }
              else
                {
                  *__result2 = *__first;
                  ++__result2;
                }
            std::copy(__buffer, __result2, __result1);
          }
          return __result1;
        }
      else
        {
          _Iter __middle = __first;
          std::advance(__middle, __len / 2);
          _Iter __begin =
            std::__stable_partition_adaptive(__first, __middle, __pred,
                                             __len / 2, __buffer,
                                             __buffer_size);
          _Iter __end =
            std::__stable_partition_adaptive(__middle, __last, __pred,
                                             __len - __len / 2,
                                             __buffer, __buffer_size);
          late_check {
            std::rotate(__begin, __middle, __end);
          }
          std::advance(__begin, std::distance(__middle, __end));
          return __begin;
        }
    }

  /**
   *  @brief Move elements for which a predicate is true to the beginning
   *         of a sequence, preserving relative ordering.
   *  @param  first   A forward iterator.
   *  @param  last    A forward iterator.
   *  @param  pred    A predicate functor.
   *  @return  An iterator @p middle such that @p pred(i) is true for each
   *  iterator @p i in the range @p [first,middle) and false for each @p i
   *  in the range @p [middle,last).
   *
   *  Performs the same function as @p partition() with the additional
   *  guarantee that the relative ordering of elements in each group is
   *  preserved, so any two elements @p x and @p y in the range
   *  @p [first,last) such that @p pred(x)==pred(y) will have the same
   *  relative ordering after calling @p stable_partition().
  */
  template<ForwardIterator _Iter, Predicate<auto, _Iter::value_type> _Pred>
    requires ShuffleIterator<_Iter>
    _Iter
    stable_partition(_Iter __first, _Iter __last,
                     _Pred __pred)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return __first;
      else
        {
          typedef _Iter::value_type _ValueType;
          typedef _Iter::difference_type _DistanceType;

          _Temporary_buffer<_Iter, _ValueType> __buf(__first,
                                                                __last);
        if (__buf.size() > 0)
          return
            std::__stable_partition_adaptive(__first, __last, __pred,
                                          _DistanceType(__buf.requested_size()),
                                          __buf.begin(), __buf.size());
        else
          return
            std::__inplace_stable_partition(__first, __last, __pred,
                                         _DistanceType(__buf.requested_size()));
        }
    }

  /**
   *  @if maint
   *  This is a helper function...
   *  @endif
  */
  template<RandomAccessIterator _Iter>
    requires LessThanComparable<_Iter::value_type>
          && HasSwap<_Iter::reference, _Iter::reference>
    _Iter
    __unguarded_partition(_Iter __first,
                          _Iter __last,
                          _GLIBCXX_ITERATOR_TRAITS_NEST(_Iter, value_type) __pivot)
    {
      while (true)
        {
          while (*__first < __pivot)
            ++__first;
          --__last;
          while (__pivot < *__last)
            --__last;
          if (!(__first < __last))
            return __first;
          std::iter_swap(__first, __last);
          ++__first;
        }
    }

  /**
   *  @if maint
   *  This is a helper function...
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires HasSwap<_Iter::reference, _Iter::reference>
    _Iter
    __unguarded_partition(_Iter __first,
                          _Iter __last,
                          _Iter::value_type __pivot,
                          _Compare __comp)
    {
      while (true)
        {
          while (__comp(*__first, __pivot))
            ++__first;
          --__last;
          while (__comp(__pivot, *__last))
            --__last;
          if (!(__first < __last))
            return __first;
          std::iter_swap(__first, __last);
          ++__first;
        }
    }

  /**
   *  @if maint
   *  @doctodo
   *  This controls some aspect of the sort routines.
   *  @endif
  */
  enum { _S_threshold = 16 };

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    __unguarded_linear_insert(_Iter __last, _Iter::value_type __val)
    {
      _Iter __next = __last;
      --__next;
      while (__val < *__next)
        {
          *__last = std_move(*__next);
          __last = __next;
          --__next;
        }
      *__last = std_move(__val);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
    void
    __unguarded_linear_insert(_Iter __last,
                              _Iter::value_type __val,
                              _Compare __comp)
    {
      _Iter __next = __last;
      --__next;
      while (__comp(__val, *__next))
        {
          *__last = std_move(*__next);
          __last = __next;
          --__next;
        }
      *__last = std_move(__val);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    __insertion_sort(_Iter __first,
                     _Iter __last)
    {
      if (__first == __last)
        return;

      for (_Iter __i = __first + 1; __i != __last; ++__i)
        {
          _Iter::value_type __val(std_move(*__i));
          if (__val < *__first)
            {
              late_check {
                std::copy_backward(__first, __i, __i + 1);
              }
              *__first = std_move(__val);
            }
          else
            std::__unguarded_linear_insert(__i, __val);
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
    void
    __insertion_sort(_Iter __first, _Iter __last, _Compare __comp)
    {
      if (__first == __last) return;

      for (_Iter __i = __first + 1; __i != __last; ++__i)
        {
          _Iter::value_type __val(std_move(*__i));
          if (__comp(__val, *__first))
            {
              late_check {
                std::copy_backward(__first, __i, __i + 1);
              }
              *__first = std_move(__val);
            }
          else
            std::__unguarded_linear_insert(__i, __val, __comp);
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    inline void
    __unguarded_insertion_sort(_Iter __first, _Iter __last)
    {
      for (_Iter __i = __first; __i != __last; ++__i)
        std::__unguarded_linear_insert(__i, *__i);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
    inline void
    __unguarded_insertion_sort(_Iter __first,
                               _Iter __last, _Compare __comp)
    {
      for (_Iter __i = __first; __i != __last; ++__i)
        std::__unguarded_linear_insert(__i, *__i, __comp);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter> 
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    __final_insertion_sort(_Iter __first,
                           _Iter __last)
    {
      if (__last - __first > int(_S_threshold))
        {
          std::__insertion_sort(__first, __first + int(_S_threshold));
          std::__unguarded_insertion_sort(__first + int(_S_threshold), __last);
        }
      else
        std::__insertion_sort(__first, __last);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
    void
    __final_insertion_sort(_Iter __first, _Iter __last, _Compare __comp)
    {
      if (__last - __first > int(_S_threshold))
        {
          std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
          std::__unguarded_insertion_sort(__first + int(_S_threshold), __last,
                                          __comp);
        }
      else
        std::__insertion_sort(__first, __last, __comp);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routines.
   *  @endif
  */
  template<typename _RandomAccessIterator>
    void
    __heap_select(_RandomAccessIterator __first,
		  _RandomAccessIterator __middle,
		  _RandomAccessIterator __last)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      std::make_heap(__first, __middle);
      for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
	if (*__i < *__first)
	  std::__pop_heap(__first, __middle, __i);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routines.
   *  @endif
  */
  template<typename _RandomAccessIterator, typename _Compare>
    void
    __heap_select(_RandomAccessIterator __first,
		  _RandomAccessIterator __middle,
		  _RandomAccessIterator __last, _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      std::make_heap(__first, __middle, __comp);
      for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
	if (__comp(*__i, *__first))
	  std::__pop_heap(__first, __middle, __i, __comp);
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routines.
   *  @endif
  */
  template<_GLIBCXX_REQ_PARM(IntegralLike, _Size)>
    inline _Size
    __lg(_Size __n)
    {
      _Size __k;
      for (__k = 0; __n != 1; __n >>= 1)
        ++__k;
      return __k;
    }

  /**
   *  @brief Sort the smallest elements of a sequence.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Sorts the smallest @p (middle-first) elements in the range
   *  @p [first,last) and moves them to the range @p [first,middle). The
   *  order of the remaining elements in the range @p [middle,last) is
   *  undefined.
   *  After the sort if @p i and @j are iterators in the range
   *  @p [first,middle) such that @i precedes @j and @k is an iterator in
   *  the range @p [middle,last) then @p *j<*i and @p *k<*i are both false.
  */
  template<RandomAccessIterator _Iter>
    requires OutputIterator<_Iter, _Iter::reference> 
          && OutputIterator<_Iter, const _Iter::value_type&> 
          && LessThanComparable<_Iter::value_type>
          && CopyConstructible<_Iter::value_type>
          && ShuffleIterator<_Iter>
    inline void
    partial_sort(_Iter __first,
                 _Iter __middle,
                 _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      std::__heap_select(__first, __middle, __last);
      std::sort_heap(__first, __middle);
    }

  /**
   *  @brief Sort the smallest elements of a sequence using a predicate
   *         for comparison.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A comparison functor.
   *  @return  Nothing.
   *
   *  Sorts the smallest @p (middle-first) elements in the range
   *  @p [first,last) and moves them to the range @p [first,middle). The
   *  order of the remaining elements in the range @p [middle,last) is
   *  undefined.
   *  After the sort if @p i and @j are iterators in the range
   *  @p [first,middle) such that @i precedes @j and @k is an iterator in
   *  the range @p [middle,last) then @p *comp(j,*i) and @p comp(*k,*i)
   *  are both false.
  */
  template<RandomAccessIterator _Iter,
           StrictWeakOrder<auto, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter> && CopyConstructible<_Compare>
    inline void
    partial_sort(_Iter __first,
                 _Iter __middle,
                 _Iter __last,
                 _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __middle);
      __glibcxx_requires_valid_range(__middle, __last);

      std::__heap_select(__first, __middle, __last, __comp);
      std::sort_heap(__first, __middle, __comp);
    }

  /**
   *  @brief Copy the smallest elements of a sequence.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  result_first   A random-access iterator.
   *  @param  result_last    Another random-access iterator.
   *  @return   An iterator indicating the end of the resulting sequence.
   *
   *  Copies and sorts the smallest N values from the range @p [first,last)
   *  to the range beginning at @p result_first, where the number of
   *  elements to be copied, @p N, is the smaller of @p (last-first) and
   *  @p (result_last-result_first).
   *  After the sort if @p i and @j are iterators in the range
   *  @p [result_first,result_first+N) such that @i precedes @j then
   *  @p *j<*i is false.
   *  The value returned is @p result_first+N.
  */
  template<InputIterator _InIter, RandomAccessIterator _RAIter>
  requires ShuffleIterator<_RAIter>
        && OutputIterator<_RAIter, _InIter::reference> 
        && HasLess<_InIter::value_type, _RAIter::value_type>
        && LessThanComparable<_RAIter::value_type>
    _RAIter
    partial_sort_copy(_InIter __first, _InIter __last,
                      _RAIter __result_first,
                      _RAIter __result_last)
    {
      typedef _InIter::value_type _InputValueType;
      typedef _RAIter::value_type _OutputValueType;
      typedef _RAIter::difference_type _DistanceType;

