text: // Algorithm implementation -*- C++ -*-
  
  // Copyright (C) 2001-2013 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 3, 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.
  
  // Under Section 7 of GPL version 3, you are granted additional
  // permissions described in the GCC Runtime Library Exception, version
  // 3.1, as published by the Free Software Foundation.
  
  // You should have received a copy of the GNU General Public License and
  // a copy of the GCC Runtime Library Exception along with this program;
  // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
  // <http://www.gnu.org/licenses/>.
  
  /*
   *
   * 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 bits/stl_algo.h
   *  This is an internal header file, included by other library headers.
   *  Do not attempt to use it directly. @headername{algorithm}
   */
  
  #ifndef _STL_ALGO_H
  #define _STL_ALGO_H 1
  
  #include <cstdlib>             // for rand
  #include <bits/algorithmfwd.h>
  #include <bits/stl_heap.h>
  #include <bits/stl_tempbuf.h>  // for _Temporary_buffer
  
  #if __cplusplus >= 201103L
  #include <random>     // for std::uniform_int_distribution
  #include <functional> // for std::bind
  #endif
  
  // See concept_check.h for the __glibcxx_*_requires macros.
  
  namespace std _GLIBCXX_VISIBILITY(default)
  {
  _GLIBCXX_BEGIN_NAMESPACE_VERSION
  
    /// Swaps the median value of *__a, *__b and *__c to *__result
    template<typename _Iterator>
      void
      __move_median_to_first(_Iterator __result, _Iterator __a,
  			   _Iterator __b, _Iterator __c)
      {
        // concept requirements
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_Iterator>::value_type>)
  
        if (*__a < *__b)
  	{
  	  if (*__b < *__c)
  	    std::iter_swap(__result, __b);
  	  else if (*__a < *__c)
  	    std::iter_swap(__result, __c);
  	  else
  	    std::iter_swap(__result, __a);
  	}
        else if (*__a < *__c)
        	std::iter_swap(__result, __a);
        else if (*__b < *__c)
  	std::iter_swap(__result, __c);
        else
  	std::iter_swap(__result, __b);
      }
  
    /// Swaps the median value of *__a, *__b and *__c under __comp to *__result
    template<typename _Iterator, typename _Compare>
      void
      __move_median_to_first(_Iterator __result, _Iterator __a,
  			   _Iterator __b, _Iterator __c,
  			   _Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_BinaryFunctionConcept<_Compare, bool,
  	    typename iterator_traits<_Iterator>::value_type,
  	    typename iterator_traits<_Iterator>::value_type>)
  
        if (__comp(*__a, *__b))
  	{
  	  if (__comp(*__b, *__c))
  	    std::iter_swap(__result, __b);
  	  else if (__comp(*__a, *__c))
  	    std::iter_swap(__result, __c);
  	  else
  	    std::iter_swap(__result, __a);
  	}
        else if (__comp(*__a, *__c))
  	std::iter_swap(__result, __a);
        else if (__comp(*__b, *__c))
  	std::iter_swap(__result, __c);
        else
  	std::iter_swap(__result, __b);
      }
  
    // for_each
  
    /// This is an overload used by find() for the Input Iterator case.
    template<typename _InputIterator, typename _Tp>
      inline _InputIterator
      __find(_InputIterator __first, _InputIterator __last,
  	   const _Tp& __val, input_iterator_tag)
      {
        while (__first != __last && !(*__first == __val))
  	++__first;
        return __first;
      }
  
    /// This is an overload used by find_if() for the Input Iterator case.
    template<typename _InputIterator, typename _Predicate>
      inline _InputIterator
      __find_if(_InputIterator __first, _InputIterator __last,
  	      _Predicate __pred, input_iterator_tag)
      {
        while (__first != __last && !bool(__pred(*__first)))
  	++__first;
        return __first;
      }
  