      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_valid_range(__result_first, __result_last);

      if (__result_first == __result_last)
        return __result_last;
      _RAIter __result_real_last = __result_first;
      while(__first != __last && __result_real_last != __result_last)
        {
          *__result_real_last = *__first;
          ++__result_real_last;
          ++__first;
        }
      std::make_heap(__result_first, __result_real_last);
      while (__first != __last)
        {
          if (*__first < *__result_first)
            {
              late_check {
                // error: conversion from
                // ‘std::Iterator<_Iter>::reference’ to non-scalar
                // type ‘value_type’ requested
                // DPG: It looks like __adjust_heap is getting an
                // archetype into its signature somehow.
                std::__adjust_heap(__result_first, _DistanceType(0),
                                   _DistanceType(__result_real_last
                                                 - __result_first),
                                   *__first);
              }
            }
          ++__first;
        }
      std::sort_heap(__result_first, __result_real_last);
      return __result_real_last;
    }

  /**
   *  @brief Copy the smallest elements of a sequence using a predicate for
   *         comparison.
   *  @param  first   An input iterator.
   *  @param  last    Another input iterator.
   *  @param  result_first   A random-access iterator.
   *  @param  result_last    Another random-access iterator.
   *  @param  comp    A comparison functor.
   *  @return   An iterator indicating the end of the resulting sequence.
   *
   *  Copies and sorts the smallest N values from the range @p [first,last)
   *  to the range beginning at @p result_first, where the number of
   *  elements to be copied, @p N, is the smaller of @p (last-first) and
   *  @p (result_last-result_first).
   *  After the sort if @p i and @j are iterators in the range
   *  @p [result_first,result_first+N) such that @i precedes @j then
   *  @p comp(*j,*i) is false.
   *  The value returned is @p result_first+N.
  */
  template<InputIterator _InIter, RandomAccessIterator _RAIter, 
           CopyConstructible _Compare>
    requires ShuffleIterator<_RAIter>
          && OutputIterator<_RAIter, _InIter::reference> 
          && BinaryPredicate<_Compare, _InIter::value_type, _RAIter::value_type>
          && StrictWeakOrder<_Compare, _RAIter::value_type>
    _RAIter
    partial_sort_copy(_InIter __first, _InIter __last,
                      _RAIter __result_first,
                      _RAIter __result_last,
                      _Compare __comp)
    {
      typedef _InIter::value_type _InputValueType;
      typedef _RAIter::value_type _OutputValueType;
      typedef _InIter::difference_type _DistanceType;

      __glibcxx_requires_valid_range(__first, __last);
      __glibcxx_requires_valid_range(__result_first, __result_last);

      if (__result_first == __result_last)
        return __result_last;
      _RAIter __result_real_last = __result_first;
      while(__first != __last && __result_real_last != __result_last)
        {
          *__result_real_last = *__first;
          ++__result_real_last;
          ++__first;
        }
      std::make_heap(__result_first, __result_real_last, __comp);
      while (__first != __last)
        {
          if (__comp(*__first, *__result_first))
            late_check {
              // error: conversion from
              // ‘std::InputIterator<_Iter>::difference_type’ to
              // non-scalar type ‘difference_type’ requested
              // DPG: Looks like another archetype issue
              std::__adjust_heap(__result_first, _DistanceType(0),
                                 _DistanceType(__result_real_last
                                               - __result_first),
                                 _InputValueType(*__first),
                                 __comp);
            }
          ++__first;
        }
      std::sort_heap(__result_first, __result_real_last, __comp);
      return __result_real_last;
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter, IntegralLike _Size>
    requires OutputIterator<_Iter, _Iter::reference>
          && OutputIterator<_Iter, const _Iter::value_type&>
          && ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
          && CopyConstructible<_Iter::value_type>
    void
    __introsort_loop(_Iter __first, _Iter __last, _Size __depth_limit)
    {
      typedef _Iter::value_type _ValueType;

      while (__last - __first > int(_S_threshold))
        {
          if (__depth_limit == 0)
            {
              std::partial_sort(__first, __last, __last);
              return;
            }
          --__depth_limit;
          _Iter __cut =
            std::__unguarded_partition
              (__first, __last,
               _ValueType(std::__median(_ValueType(*__first),
                                        _ValueType(*(__first
                                                     + (__last
                                                        - __first)
                                                     / 2)),
                                        _ValueType(*(__last - 1)))));
          std::__introsort_loop(__cut, __last, __depth_limit);
          __last = __cut;
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the sort routine.
   *  @endif
  */
  template<RandomAccessIterator _Iter,
           IntegralLike _Size,
           StrictWeakOrder<auto, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter> && CopyConstructible<_Compare>
    void
    __introsort_loop(_Iter __first, _Iter __last,
                     _Size __depth_limit, _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;

      while (__last - __first > int(_S_threshold))
        {
          if (__depth_limit == 0)
            {
              std::partial_sort(__first, __last, __last, __comp);
              return;
            }
          --__depth_limit;
          _Iter __cut =
            std::__unguarded_partition
              (__first, __last,
               _ValueType(std::__median(_ValueType(*__first),
                                        _ValueType(*(__first
                                                     + (__last
                                                        - __first)
                                                     / 2)),
                                        _ValueType(*(__last - 1)),
                                        __comp)),
                                       __comp);
          std::__introsort_loop(__cut, __last, __depth_limit, __comp);
          __last = __cut;
        }
    }

  /**
   *  @brief Sort the elements of a sequence.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range @p [first,last) in ascending order,
   *  such that @p *(i+1)<*i is false for each iterator @p i in the range
   *  @p [first,last-1).
   *
   *  The relative ordering of equivalent elements is not preserved, use
   *  @p stable_sort() if this is needed.
  */
  template<RandomAccessIterator _Iter>
    requires OutputIterator<_Iter, _Iter::reference>
          && OutputIterator<_Iter, const _Iter::value_type&>
          && LessThanComparable<_Iter::value_type>
          && ShuffleIterator<_Iter>
          && CopyConstructible<_Iter::value_type>
    inline void
    sort(_Iter __first, _Iter __last)

    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first != __last)
	{
	  std::__introsort_loop(__first, __last,
	    _Iter::difference_type(std::__lg(__last - __first) * 2));
	  std::__final_insertion_sort(__first, __last);
	}
    }

  /**
   *  @brief Sort the elements of a sequence using a predicate for comparison.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A comparison functor.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range @p [first,last) in ascending order,
   *  such that @p comp(*(i+1),*i) is false for every iterator @p i in the
   *  range @p [first,last-1).
   *
   *  The relative ordering of equivalent elements is not preserved, use
   *  @p stable_sort() if this is needed.
  */
  template<RandomAccessIterator _Iter,
           StrictWeakOrder<auto, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter> && CopyConstructible<_Compare>
    inline void
    sort(_Iter __first, _Iter __last, _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first != __last)
	{
	  std::__introsort_loop(__first, __last,
   	    _Iter::difference_type(std::__lg(__last - __first) * 2),
	    __comp);
	  std::__final_insertion_sort(__first, __last, __comp);
	}
    }

  /**
   *  @brief Finds the first position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  An iterator pointing to the first element "not less than" @a val,
   *           or end() if every element is less than @a val.
   *  @ingroup binarysearch
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasLess<_Iter::value_type, _Tp>
    _Iter
    lower_bound(_Iter __first, _Iter __last,
                const _Tp& __val)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned(__first, __last, __val);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (*__middle < __val)
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
          else
            __len = __half;
        }
      return __first;
    }

  /**
   *  @brief Finds the first position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An iterator pointing to the first element "not less than" @a val,
   *           or end() if every element is less than @a val.
   *  @ingroup binarysearch
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<ForwardIterator _Iter, typename _Tp,
           BinaryPredicate<auto, _Iter::value_type, _Tp> _Compare>
    requires CopyConstructible<_Compare>
    _Iter
    lower_bound(_Iter __first, _Iter __last,
                const _Tp& __val, _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned_pred(__first, __last, __val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (__comp(*__middle, __val))
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
          else
            __len = __half;
        }
      return __first;
    }

  /**
   *  @brief Finds the last position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  An iterator pointing to the first element greater than @a val,
   *           or end() if no elements are greater than @a val.
   *  @ingroup binarysearch
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasLess<_Tp, _Iter::value_type>
    _Iter
    upper_bound(_Iter __first, _Iter __last,
                const _Tp& __val)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned(__first, __last, __val);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (__val < *__middle)
            __len = __half;
          else
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
        }
      return __first;
    }

  /**
   *  @brief Finds the last position in which @a val could be inserted
   *         without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An iterator pointing to the first element greater than @a val,
   *           or end() if no elements are greater than @a val.
   *  @ingroup binarysearch
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<ForwardIterator _Iter, typename _Tp,
           BinaryPredicate<auto, _Tp, _Iter::value_type> _Compare>
    requires CopyConstructible<_Compare>
    _Iter
    upper_bound(_Iter __first, _Iter __last,
                const _Tp& __val, _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned_pred(__first, __last, __val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (__comp(__val, *__middle))
            __len = __half;
          else
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
        }
      return __first;
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<BidirectionalIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    __merge_without_buffer(_Iter __first,
                           _Iter __middle,
                           _Iter __last,
                           _Iter::difference_type __len1, 
                           _Iter::difference_type __len2)
    {
      if (__len1 == 0 || __len2 == 0)
        return;
      if (__len1 + __len2 == 2)
        {
          if (*__middle < *__first)
            std::iter_swap(__first, __middle);
          return;
        }
      _Iter __first_cut = __first;
      _Iter __second_cut = __middle;
      _Iter::difference_type __len11 = 0;
      _Iter::difference_type __len22 = 0;
      if (__len1 > __len2)
        {
          __len11 = __len1 / 2;
          std::advance(__first_cut, __len11);
          __second_cut = std::lower_bound(__middle, __last, 
                                          _Iter::value_type(*__first_cut));
          __len22 = std::distance(__middle, __second_cut);
        }
      else
        {
          __len22 = __len2 / 2;
          std::advance(__second_cut, __len22);
          __first_cut = std::upper_bound(__first, __middle, 
                                         _Iter::value_type(*__second_cut));
          __len11 = std::distance(__first, __first_cut);
        }
      std::rotate(__first_cut, __middle, __second_cut);
      _Iter __new_middle = __first_cut;
      std::advance(__new_middle, std::distance(__middle, __second_cut));
      std::__merge_without_buffer(__first, __first_cut, __new_middle,
                                  __len11, __len22);
      std::__merge_without_buffer(__new_middle, __second_cut, __last,
                                  __len1 - __len11, __len2 - __len22);
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<BidirectionalIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
          && CopyConstructible<_Compare>
    void
    __merge_without_buffer(_Iter __first,
                           _Iter __middle,
                           _Iter __last,
                           _Iter::difference_type __len1, 
                           _Iter::difference_type __len2,
                           _Compare __comp)
    {
      if (__len1 == 0 || __len2 == 0)
        return;
      if (__len1 + __len2 == 2)
        {
          if (__comp(*__middle, *__first))
            std::iter_swap(__first, __middle);
          return;
        }
      _Iter __first_cut = __first;
      _Iter __second_cut = __middle;
      _Iter::difference_type __len11 = 0;
      _Iter::difference_type __len22 = 0;
      if (__len1 > __len2)
        {
          __len11 = __len1 / 2;
          std::advance(__first_cut, __len11);
          __second_cut = std::lower_bound(__middle, __last, 
                                          _Iter::value_type(*__first_cut),
                                          __comp);
          __len22 = std::distance(__middle, __second_cut);
        }
      else
        {
          __len22 = __len2 / 2;
          std::advance(__second_cut, __len22);
          __first_cut = std::upper_bound(__first, __middle, 
                                         _Iter::value_type(*__second_cut),
                                         __comp);
          __len11 = std::distance(__first, __first_cut);
        }
      std::rotate(__first_cut, __middle, __second_cut);
      _Iter __new_middle = __first_cut;
      std::advance(__new_middle, std::distance(__middle, __second_cut));
      std::__merge_without_buffer(__first, __first_cut, __new_middle,
                                  __len11, __len22, __comp);
      std::__merge_without_buffer(__new_middle, __second_cut, __last,
                                  __len1 - __len11, __len2 - __len22, __comp);
    }

  /**
   *  @if maint
   *  This is a helper function for the stable sorting routines.
   *  @endif
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    __inplace_stable_sort(_Iter __first,
                          _Iter __last)
    {
      if (__last - __first < 15)
        {
          std::__insertion_sort(__first, __last);
          return;
        }
      _Iter __middle = __first + (__last - __first) / 2;
      std::__inplace_stable_sort(__first, __middle);
      std::__inplace_stable_sort(__middle, __last);
      std::__merge_without_buffer(__first, __middle, __last,
                                  __middle - __first,
                                  __last - __middle);
    }

  /**
   *  @if maint
   *  This is a helper function for the stable sorting routines.
   *  @endif
  */
  template<RandomAccessIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
          && CopyConstructible<_Compare>
    void
    __inplace_stable_sort(_Iter __first,
                          _Iter __last, _Compare __comp)
    {
      if (__last - __first < 15)
        {
          std::__insertion_sort(__first, __last, __comp);
          return;
        }
      _Iter __middle = __first + (__last - __first) / 2;
      std::__inplace_stable_sort(__first, __middle, __comp);
      std::__inplace_stable_sort(__middle, __last, __comp);
      std::__merge_without_buffer(__first, __middle, __last,
                                  __middle - __first,
                                  __last - __middle,
                                  __comp);
    }

  /**
   *  @brief Merges two sorted ranges.
   *  @param  first1  An iterator.
   *  @param  first2  Another iterator.
   *  @param  last1   Another iterator.
   *  @param  last2   Another iterator.
   *  @param  result  An iterator pointing to the end of the merged range.
   *  @return  An iterator pointing to the first element "not less than" @a val.
   *
   *  Merges the ranges [first1,last1) and [first2,last2) into the sorted range
   *  [result, result + (last1-first1) + (last2-first2)).  Both input ranges
   *  must be sorted, and the output range must not overlap with either of
   *  the input ranges.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, 
           typename _OutIter>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && HasLess<_InIter2::value_type, _InIter1::value_type>
    _OutIter
    merge(_InIter1 __first1, _InIter1 __last1,
          _InIter2 __first2, _InIter2 __last2,
          _OutIter __result)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        {
          if (*__first2 < *__first1)
            {
              *__result = *__first2;
              ++__first2;
            }
          else
            {
              *__result = *__first1;
              ++__first1;
            }
          ++__result;
        }
      return std::copy(__first2, __last2, std::copy(__first1, __last1,
                                                    __result));
    }

  /**
   *  @brief Merges two sorted ranges.
   *  @param  first1  An iterator.
   *  @param  first2  Another iterator.
   *  @param  last1   Another iterator.
   *  @param  last2   Another iterator.
   *  @param  result  An iterator pointing to the end of the merged range.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An iterator pointing to the first element "not less than" @a val.
   *
   *  Merges the ranges [first1,last1) and [first2,last2) into the sorted range
   *  [result, result + (last1-first1) + (last2-first2)).  Both input ranges
   *  must be sorted, and the output range must not overlap with either of
   *  the input ranges.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, 
           typename _OutIter,
           BinaryPredicate<auto, _InIter2::value_type, 
                           _InIter1::value_type> _Compare>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && CopyConstructible<_Compare>
    _OutIter
    merge(_InIter1 __first1, _InIter1 __last1,
          _InIter2 __first2, _InIter2 __last2,
          _OutIter __result, _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        {
          if (__comp(*__first2, *__first1))
            {
              *__result = *__first2;
              ++__first2;
            }
          else
            {
              *__result = *__first1;
              ++__first1;
            }
          ++__result;
        }
      return std::copy(__first2, __last2, std::copy(__first1, __last1,
                                                    __result));
    }

  template<typename _RandomAccessIterator1, typename _RandomAccessIterator2,
           typename _Distance>
    void
    __merge_sort_loop(_RandomAccessIterator1 __first,
                      _RandomAccessIterator1 __last,
                      _RandomAccessIterator2 __result,
                      _Distance __step_size)
    {
      const _Distance __two_step = 2 * __step_size;

      while (__last - __first >= __two_step)
        {
          __result = std::merge(__first, __first + __step_size,
                                __first + __step_size, __first + __two_step,
                                __result);
          __first += __two_step;
        }

      __step_size = std::min(_Distance(__last - __first), __step_size);
      std::merge(__first, __first + __step_size, __first + __step_size, __last,
                 __result);
    }

  template<typename _RandomAccessIterator1, typename _RandomAccessIterator2,
           typename _Distance, typename _Compare>
    void
    __merge_sort_loop(_RandomAccessIterator1 __first,
                      _RandomAccessIterator1 __last,
                      _RandomAccessIterator2 __result, _Distance __step_size,
                      _Compare __comp)
    {
      const _Distance __two_step = 2 * __step_size;

      while (__last - __first >= __two_step)
        {
          __result = std::merge(__first, __first + __step_size,
                                __first + __step_size, __first + __two_step,
                                __result,
                                __comp);
          __first += __two_step;
        }
      __step_size = std::min(_Distance(__last - __first), __step_size);

      std::merge(__first, __first + __step_size,
                 __first + __step_size, __last,
                 __result,
                 __comp);
    }

  enum { _S_chunk_size = 7 };

  template<typename _RandomAccessIterator, typename _Distance>
    void
    __chunk_insertion_sort(_RandomAccessIterator __first,
                           _RandomAccessIterator __last,
                           _Distance __chunk_size)
    {
      while (__last - __first >= __chunk_size)
        {
          std::__insertion_sort(__first, __first + __chunk_size);
          __first += __chunk_size;
        }
      std::__insertion_sort(__first, __last);
    }

  template<typename _RandomAccessIterator, typename _Distance, typename _Compare>
    void
    __chunk_insertion_sort(_RandomAccessIterator __first,
                           _RandomAccessIterator __last,
                           _Distance __chunk_size, _Compare __comp)
    {
      while (__last - __first >= __chunk_size)
        {
          std::__insertion_sort(__first, __first + __chunk_size, __comp);
          __first += __chunk_size;
        }
      std::__insertion_sort(__first, __last, __comp);
    }

  template<typename _RandomAccessIterator, typename _Pointer>
    void
    __merge_sort_with_buffer(_RandomAccessIterator __first,
                             _RandomAccessIterator __last,
                             _Pointer __buffer)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
        _Distance;

      const _Distance __len = __last - __first;
      const _Pointer __buffer_last = __buffer + __len;

      _Distance __step_size = _S_chunk_size;
      std::__chunk_insertion_sort(__first, __last, __step_size);

      while (__step_size < __len)
        {
          std::__merge_sort_loop(__first, __last, __buffer, __step_size);
          __step_size *= 2;
          std::__merge_sort_loop(__buffer, __buffer_last, __first, __step_size);
          __step_size *= 2;
        }
    }

  template<typename _RandomAccessIterator, typename _Pointer, typename _Compare>
    void
    __merge_sort_with_buffer(_RandomAccessIterator __first,
                             _RandomAccessIterator __last,
                             _Pointer __buffer, _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::difference_type
        _Distance;

      const _Distance __len = __last - __first;
      const _Pointer __buffer_last = __buffer + __len;