    /// This is an overload used by find() for the RAI case.
    template<typename _RandomAccessIterator, typename _Tp>
      _RandomAccessIterator
      __find(_RandomAccessIterator __first, _RandomAccessIterator __last,
  	   const _Tp& __val, random_access_iterator_tag)
      {
        typename iterator_traits<_RandomAccessIterator>::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;
  	}
      }
  
    /// This is an overload used by find_if() for the RAI case.
    template<typename _RandomAccessIterator, typename _Predicate>
      _RandomAccessIterator
      __find_if(_RandomAccessIterator __first, _RandomAccessIterator __last,
  	      _Predicate __pred, random_access_iterator_tag)
      {
        typename iterator_traits<_RandomAccessIterator>::difference_type
  	__trip_count = (__last - __first) >> 2;
  
        for (; __trip_count > 0; --__trip_count)
  	{
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  	}
  
        switch (__last - __first)
  	{
  	case 3:
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  	case 2:
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  	case 1:
  	  if (__pred(*__first))
  	    return __first;
  	  ++__first;
  	case 0:
  	default:
  	  return __last;
  	}
      }
  
    /// This is an overload used by find_if_not() for the Input Iterator case.
    template<typename _InputIterator, typename _Predicate>
      inline _InputIterator
      __find_if_not(_InputIterator __first, _InputIterator __last,
  		  _Predicate __pred, input_iterator_tag)
      {
        while (__first != __last && bool(__pred(*__first)))
  	++__first;
        return __first;
      }
  
    /// This is an overload used by find_if_not() for the RAI case.
    template<typename _RandomAccessIterator, typename _Predicate>
      _RandomAccessIterator
      __find_if_not(_RandomAccessIterator __first, _RandomAccessIterator __last,
  		  _Predicate __pred, random_access_iterator_tag)
      {
        typename iterator_traits<_RandomAccessIterator>::difference_type
  	__trip_count = (__last - __first) >> 2;
  
        for (; __trip_count > 0; --__trip_count)
  	{
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  	}
  
        switch (__last - __first)
  	{
  	case 3:
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  	case 2:
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  	case 1:
  	  if (!bool(__pred(*__first)))
  	    return __first;
  	  ++__first;
  	case 0:
  	default:
  	  return __last;
  	}
      }
  
    /// Provided for stable_partition to use.
    template<typename _InputIterator, typename _Predicate>
      inline _InputIterator
      __find_if_not(_InputIterator __first, _InputIterator __last,
  		  _Predicate __pred)
      {
        return std::__find_if_not(__first, __last, __pred,
  				std::__iterator_category(__first));
      }
  
    /// Like find_if_not(), but uses and updates a count of the
    /// remaining range length instead of comparing against an end
    /// iterator.
    template<typename _InputIterator, typename _Predicate, typename _Distance>
      _InputIterator
      __find_if_not_n(_InputIterator __first, _Distance& __len, _Predicate __pred)
      {
        for (; __len; --__len, ++__first)
  	if (!bool(__pred(*__first)))
  	  break;
        return __first;
      }
  
    // set_difference
    // set_intersection
    // set_symmetric_difference
    // set_union
    // for_each
    // find
    // find_if
    // find_first_of
    // adjacent_find
    // count
    // count_if
    // search
  
    /**
     *  This is an uglified
     *  search_n(_ForwardIterator, _ForwardIterator, _Integer, const _Tp&)
     *  overloaded for forward iterators.
    */
    template<typename _ForwardIterator, typename _Integer, typename _Tp>
      _ForwardIterator
      __search_n(_ForwardIterator __first, _ForwardIterator __last,
  	       _Integer __count, const _Tp& __val,
  	       std::forward_iterator_tag)
      {
        __first = _GLIBCXX_STD_A::find(__first, __last, __val);
        while (__first != __last)
  	{
  	  typename iterator_traits<_ForwardIterator>::difference_type
  	    __n = __count;
  	  _ForwardIterator __i = __first;
  	  ++__i;
  	  while (__i != __last && __n != 1 && *__i == __val)
  	    {
  	      ++__i;
  	      --__n;
  	    }
  	  if (__n == 1)
  	    return __first;
  	  if (__i == __last)
  	    return __last;
  	  __first = _GLIBCXX_STD_A::find(++__i, __last, __val);
  	}
        return __last;
      }
  