      _Distance __step_size = _S_chunk_size;
      std::__chunk_insertion_sort(__first, __last, __step_size, __comp);

      while (__step_size < __len)
        {
          std::__merge_sort_loop(__first, __last, __buffer,
                                 __step_size, __comp);
          __step_size *= 2;
          std::__merge_sort_loop(__buffer, __buffer_last, __first,
                                 __step_size, __comp);
          __step_size *= 2;
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
           typename _BidirectionalIterator3>
    _BidirectionalIterator3
    __merge_backward(_BidirectionalIterator1 __first1,
                     _BidirectionalIterator1 __last1,
                     _BidirectionalIterator2 __first2,
                     _BidirectionalIterator2 __last2,
                     _BidirectionalIterator3 __result)
    {
      if (__first1 == __last1)
        return std::copy_backward(__first2, __last2, __result);
      if (__first2 == __last2)
        return std::copy_backward(__first1, __last1, __result);
      --__last1;
      --__last2;
      while (true)
        {
          if (*__last2 < *__last1)
            {
              *--__result = *__last1;
              if (__first1 == __last1)
                return std::copy_backward(__first2, ++__last2, __result);
              --__last1;
            }
          else
            {
              *--__result = *__last2;
              if (__first2 == __last2)
                return std::copy_backward(__first1, ++__last1, __result);
              --__last2;
            }
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
           typename _BidirectionalIterator3, typename _Compare>
    _BidirectionalIterator3
    __merge_backward(_BidirectionalIterator1 __first1,
                     _BidirectionalIterator1 __last1,
                     _BidirectionalIterator2 __first2,
                     _BidirectionalIterator2 __last2,
                     _BidirectionalIterator3 __result,
                     _Compare __comp)
    {
      if (__first1 == __last1)
        return std::copy_backward(__first2, __last2, __result);
      if (__first2 == __last2)
        return std::copy_backward(__first1, __last1, __result);
      --__last1;
      --__last2;
      while (true)
        {
          if (__comp(*__last2, *__last1))
            {
              *--__result = *__last1;
              if (__first1 == __last1)
                return std::copy_backward(__first2, ++__last2, __result);
              --__last1;
            }
          else
            {
              *--__result = *__last2;
              if (__first2 == __last2)
                return std::copy_backward(__first1, ++__last1, __result);
              --__last2;
            }
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
           typename _Distance>
    _BidirectionalIterator1
    __rotate_adaptive(_BidirectionalIterator1 __first,
                      _BidirectionalIterator1 __middle,
                      _BidirectionalIterator1 __last,
                      _Distance __len1, _Distance __len2,
                      _BidirectionalIterator2 __buffer,
                      _Distance __buffer_size)
    {
      _BidirectionalIterator2 __buffer_end;
      if (__len1 > __len2 && __len2 <= __buffer_size)
        {
          __buffer_end = std::copy(__middle, __last, __buffer);
          std::copy_backward(__first, __middle, __last);
          return std::copy(__buffer, __buffer_end, __first);
        }
      else if (__len1 <= __buffer_size)
        {
          __buffer_end = std::copy(__first, __middle, __buffer);
          std::copy(__middle, __last, __first);
          return std::copy_backward(__buffer, __buffer_end, __last);
        }
      else
        {
          std::rotate(__first, __middle, __last);
          std::advance(__first, std::distance(__middle, __last));
          return __first;
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<typename _BidirectionalIterator, typename _Distance,
           typename _Pointer>
    void
    __merge_adaptive(_BidirectionalIterator __first,
                     _BidirectionalIterator __middle,
                     _BidirectionalIterator __last,
                     _Distance __len1, _Distance __len2,
                     _Pointer __buffer, _Distance __buffer_size)
    {
      if (__len1 <= __len2 && __len1 <= __buffer_size)
        {
          _Pointer __buffer_end = std::copy(__first, __middle, __buffer);
          std::merge(__buffer, __buffer_end, __middle, __last, __first);
        }
      else if (__len2 <= __buffer_size)
        {
          _Pointer __buffer_end = std::copy(__middle, __last, __buffer);
          std::__merge_backward(__first, __middle, __buffer,
                                __buffer_end, __last);
        }
      else
        {
          _BidirectionalIterator __first_cut = __first;
          _BidirectionalIterator __second_cut = __middle;
          _Distance __len11 = 0;
          _Distance __len22 = 0;
          if (__len1 > __len2)
            {
              __len11 = __len1 / 2;
              std::advance(__first_cut, __len11);
              __second_cut = std::lower_bound(__middle, __last,
                                              *__first_cut);
              __len22 = std::distance(__middle, __second_cut);
            }
          else
            {
              __len22 = __len2 / 2;
              std::advance(__second_cut, __len22);
              __first_cut = std::upper_bound(__first, __middle,
                                             *__second_cut);
              __len11 = std::distance(__first, __first_cut);
            }
          _BidirectionalIterator __new_middle =
            std::__rotate_adaptive(__first_cut, __middle, __second_cut,
                                   __len1 - __len11, __len22, __buffer,
                                   __buffer_size);
          std::__merge_adaptive(__first, __first_cut, __new_middle, __len11,
                                __len22, __buffer, __buffer_size);
          std::__merge_adaptive(__new_middle, __second_cut, __last,
                                __len1 - __len11,
                                __len2 - __len22, __buffer, __buffer_size);
        }
    }

  /**
   *  @if maint
   *  This is a helper function for the merge routines.
   *  @endif
  */
  template<typename _BidirectionalIterator, typename _Distance, typename _Pointer,
           typename _Compare>
    void
    __merge_adaptive(_BidirectionalIterator __first,
                     _BidirectionalIterator __middle,
                     _BidirectionalIterator __last,
                     _Distance __len1, _Distance __len2,
                     _Pointer __buffer, _Distance __buffer_size,
                     _Compare __comp)
    {
      if (__len1 <= __len2 && __len1 <= __buffer_size)
        {
          _Pointer __buffer_end = std::copy(__first, __middle, __buffer);
          std::merge(__buffer, __buffer_end, __middle, __last, __first, __comp);
        }
      else if (__len2 <= __buffer_size)
        {
          _Pointer __buffer_end = std::copy(__middle, __last, __buffer);
          std::__merge_backward(__first, __middle, __buffer, __buffer_end,
                                __last, __comp);
        }
      else
        {
          _BidirectionalIterator __first_cut = __first;
          _BidirectionalIterator __second_cut = __middle;
          _Distance __len11 = 0;
          _Distance __len22 = 0;
          if (__len1 > __len2)
            {
              __len11 = __len1 / 2;
              std::advance(__first_cut, __len11);
              __second_cut = std::lower_bound(__middle, __last, *__first_cut,
                                              __comp);
              __len22 = std::distance(__middle, __second_cut);
            }
          else
            {
              __len22 = __len2 / 2;
              std::advance(__second_cut, __len22);
              __first_cut = std::upper_bound(__first, __middle, *__second_cut,
                                             __comp);
              __len11 = std::distance(__first, __first_cut);
            }
          _BidirectionalIterator __new_middle =
            std::__rotate_adaptive(__first_cut, __middle, __second_cut,
                                   __len1 - __len11, __len22, __buffer,
                                   __buffer_size);
          std::__merge_adaptive(__first, __first_cut, __new_middle, __len11,
                                __len22, __buffer, __buffer_size, __comp);
          std::__merge_adaptive(__new_middle, __second_cut, __last,
                                __len1 - __len11,
                                __len2 - __len22, __buffer,
                                __buffer_size, __comp);
        }
    }

  /**
   *  @brief Merges two sorted ranges in place.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Merges two sorted and consecutive ranges, [first,middle) and
   *  [middle,last), and puts the result in [first,last).  The output will
   *  be sorted.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
   *
   *  If enough additional memory is available, this takes (last-first)-1
   *  comparisons.  Otherwise an NlogN algorithm is used, where N is
   *  distance(first,last).
  */
  template<BidirectionalIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    void
    inplace_merge(_Iter __first,
                  _Iter __middle,
                  _Iter __last)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_sorted(__first, __middle);
      __glibcxx_requires_sorted(__middle, __last);

      if (__first == __middle || __middle == __last)
        return;

      _DistanceType __len1 = std::distance(__first, __middle);
      _DistanceType __len2 = std::distance(__middle, __last);

      _Temporary_buffer<_Iter, _ValueType> __buf(__first,
                                                                  __last);
      if (__buf.begin() == 0)
        std::__merge_without_buffer(__first, __middle, __last, __len1, __len2);
      else
        std::__merge_adaptive(__first, __middle, __last, __len1, __len2,
                              __buf.begin(), _DistanceType(__buf.size()));
    }

  /**
   *  @brief Merges two sorted ranges in place.
   *  @param  first   An iterator.
   *  @param  middle  Another iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A functor to use for comparisons.
   *  @return  Nothing.
   *
   *  Merges two sorted and consecutive ranges, [first,middle) and
   *  [middle,last), and puts the result in [first,last).  The output will
   *  be sorted.  The sort is @e stable, that is, for equivalent
   *  elements in the two ranges, elements from the first range will always
   *  come before elements from the second.
   *
   *  If enough additional memory is available, this takes (last-first)-1
   *  comparisons.  Otherwise an NlogN algorithm is used, where N is
   *  distance(first,last).
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<BidirectionalIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
          && CopyConstructible<_Compare>
    void
    inplace_merge(_Iter __first,
                  _Iter __middle,
                  _Iter __last,
                  _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_sorted_pred(__first, __middle, __comp);
      __glibcxx_requires_sorted_pred(__middle, __last, __comp);

      if (__first == __middle || __middle == __last)
        return;

      const _DistanceType __len1 = std::distance(__first, __middle);
      const _DistanceType __len2 = std::distance(__middle, __last);

      _Temporary_buffer<_Iter, _ValueType> __buf(__first,
                                                                  __last);
      if (__buf.begin() == 0)
        std::__merge_without_buffer(__first, __middle, __last, __len1,
                                    __len2, __comp);
      else
        std::__merge_adaptive(__first, __middle, __last, __len1, __len2,
                              __buf.begin(), _DistanceType(__buf.size()),
                              __comp);
    }

  template<typename _RandomAccessIterator, typename _Pointer,
           typename _Distance>
    void
    __stable_sort_adaptive(_RandomAccessIterator __first,
                           _RandomAccessIterator __last,
                           _Pointer __buffer, _Distance __buffer_size)
    {
      const _Distance __len = (__last - __first + 1) / 2;
      const _RandomAccessIterator __middle = __first + __len;
      if (__len > __buffer_size)
        {
          std::__stable_sort_adaptive(__first, __middle,
                                      __buffer, __buffer_size);
          std::__stable_sort_adaptive(__middle, __last,
                                      __buffer, __buffer_size);
        }
      else
        {
          std::__merge_sort_with_buffer(__first, __middle, __buffer);
          std::__merge_sort_with_buffer(__middle, __last, __buffer);
        }
      std::__merge_adaptive(__first, __middle, __last,
                            _Distance(__middle - __first),
                            _Distance(__last - __middle),
                            __buffer, __buffer_size);
    }

  template<typename _RandomAccessIterator, typename _Pointer,
           typename _Distance, typename _Compare>
    void
    __stable_sort_adaptive(_RandomAccessIterator __first,
                           _RandomAccessIterator __last,
                           _Pointer __buffer, _Distance __buffer_size,
                           _Compare __comp)
    {
      const _Distance __len = (__last - __first + 1) / 2;
      const _RandomAccessIterator __middle = __first + __len;
      if (__len > __buffer_size)
        {
          std::__stable_sort_adaptive(__first, __middle, __buffer,
                                      __buffer_size, __comp);
          std::__stable_sort_adaptive(__middle, __last, __buffer,
                                      __buffer_size, __comp);
        }
      else
        {
          std::__merge_sort_with_buffer(__first, __middle, __buffer, __comp);
          std::__merge_sort_with_buffer(__middle, __last, __buffer, __comp);
        }
      std::__merge_adaptive(__first, __middle, __last,
                            _Distance(__middle - __first),
                            _Distance(__last - __middle),
                            __buffer, __buffer_size,
                            __comp);
    }

  /**
   *  @brief Sort the elements of a sequence, preserving the relative order
   *         of equivalent elements.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range @p [first,last) in ascending order,
   *  such that @p *(i+1)<*i is false for each iterator @p i in the range
   *  @p [first,last-1).
   *
   *  The relative ordering of equivalent elements is preserved, so any two
   *  elements @p x and @p y in the range @p [first,last) such that
   *  @p x<y is false and @p y<x is false will have the same relative
   *  ordering after calling @p stable_sort().
  */
  template<RandomAccessIterator _Iter>
    requires ShuffleIterator<_Iter>
          && LessThanComparable<_Iter::value_type>
    inline void
    stable_sort(_Iter __first, _Iter __last)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_valid_range(__first, __last);

      _Temporary_buffer<_Iter, _ValueType> __buf(__first,
								 __last);
      if (__buf.begin() == 0)
        std::__inplace_stable_sort(__first, __last);
      else
	std::__stable_sort_adaptive(__first, __last, __buf.begin(),
				    _DistanceType(__buf.size()));
    }

  /**
   *  @brief Sort the elements of a sequence using a predicate for comparison,
   *         preserving the relative order of equivalent elements.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A comparison functor.
   *  @return  Nothing.
   *
   *  Sorts the elements in the range @p [first,last) in ascending order,
   *  such that @p comp(*(i+1),*i) is false for each iterator @p i in the
   *  range @p [first,last-1).
   *
   *  The relative ordering of equivalent elements is preserved, so any two
   *  elements @p x and @p y in the range @p [first,last) such that
   *  @p comp(x,y) is false and @p comp(y,x) is false will have the same
   *  relative ordering after calling @p stable_sort().
  */
  template<RandomAccessIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires ShuffleIterator<_Iter>
          && CopyConstructible<_Compare>
    inline void
    stable_sort(_Iter __first, _Iter __last,
                _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_valid_range(__first, __last);

      _Temporary_buffer<_Iter, _ValueType> __buf(__first,
								 __last);
      if (__buf.begin() == 0)
        std::__inplace_stable_sort(__first, __last, __comp);
      else
	std::__stable_sort_adaptive(__first, __last, __buf.begin(),
				    _DistanceType(__buf.size()), __comp);
    }


  template<typename _RandomAccessIterator, typename _Size>
    void
    __introselect(_RandomAccessIterator __first, _RandomAccessIterator __nth,
		  _RandomAccessIterator __last, _Size __depth_limit)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > 3)
	{
	  if (__depth_limit == 0)
	    {
	      std::__heap_select(__first, __nth + 1, __last);
	      // Place the nth largest element in its final position.
	      std::iter_swap(__first, __nth);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last
								  - 1))));
	  if (__cut <= __nth)
	    __first = __cut;
	  else
	    __last = __cut;
	}
      std::__insertion_sort(__first, __last);
    }

  template<typename _RandomAccessIterator, typename _Size, typename _Compare>
    void
    __introselect(_RandomAccessIterator __first, _RandomAccessIterator __nth,
		  _RandomAccessIterator __last, _Size __depth_limit,
		  _Compare __comp)
    {
      typedef typename iterator_traits<_RandomAccessIterator>::value_type
	_ValueType;

      while (__last - __first > 3)
	{
	  if (__depth_limit == 0)
	    {
	      std::__heap_select(__first, __nth + 1, __last, __comp);
	      // Place the nth largest element in its final position.
	      std::iter_swap(__first, __nth);
	      return;
	    }
	  --__depth_limit;
	  _RandomAccessIterator __cut =
	    std::__unguarded_partition(__first, __last,
				       _ValueType(std::__median(*__first,
								*(__first
								  + (__last
								     - __first)
								  / 2),
								*(__last - 1),
								__comp)),
				       __comp);
	  if (__cut <= __nth)
	    __first = __cut;
	  else
	    __last = __cut;
	}
      std::__insertion_sort(__first, __last, __comp);
    }

  /**
   *  @brief Sort a sequence just enough to find a particular position.
   *  @param  first   An iterator.
   *  @param  nth     Another iterator.
   *  @param  last    Another iterator.
   *  @return  Nothing.
   *
   *  Rearranges the elements in the range @p [first,last) so that @p *nth
   *  is the same element that would have been in that position had the
   *  whole sequence been sorted.
   *  whole sequence been sorted. The elements either side of @p *nth are
   *  not completely sorted, but for any iterator @i in the range
   *  @p [first,nth) and any iterator @j in the range @p [nth,last) it
   *  holds that @p *j<*i is false.
  */
  template<RandomAccessIterator _Iter>
    _GLIBCXX_WHERE(LessThanComparable<_Iter::value_type>,
                   HasSwap<_Iter::reference, _Iter::reference>,
                   CopyAssignable<_Iter::reference>, 
                   CopyConstructible<_Iter::value_type>)
    inline void
    nth_element(_Iter __first, _Iter __nth, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __nth);
      __glibcxx_requires_valid_range(__nth, __last);

      if (__first == __last || __nth == __last)
	return;

      std::__introselect(__first, __nth, __last,
			 std::__lg(__last - __first) * 2);
    }

  /**
   *  @brief Sort a sequence just enough to find a particular position
   *         using a predicate for comparison.
   *  @param  first   An iterator.
   *  @param  nth     Another iterator.
   *  @param  last    Another iterator.
   *  @param  comp    A comparison functor.
   *  @return  Nothing.
   *
   *  Rearranges the elements in the range @p [first,last) so that @p *nth
   *  is the same element that would have been in that position had the
   *  whole sequence been sorted. The elements either side of @p *nth are
   *  not completely sorted, but for any iterator @i in the range
   *  @p [first,nth) and any iterator @j in the range @p [nth,last) it
   *  holds that @p comp(*j,*i) is false.
  */
  template<RandomAccessIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    _GLIBCXX_WHERE(HasSwap<_Iter::reference, _Iter::reference>,
                   CopyAssignable<_Iter::reference>, 
                   CopyConstructible<_Iter::value_type>)
    inline void
    nth_element(_Iter __first,  _Iter __nth, _Iter __last, _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __nth);
      __glibcxx_requires_valid_range(__nth, __last);

      if (__first == __last || __nth == __last)
	return;

      std::__introselect(__first, __nth, __last,
			 std::__lg(__last - __first) * 2, __comp);
    }

  /**
   *  @brief Finds the largest subrange in which @a val could be inserted
   *         at any place in it without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  An pair of iterators defining the subrange.
   *  @ingroup binarysearch
   *
   *  This is equivalent to
   *  @code
   *    std::make_pair(lower_bound(first, last, val),
   *                   upper_bound(first, last, val))
   *  @endcode
   *  but does not actually call those functions.
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasLess<_Tp, _Iter::value_type>
          && HasLess<_Iter::value_type, _Tp>
    pair<_Iter, _Iter>
    equal_range(_Iter __first, _Iter __last,
                const _Tp& __val)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned(__first, __last, __val);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle, __left, __right;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (*__middle < __val)
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
          else if (__val < *__middle)
            __len = __half;
          else
            {
              __left = std::lower_bound(__first, __middle, __val);
              std::advance(__first, __len);
              __right = std::upper_bound(++__middle, __first, __val);
              return pair<_Iter, _Iter>(__left, __right);
            }
        }
      return pair<_Iter, _Iter>(__first, __first);
    }

  /**
   *  @brief Finds the largest subrange in which @a val could be inserted
   *         at any place in it without changing the ordering.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  An pair of iterators defining the subrange.
   *  @ingroup binarysearch
   *
   *  This is equivalent to
   *  @code
   *    std::make_pair(lower_bound(first, last, val, comp),
   *                   upper_bound(first, last, val, comp))
   *  @endcode
   *  but does not actually call those functions.
  */
  template<ForwardIterator _Iter, typename _Tp,
           CopyConstructible _Compare>
    requires BinaryPredicate<_Compare, _Iter::value_type, _Tp>
          && BinaryPredicate<_Compare, _Tp, _Iter::value_type>
    pair<_Iter, _Iter>
    equal_range(_Iter __first, _Iter __last,
                const _Tp& __val,
                _Compare __comp)
    {
      typedef _Iter::value_type _ValueType;
      typedef _Iter::difference_type _DistanceType;

      __glibcxx_requires_partitioned_pred(__first, __last, __val, __comp);

      _DistanceType __len = std::distance(__first, __last);
      _DistanceType __half;
      _Iter __middle, __left, __right;

      while (__len > 0)
        {
          __half = __len >> 1;
          __middle = __first;
          std::advance(__middle, __half);
          if (__comp(*__middle, __val))
            {
              __first = __middle;
              ++__first;
              __len = __len - __half - 1;
            }
          else if (__comp(__val, *__middle))
            __len = __half;
          else
            {
              __left = std::lower_bound(__first, __middle, __val, __comp);
              std::advance(__first, __len);
              __right = std::upper_bound(++__middle, __first, __val, __comp);
              return pair<_Iter, _Iter>(__left, __right);
            }
        }
      return pair<_Iter, _Iter>(__first, __first);
    }