    /**
     *  This is an uglified
     *  search_n(_ForwardIterator, _ForwardIterator, _Integer, const _Tp&)
     *  overloaded for random access iterators.
    */
    template<typename _RandomAccessIter, typename _Integer, typename _Tp>
      _RandomAccessIter
      __search_n(_RandomAccessIter __first, _RandomAccessIter __last,
  	       _Integer __count, const _Tp& __val, 
  	       std::random_access_iterator_tag)
      {
        
        typedef typename std::iterator_traits<_RandomAccessIter>::difference_type
  	_DistanceType;
  
        _DistanceType __tailSize = __last - __first;
        _DistanceType __remainder = __count;
  
        while (__remainder <= __tailSize) // the main loop...
  	{
  	  __first += __remainder;
  	  __tailSize -= __remainder;
  	  // __first here is always pointing to one past the last element of
  	  // next possible match.
  	  _RandomAccessIter __backTrack = __first; 
  	  while (*--__backTrack == __val)
  	    {
  	      if (--__remainder == 0)
  	        return (__first - __count); // Success
  	    }
  	  __remainder = __count + 1 - (__first - __backTrack);
  	}
        return __last; // Failure
      }
  
    // search_n
  
    /**
     *  This is an uglified
     *  search_n(_ForwardIterator, _ForwardIterator, _Integer, const _Tp&,
     *	       _BinaryPredicate)
     *  overloaded for forward iterators.
    */
    template<typename _ForwardIterator, typename _Integer, typename _Tp,
             typename _BinaryPredicate>
      _ForwardIterator
      __search_n(_ForwardIterator __first, _ForwardIterator __last,
  	       _Integer __count, const _Tp& __val,
  	       _BinaryPredicate __binary_pred, std::forward_iterator_tag)
      {
        while (__first != __last && !bool(__binary_pred(*__first, __val)))
          ++__first;
  
        while (__first != __last)
  	{
  	  typename iterator_traits<_ForwardIterator>::difference_type
  	    __n = __count;
  	  _ForwardIterator __i = __first;
  	  ++__i;
  	  while (__i != __last && __n != 1 && bool(__binary_pred(*__i, __val)))
  	    {
  	      ++__i;
  	      --__n;
  	    }
  	  if (__n == 1)
  	    return __first;
  	  if (__i == __last)
  	    return __last;
  	  __first = ++__i;
  	  while (__first != __last
  		 && !bool(__binary_pred(*__first, __val)))
  	    ++__first;
  	}
        return __last;
      }
  
    /**
     *  This is an uglified
     *  search_n(_ForwardIterator, _ForwardIterator, _Integer, const _Tp&,
     *	       _BinaryPredicate)
     *  overloaded for random access iterators.
    */
    template<typename _RandomAccessIter, typename _Integer, typename _Tp,
  	   typename _BinaryPredicate>
      _RandomAccessIter
      __search_n(_RandomAccessIter __first, _RandomAccessIter __last,
  	       _Integer __count, const _Tp& __val,
  	       _BinaryPredicate __binary_pred, std::random_access_iterator_tag)
      {
        
        typedef typename std::iterator_traits<_RandomAccessIter>::difference_type
  	_DistanceType;
  
        _DistanceType __tailSize = __last - __first;
        _DistanceType __remainder = __count;
  
        while (__remainder <= __tailSize) // the main loop...
  	{
  	  __first += __remainder;
  	  __tailSize -= __remainder;
  	  // __first here is always pointing to one past the last element of
  	  // next possible match.
  	  _RandomAccessIter __backTrack = __first; 
  	  while (__binary_pred(*--__backTrack, __val))
  	    {
  	      if (--__remainder == 0)
  	        return (__first - __count); // Success
  	    }
  	  __remainder = __count + 1 - (__first - __backTrack);
  	}
        return __last; // Failure
      }
  