  /**
   *  @brief Determines whether an element exists in a range.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @return  True if @a val (or its equivelent) is in [@a first,@a last ].
   *  @ingroup binarysearch
   *
   *  Note that this does not actually return an iterator to @a val.  For
   *  that, use std::find or a container's specialized find member functions.
  */
  template<ForwardIterator _Iter, typename _Tp>
    requires HasLess<_Tp, _Iter::value_type>
          && HasLess<_Iter::value_type, _Tp>
    bool
    binary_search(_Iter __first, _Iter __last,
                  const _Tp& __val)
    {
      __glibcxx_requires_partitioned(__first, __last, __val);

      _Iter __i = std::lower_bound(__first, __last, __val);
      return __i != __last && !(__val < *__i);
    }

  /**
   *  @brief Determines whether an element exists in a range.
   *  @param  first   An iterator.
   *  @param  last    Another iterator.
   *  @param  val     The search term.
   *  @param  comp    A functor to use for comparisons.
   *  @return  True if @a val (or its equivelent) is in [@a first,@a last ].
   *  @ingroup binarysearch
   *
   *  Note that this does not actually return an iterator to @a val.  For
   *  that, use std::find or a container's specialized find member functions.
   *
   *  The comparison function should have the same effects on ordering as
   *  the function used for the initial sort.
  */
  template<ForwardIterator _Iter, typename _Tp, CopyConstructible _Compare>
    requires BinaryPredicate<_Compare, _Iter::value_type, _Tp>
          && BinaryPredicate<_Compare, _Tp, _Iter::value_type>
    bool
    binary_search(_Iter __first, _Iter __last,
                  const _Tp& __val, _Compare __comp)
    {
      __glibcxx_requires_partitioned_pred(__first, __last, __val, __comp);

      _Iter __i = std::lower_bound(__first, __last, __val, __comp);
      return __i != __last && !__comp(__val, *__i);
    }

  // Set algorithms: includes, set_union, set_intersection, set_difference,
  // set_symmetric_difference.  All of these algorithms have the precondition
  // that their input ranges are sorted and the postcondition that their output
  // ranges are sorted.

  /**
   *  @brief Determines whether all elements of a sequence exists in a range.
   *  @param  first1  Start of search range.
   *  @param  last1   End of search range.
   *  @param  first2  Start of sequence
   *  @param  last2   End of sequence.
   *  @return  True if each element in [first2,last2) is contained in order
   *  within [first1,last1).  False otherwise.
   *  @ingroup setoperations
   *
   *  This operation expects both [first1,last1) and [first2,last2) to be
   *  sorted.  Searches for the presence of each element in [first2,last2)
   *  within [first1,last1).  The iterators over each range only move forward,
   *  so this is a linear algorithm.  If an element in [first2,last2) is not
   *  found before the search iterator reaches @a last2, false is returned.
  */
  template<InputIterator _Iter1, InputIterator _Iter2>
    requires HasLess<_Iter1::value_type, _Iter2::value_type>
          && HasLess<_Iter2::value_type, _Iter1::value_type>
    bool
    includes(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        if (*__first2 < *__first1)
          return false;
        else if(*__first1 < *__first2)
          ++__first1;
        else
          ++__first1, ++__first2;

      return __first2 == __last2;
    }

  /**
   *  @brief Determines whether all elements of a sequence exists in a range
   *  using comparison.
   *  @param  first1  Start of search range.
   *  @param  last1   End of search range.
   *  @param  first2  Start of sequence
   *  @param  last2   End of sequence.
   *  @param  comp    Comparison function to use.
   *  @return  True if each element in [first2,last2) is contained in order
   *  within [first1,last1) according to comp.  False otherwise.
   *  @ingroup setoperations
   *
   *  This operation expects both [first1,last1) and [first2,last2) to be
   *  sorted.  Searches for the presence of each element in [first2,last2)
   *  within [first1,last1), using comp to decide.  The iterators over each
   *  range only move forward, so this is a linear algorithm.  If an element
   *  in [first2,last2) is not found before the search iterator reaches @a
   *  last2, false is returned.
  */
  template<InputIterator _Iter1, InputIterator _Iter2, 
           CopyConstructible _Compare>
    requires BinaryPredicate<_Compare, _Iter1::value_type, _Iter2::value_type>
          && BinaryPredicate<_Compare, _Iter2::value_type, _Iter1::value_type>
    bool
    includes(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2, _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        if (__comp(*__first2, *__first1))
          return false;
        else if(__comp(*__first1, *__first2))
          ++__first1;
        else
          ++__first1, ++__first2;

      return __first2 == __last2;
    }

  /**
   *  @brief Return the union of two sorted ranges.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  each range in order to the output range.  Iterators increment for each
   *  range.  When the current element of one range is less than the other,
   *  that element is copied and the iterator advanced.  If an element is
   *  contained in both ranges, the element from the first range is copied and
   *  both ranges advance.  The output range may not overlap either input
   *  range.
  */
   template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && HasLess<_InIter2::value_type, _InIter1::value_type>
          && HasLess<_InIter1::value_type, _InIter2::value_type>
    _OutIter
    set_union(_InIter1 __first1, _InIter1 __last1,
              _InIter2 __first2, _InIter2 __last2,
              _OutIter __result)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        {
          if (*__first1 < *__first2)
            {
              *__result = *__first1;
              ++__first1;
            }
          else if (*__first2 < *__first1)
            {
              *__result = *__first2;
              ++__first2;
            }
          else
            {
              *__result = *__first1;
              ++__first1;
              ++__first2;
            }
          ++__result;
        }
      return std::copy(__first2, __last2, std::copy(__first1, __last1,
                                                    __result));
    }

  /**
   *  @brief Return the union of two sorted ranges using a comparison functor.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @param  comp    The comparison functor.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  each range in order to the output range.  Iterators increment for each
   *  range.  When the current element of one range is less than the other
   *  according to @a comp, that element is copied and the iterator advanced.
   *  If an equivalent element according to @a comp is contained in both
   *  ranges, the element from the first range is copied and both ranges
   *  advance.  The output range may not overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter,
           CopyConstructible _Compare>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && BinaryPredicate<_Compare, _InIter1::value_type, _InIter2::value_type>
          && BinaryPredicate<_Compare, _InIter2::value_type, _InIter1::value_type>
    _OutIter
    set_union(_InIter1 __first1, _InIter1 __last1,
              _InIter2 __first2, _InIter2 __last2,
              _OutIter __result, _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        {
          if (__comp(*__first1, *__first2))
            {
              *__result = *__first1;
              ++__first1;
            }
          else if (__comp(*__first2, *__first1))
            {
              *__result = *__first2;
              ++__first2;
            }
          else
            {
              *__result = *__first1;
              ++__first1;
              ++__first2;
            }
          ++__result;
        }
      return std::copy(__first2, __last2, std::copy(__first1, __last1,
                                                    __result));
    }

  /**
   *  @brief Return the intersection of two sorted ranges.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  both ranges in order to the output range.  Iterators increment for each
   *  range.  When the current element of one range is less than the other,
   *  that iterator advances.  If an element is contained in both ranges, the
   *  element from the first range is copied and both ranges advance.  The
   *  output range may not overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && HasLess<_InIter2::value_type, _InIter1::value_type>
          && HasLess<_InIter1::value_type, _InIter2::value_type>
    _OutIter
    set_intersection(_InIter1 __first1, _InIter1 __last1,
                     _InIter2 __first2, _InIter2 __last2,
                     _OutIter __result)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        if (*__first1 < *__first2)
          ++__first1;
        else if (*__first2 < *__first1)
          ++__first2;
        else
          {
            *__result = *__first1;
            ++__first1;
            ++__first2;
            ++__result;
          }
      return __result;
    }

  /**
   *  @brief Return the intersection of two sorted ranges using comparison
   *  functor.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @param  comp    The comparison functor.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  both ranges in order to the output range.  Iterators increment for each
   *  range.  When the current element of one range is less than the other
   *  according to @a comp, that iterator advances.  If an element is
   *  contained in both ranges according to @a comp, the element from the
   *  first range is copied and both ranges advance.  The output range may not
   *  overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter,
           CopyConstructible _Compare>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && BinaryPredicate<_Compare, _InIter1::value_type, _InIter2::value_type>
          && BinaryPredicate<_Compare, _InIter2::value_type, _InIter1::value_type>
    _OutIter
    set_intersection(_InIter1 __first1, _InIter1 __last1,
                     _InIter2 __first2, _InIter2 __last2,
                     _OutIter __result, _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        if (__comp(*__first1, *__first2))
          ++__first1;
        else if (__comp(*__first2, *__first1))
          ++__first2;
        else
          {
            *__result = *__first1;
            ++__first1;
            ++__first2;
            ++__result;
          }
      return __result;
    }

  /**
   *  @brief Return the difference of two sorted ranges.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  the first range but not the second in order to the output range.
   *  Iterators increment for each range.  When the current element of the
   *  first range is less than the second, that element is copied and the
   *  iterator advances.  If the current element of the second range is less,
   *  the iterator advances, but no element is copied.  If an element is
   *  contained in both ranges, no elements are copied and both ranges
   *  advance.  The output range may not overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && HasLess<_InIter2::value_type, _InIter1::value_type>
          && HasLess<_InIter1::value_type, _InIter2::value_type>
    _OutIter
    set_difference(_InIter1 __first1, _InIter1 __last1,
                   _InIter2 __first2, _InIter2 __last2,
                   _OutIter __result)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        if (*__first1 < *__first2)
          {
            *__result = *__first1;
            ++__first1;
            ++__result;
          }
        else if (*__first2 < *__first1)
          ++__first2;
        else
          {
            ++__first1;
            ++__first2;
          }
      return std::copy(__first1, __last1, __result);
    }

  /**
   *  @brief  Return the difference of two sorted ranges using comparison
   *  functor.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @param  comp    The comparison functor.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  the first range but not the second in order to the output range.
   *  Iterators increment for each range.  When the current element of the
   *  first range is less than the second according to @a comp, that element
   *  is copied and the iterator advances.  If the current element of the
   *  second range is less, no element is copied and the iterator advances.
   *  If an element is contained in both ranges according to @a comp, no
   *  elements are copied and both ranges advance.  The output range may not
   *  overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, 
           typename _OutIter, CopyConstructible _Compare>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && BinaryPredicate<_Compare, _InIter1::value_type, _InIter2::value_type>
          && BinaryPredicate<_Compare, _InIter2::value_type, _InIter1::value_type>
    _OutIter
    set_difference(_InIter1 __first1, _InIter1 __last1,
                   _InIter2 __first2, _InIter2 __last2,
                   _OutIter __result, _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        if (__comp(*__first1, *__first2))
          {
            *__result = *__first1;
            ++__first1;
            ++__result;
          }
        else if (__comp(*__first2, *__first1))
          ++__first2;
        else
          {
            ++__first1;
            ++__first2;
          }
      return std::copy(__first1, __last1, __result);
    }

  /**
   *  @brief  Return the symmetric difference of two sorted ranges.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  one range but not the other in order to the output range.  Iterators
   *  increment for each range.  When the current element of one range is less
   *  than the other, that element is copied and the iterator advances.  If an
   *  element is contained in both ranges, no elements are copied and both
   *  ranges advance.  The output range may not overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, typename _OutIter>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && HasLess<_InIter2::value_type, _InIter1::value_type>
          && HasLess<_InIter1::value_type, _InIter2::value_type>
    _OutIter
    set_symmetric_difference(_InIter1 __first1, _InIter1 __last1,
                             _InIter2 __first2, _InIter2 __last2,
                             _OutIter __result)
    {
      __glibcxx_requires_sorted(__first1, __last1);
      __glibcxx_requires_sorted(__first2, __last2);

      while (__first1 != __last1 && __first2 != __last2)
        if (*__first1 < *__first2)
          {
            *__result = *__first1;
            ++__first1;
            ++__result;
          }
        else if (*__first2 < *__first1)
          {
            *__result = *__first2;
            ++__first2;
            ++__result;
          }
        else
          {
            ++__first1;
            ++__first2;
          }
      return std::copy(__first2, __last2, std::copy(__first1,
                                                    __last1, __result));
    }

  /**
   *  @brief  Return the symmetric difference of two sorted ranges using
   *  comparison functor.
   *  @param  first1  Start of first range.
   *  @param  last1   End of first range.
   *  @param  first2  Start of second range.
   *  @param  last2   End of second range.
   *  @param  comp    The comparison functor.
   *  @return  End of the output range.
   *  @ingroup setoperations
   *
   *  This operation iterates over both ranges, copying elements present in
   *  one range but not the other in order to the output range.  Iterators
   *  increment for each range.  When the current element of one range is less
   *  than the other according to @a comp, that element is copied and the
   *  iterator advances.  If an element is contained in both ranges according
   *  to @a comp, no elements are copied and both ranges advance.  The output
   *  range may not overlap either input range.
  */
  template<InputIterator _InIter1, InputIterator _InIter2, 
           typename _OutIter, CopyConstructible _Compare>
    requires OutputIterator<_OutIter, _InIter1::reference>
          && OutputIterator<_OutIter, _InIter2::reference>
          && BinaryPredicate<_Compare, _InIter1::value_type, _InIter2::value_type>
          && BinaryPredicate<_Compare, _InIter2::value_type, _InIter1::value_type>
    _OutIter
    set_symmetric_difference(_InIter1 __first1, _InIter1 __last1,
                             _InIter2 __first2, _InIter2 __last2,
                             _OutIter __result,
                             _Compare __comp)
    {
      __glibcxx_requires_sorted_pred(__first1, __last1, __comp);
      __glibcxx_requires_sorted_pred(__first2, __last2, __comp);

      while (__first1 != __last1 && __first2 != __last2)
        if (__comp(*__first1, *__first2))
          {
            *__result = *__first1;
            ++__first1;
            ++__result;
          }
        else if (__comp(*__first2, *__first1))
          {
            *__result = *__first2;
            ++__first2;
            ++__result;
          }
        else
          {
            ++__first1;
            ++__first2;
          }
      return std::copy(__first2, __last2, std::copy(__first1,
                                                    __last1, __result));
    }

  // min_element and max_element, with and without an explicitly supplied
  // comparison function.

  /**
   *  @brief  Return the maximum element in a range.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @return  Iterator referencing the first instance of the largest value.
  */
   template<ForwardIterator _Iter>
    requires LessThanComparable<_Iter::value_type>
    _Iter
    max_element(_Iter __first, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return __first;
      _Iter __result = __first;
      while (++__first != __last)
        if (*__result < *__first)
          __result = __first;
      return __result;
    }

  /**
   *  @brief  Return the maximum element in a range using comparison functor.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @param  comp   Comparison functor.
   *  @return  Iterator referencing the first instance of the largest value
   *  according to comp.
  */
  template<ForwardIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires CopyConstructible<_Compare>
    _Iter
    max_element(_Iter __first, _Iter __last,
                _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last) return __first;
      _Iter __result = __first;
      while (++__first != __last)
        if (__comp(*__result, *__first)) __result = __first;
      return __result;
    }

  /**
   *  @brief  Return the minimum element in a range.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @return  Iterator referencing the first instance of the smallest value.
  */
   template<ForwardIterator _Iter>
    requires LessThanComparable<_Iter::value_type>
    _Iter
    min_element(_Iter __first, _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return __first;
      _Iter __result = __first;
      while (++__first != __last)
        if (*__first < *__result)
          __result = __first;
      return __result;
    }

  /**
   *  @brief  Return the minimum element in a range using comparison functor.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @param  comp   Comparison functor.
   *  @return  Iterator referencing the first instance of the smallest value
   *  according to comp.
  */
  template<ForwardIterator _Iter, 
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires CopyConstructible<_Compare>
    _Iter
    min_element(_Iter __first, _Iter __last,
                _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return __first;
      _Iter __result = __first;
      while (++__first != __last)
        if (__comp(*__first, *__result))
          __result = __first;
      return __result;
    }

  // next_permutation and prev_permutation, with and without an explicitly
  // supplied comparison function.

  /**
   *  @brief  Permute range into the next "dictionary" ordering.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @return  False if wrapped to first permutation, true otherwise.
   *
   *  Treats all permutations of the range as a set of "dictionary" sorted
   *  sequences.  Permutes the current sequence into the next one of this set.
   *  Returns true if there are more sequences to generate.  If the sequence
   *  is the largest of the set, the smallest is generated and false returned.
  */
  template<BidirectionalIterator _Iter>
    requires LessThanComparable<_Iter::value_type>
          && HasSwap<_Iter::reference, _Iter::reference>
    bool
    next_permutation(_Iter __first,
                     _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return false;
      _Iter __i = __first;
      ++__i;
      if (__i == __last)
        return false;
      __i = __last;
      --__i;

      for(;;)
        {
          _Iter __ii = __i;
          --__i;
          if (*__i < *__ii)
            {
              _Iter __j = __last;
              while (!(*__i < *--__j))
                {}
              std::iter_swap(__i, __j);
              std::reverse(__ii, __last);
              return true;
            }
          if (__i == __first)
            {
              std::reverse(__first, __last);
              return false;
            }
        }
    }

  /**
   *  @brief  Permute range into the next "dictionary" ordering using
   *  comparison functor.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @param  comp
   *  @return  False if wrapped to first permutation, true otherwise.
   *
   *  Treats all permutations of the range [first,last) as a set of
   *  "dictionary" sorted sequences ordered by @a comp.  Permutes the current
   *  sequence into the next one of this set.  Returns true if there are more
   *  sequences to generate.  If the sequence is the largest of the set, the
   *  smallest is generated and false returned.
  */
  template<BidirectionalIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires HasSwap<_Iter::reference, _Iter::reference>
          && CopyConstructible<_Compare>
    bool
    next_permutation(_Iter __first,
                     _Iter __last, _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return false;
      _Iter __i = __first;
      ++__i;
      if (__i == __last)
        return false;
      __i = __last;
      --__i;

      for(;;)
        {
          _Iter __ii = __i;
          --__i;
          if (__comp(*__i, *__ii))
            {
              _Iter __j = __last;
              while (!__comp(*__i, *--__j))
                {}
              std::iter_swap(__i, __j);
              std::reverse(__ii, __last);
              return true;
            }
          if (__i == __first)
            {
              std::reverse(__first, __last);
              return false;
            }
        }
    }

  /**
   *  @brief  Permute range into the previous "dictionary" ordering.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @return  False if wrapped to last permutation, true otherwise.
   *
   *  Treats all permutations of the range as a set of "dictionary" sorted
   *  sequences.  Permutes the current sequence into the previous one of this
   *  set.  Returns true if there are more sequences to generate.  If the
   *  sequence is the smallest of the set, the largest is generated and false
   *  returned.
  */
  template<BidirectionalIterator _Iter>
    requires LessThanComparable<_Iter::value_type>
          && HasSwap<_Iter::reference, _Iter::reference>
    bool
    prev_permutation(_Iter __first,
                     _Iter __last)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return false;
      _Iter __i = __first;
      ++__i;
      if (__i == __last)
        return false;
      __i = __last;
      --__i;

      for(;;)
        {
          _Iter __ii = __i;
          --__i;
          if (*__ii < *__i)
            {
              _Iter __j = __last;
              while (!(*--__j < *__i))
                {}
              std::iter_swap(__i, __j);
              std::reverse(__ii, __last);
              return true;
            }
          if (__i == __first)
            {
              std::reverse(__first, __last);
              return false;
            }
        }
    }

  /**
   *  @brief  Permute range into the previous "dictionary" ordering using
   *  comparison functor.
   *  @param  first  Start of range.
   *  @param  last   End of range.
   *  @param  comp
   *  @return  False if wrapped to last permutation, true otherwise.
   *
   *  Treats all permutations of the range [first,last) as a set of
   *  "dictionary" sorted sequences ordered by @a comp.  Permutes the current
   *  sequence into the previous one of this set.  Returns true if there are
   *  more sequences to generate.  If the sequence is the smallest of the set,
   *  the largest is generated and false returned.
  */
  template<BidirectionalIterator _Iter,
           BinaryPredicate<auto, _Iter::value_type, _Iter::value_type> _Compare>
    requires HasSwap<_Iter::reference, _Iter::reference>
    bool
    prev_permutation(_Iter __first,
                     _Iter __last, _Compare __comp)
    {
      __glibcxx_requires_valid_range(__first, __last);

      if (__first == __last)
        return false;
      _Iter __i = __first;
      ++__i;
      if (__i == __last)
        return false;
      __i = __last;
      --__i;

      for(;;)
        {
          _Iter __ii = __i;
          --__i;
          if (__comp(*__ii, *__i))
            {
              _Iter __j = __last;
              while (!__comp(*--__j, *__i))
                {}
              std::iter_swap(__i, __j);
              std::reverse(__ii, __last);
              return true;
            }
          if (__i == __first)
            {
              std::reverse(__first, __last);
              return false;
            }
        }
    }

  /**
   *  @brief  Find element from a set in a sequence.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of match candidates.
   *  @param  last2   End of match candidates.
   *  @return   The first iterator @c i in the range
   *  @p [first1,last1) such that @c *i == @p *(i2) such that i2 is an
   *  interator in [first2,last2), or @p last1 if no such iterator exists.
   *
   *  Searches the range @p [first1,last1) for an element that is equal to
   *  some element in the range [first2,last2).  If found, returns an iterator
   *  in the range [first1,last1), otherwise returns @p last1.
  */
  template<InputIterator _InIter, ForwardIterator _ForIter>
    requires HasEqualTo<_InIter::value_type, _ForIter::value_type>
    _InIter
    find_first_of(_InIter __first1, _InIter __last1,
                  _ForIter __first2, _ForIter __last2)
    {
      __glibcxx_requires_valid_range(__first1, __last1);
      __glibcxx_requires_valid_range(__first2, __last2);

      for ( ; __first1 != __last1; ++__first1)
        for (_ForIter __iter = __first2; __iter != __last2; ++__iter)
          if (*__first1 == *__iter)
            return __first1;
      return __last1;
    }

  /**
   *  @brief  Find element from a set in a sequence using a predicate.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of match candidates.
   *  @param  last2   End of match candidates.
   *  @param  comp    Predicate to use.
   *  @return   The first iterator @c i in the range
   *  @p [first1,last1) such that @c comp(*i, @p *(i2)) is true and i2 is an
   *  interator in [first2,last2), or @p last1 if no such iterator exists.
   *
   *  Searches the range @p [first1,last1) for an element that is equal to
   *  some element in the range [first2,last2).  If found, returns an iterator in
   *  the range [first1,last1), otherwise returns @p last1.
  */
  template<InputIterator _InIter, ForwardIterator _ForIter,
           BinaryPredicate<auto, _InIter::value_type, 
                           _ForIter::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _InIter
    find_first_of(_InIter __first1, _InIter __last1,
                  _ForIter __first2, _ForIter __last2,
                  _Pred __comp)
    {
      __glibcxx_requires_valid_range(__first1, __last1);
      __glibcxx_requires_valid_range(__first2, __last2);

      for ( ; __first1 != __last1; ++__first1)
        for (_ForIter __iter = __first2; __iter != __last2; ++__iter)
          if (__comp(*__first1, *__iter))
            return __first1;
      return __last1;
    }


  /**
   *  @brief  Find last matching subsequence in a sequence.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of sequence to match.
   *  @param  last2   End of sequence to match.
   *  @return   The last iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that @c *(i+N) == @p *(first2+N)
   *  for each @c N in the range @p [0,last2-first2), or @p last1 if no
   *  such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2) and
   *  returns an iterator to the first element of the sub-sequence, or
   *  @p last1 if the sub-sequence is not found.  The sub-sequence will be the
   *  last such subsequence contained in [first,last1).
   *
   *  Because the sub-sequence must lie completely within the range
   *  @p [first1,last1) it must start at a position less than
   *  @p last1-(last2-first2) where @p last2-first2 is the length of the
   *  sub-sequence.
   *  This means that the returned iterator @c i will be in the range
   *  @p [first1,last1-(last2-first2))
  */
  template<ForwardIterator _Iter1, ForwardIterator _Iter2>
    requires HasEqualTo<_Iter1::value_type, _Iter2::value_type>
    _Iter1
    find_end(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2)
    {
      if (__first2 == __last2)
        return __last1;
      else
        {
          _Iter1 __result = __last1;
          while (1)
            {
              _Iter1 __new_result
                = std::search(__first1, __last1, __first2, __last2);
              if (__new_result == __last1)
                return __result;
              else
                {
                  __result = __new_result;
                  __first1 = __new_result;
                  ++__first1;
                }
            }
        }
    }

  /**
   *  @brief  Find last matching subsequence in a sequence using a predicate.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of sequence to match.
   *  @param  last2   End of sequence to match.
   *  @param  comp    The predicate to use.
   *  @return   The last iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that @c predicate(*(i+N), @p
   *  (first2+N)) is true for each @c N in the range @p [0,last2-first2), or
   *  @p last1 if no such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2) using
   *  comp as a predicate and returns an iterator to the first element of the
   *  sub-sequence, or @p last1 if the sub-sequence is not found.  The
   *  sub-sequence will be the last such subsequence contained in
   *  [first,last1).
   *
   *  Because the sub-sequence must lie completely within the range
   *  @p [first1,last1) it must start at a position less than
   *  @p last1-(last2-first2) where @p last2-first2 is the length of the
   *  sub-sequence.
   *  This means that the returned iterator @c i will be in the range
   *  @p [first1,last1-(last2-first2))
  */
  template<ForwardIterator _Iter1, ForwardIterator _Iter2,
           BinaryPredicate<auto, _Iter1::value_type, _Iter2::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _Iter1
    find_end(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2,
             _Pred __comp)
    {
      if (__first2 == __last2)
        return __last1;
      else
        {
          _Iter1 __result = __last1;
          while (1)
            {
              _Iter1 __new_result
                = std::search(__first1, __last1, __first2, __last2, __comp);
              if (__new_result == __last1)
                return __result;
              else
                {
                  __result = __new_result;
                  __first1 = __new_result;
                  ++__first1;
                }
            }
        }
    }

  /**
   *  @brief  Find last matching subsequence in a sequence.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of sequence to match.
   *  @param  last2   End of sequence to match.
   *  @return   The last iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that @c *(i+N) == @p *(first2+N)
   *  for each @c N in the range @p [0,last2-first2), or @p last1 if no
   *  such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2) and
   *  returns an iterator to the first element of the sub-sequence, or
   *  @p last1 if the sub-sequence is not found.  The sub-sequence will be the
   *  last such subsequence contained in [first,last1).
   *
   *  Because the sub-sequence must lie completely within the range
   *  @p [first1,last1) it must start at a position less than
   *  @p last1-(last2-first2) where @p last2-first2 is the length of the
   *  sub-sequence.
   *  This means that the returned iterator @c i will be in the range
   *  @p [first1,last1-(last2-first2))
  */
  template<BidirectionalIterator _Iter1, BidirectionalIterator _Iter2>
  requires HasEqualTo<BidirectionalIterator<_Iter1>::value_type, 
                      BidirectionalIterator<_Iter2>::value_type>
    _Iter1
    find_end(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2)
    {
      late_check {
      typedef reverse_iterator<_Iter1> _RevIterator1;
      typedef reverse_iterator<_Iter2> _RevIterator2;

      _RevIterator1 __rlast1(__first1);
      _RevIterator2 __rlast2(__first2);
      _RevIterator1 __rresult = std::search(_RevIterator1(__last1), __rlast1,
                                            _RevIterator2(__last2), __rlast2);

      if (__rresult == __rlast1)
        return __last1;
      else
        {
          _Iter1 __result = __rresult.base();
          std::advance(__result, -std::distance(__first2, __last2));
          return __result;
        }
      }
    }

  /**
   *  @brief  Find last matching subsequence in a sequence using a predicate.
   *  @param  first1  Start of range to search.
   *  @param  last1   End of range to search.
   *  @param  first2  Start of sequence to match.
   *  @param  last2   End of sequence to match.
   *  @param  comp    The predicate to use.
   *  @return   The last iterator @c i in the range
   *  @p [first1,last1-(last2-first2)) such that @c predicate(*(i+N), @p
   *  (first2+N)) is true for each @c N in the range @p [0,last2-first2), or
   *  @p last1 if no such iterator exists.
   *
   *  Searches the range @p [first1,last1) for a sub-sequence that compares
   *  equal value-by-value with the sequence given by @p [first2,last2) using
   *  comp as a predicate and returns an iterator to the first element of the
   *  sub-sequence, or @p last1 if the sub-sequence is not found.  The
   *  sub-sequence will be the last such subsequence contained in
   *  [first,last1).
   *
   *  Because the sub-sequence must lie completely within the range
   *  @p [first1,last1) it must start at a position less than
   *  @p last1-(last2-first2) where @p last2-first2 is the length of the
   *  sub-sequence.
   *  This means that the returned iterator @c i will be in the range
   *  @p [first1,last1-(last2-first2))
  */
  template<BidirectionalIterator _Iter1, BidirectionalIterator _Iter2, 
           BinaryPredicate<auto, BidirectionalIterator<_Iter1>::value_type,
                           BidirectionalIterator<_Iter2>::value_type> _Pred>
    requires CopyConstructible<_Pred>
    _Iter1
    find_end(_Iter1 __first1, _Iter1 __last1,
             _Iter2 __first2, _Iter2 __last2,
             _Pred __comp)
    {
      late_check {
      typedef reverse_iterator<_Iter1> _RevIterator1;
      typedef reverse_iterator<_Iter2> _RevIterator2;

      _RevIterator1 __rlast1(__first1);
      _RevIterator2 __rlast2(__first2);
      _RevIterator1 __rresult = std::search(_RevIterator1(__last1), __rlast1,
                                            _RevIterator2(__last2), __rlast2,
                                            __comp);

      if (__rresult == __rlast1)
        return __last1;
      else
        {
          _Iter1 __result = __rresult.base();
          std::advance(__result, -std::distance(__first2, __last2));
          return __result;
        }
      }
    }

_GLIBCXX_END_NAMESPACE

#endif /* _ALGO_H */