    // find_end for forward iterators.
    template<typename _ForwardIterator1, typename _ForwardIterator2>
      _ForwardIterator1
      __find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	       _ForwardIterator2 __first2, _ForwardIterator2 __last2,
  	       forward_iterator_tag, forward_iterator_tag)
      {
        if (__first2 == __last2)
  	return __last1;
        else
  	{
  	  _ForwardIterator1 __result = __last1;
  	  while (1)
  	    {
  	      _ForwardIterator1 __new_result
  		= _GLIBCXX_STD_A::search(__first1, __last1, __first2, __last2);
  	      if (__new_result == __last1)
  		return __result;
  	      else
  		{
  		  __result = __new_result;
  		  __first1 = __new_result;
  		  ++__first1;
  		}
  	    }
  	}
      }
  
    template<typename _ForwardIterator1, typename _ForwardIterator2,
  	   typename _BinaryPredicate>
      _ForwardIterator1
      __find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	       _ForwardIterator2 __first2, _ForwardIterator2 __last2,
  	       forward_iterator_tag, forward_iterator_tag,
  	       _BinaryPredicate __comp)
      {
        if (__first2 == __last2)
  	return __last1;
        else
  	{
  	  _ForwardIterator1 __result = __last1;
  	  while (1)
  	    {
  	      _ForwardIterator1 __new_result
  		= _GLIBCXX_STD_A::search(__first1, __last1, __first2,
  					 __last2, __comp);
  	      if (__new_result == __last1)
  		return __result;
  	      else
  		{
  		  __result = __new_result;
  		  __first1 = __new_result;
  		  ++__first1;
  		}
  	    }
  	}
      }
  
    // find_end for bidirectional iterators (much faster).
    template<typename _BidirectionalIterator1, typename _BidirectionalIterator2>
      _BidirectionalIterator1
      __find_end(_BidirectionalIterator1 __first1,
  	       _BidirectionalIterator1 __last1,
  	       _BidirectionalIterator2 __first2,
  	       _BidirectionalIterator2 __last2,
  	       bidirectional_iterator_tag, bidirectional_iterator_tag)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator1>)
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator2>)
  
        typedef reverse_iterator<_BidirectionalIterator1> _RevIterator1;
        typedef reverse_iterator<_BidirectionalIterator2> _RevIterator2;
  
        _RevIterator1 __rlast1(__first1);
        _RevIterator2 __rlast2(__first2);
        _RevIterator1 __rresult = _GLIBCXX_STD_A::search(_RevIterator1(__last1),
  						       __rlast1,
  						       _RevIterator2(__last2),
  						       __rlast2);
  
        if (__rresult == __rlast1)
  	return __last1;
        else
  	{
  	  _BidirectionalIterator1 __result = __rresult.base();
  	  std::advance(__result, -std::distance(__first2, __last2));
  	  return __result;
  	}
      }
  
    template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
  	   typename _BinaryPredicate>
      _BidirectionalIterator1
      __find_end(_BidirectionalIterator1 __first1,
  	       _BidirectionalIterator1 __last1,
  	       _BidirectionalIterator2 __first2,
  	       _BidirectionalIterator2 __last2,
  	       bidirectional_iterator_tag, bidirectional_iterator_tag,
  	       _BinaryPredicate __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator1>)
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator2>)
  
        typedef reverse_iterator<_BidirectionalIterator1> _RevIterator1;
        typedef reverse_iterator<_BidirectionalIterator2> _RevIterator2;
  
        _RevIterator1 __rlast1(__first1);
        _RevIterator2 __rlast2(__first2);
        _RevIterator1 __rresult = std::search(_RevIterator1(__last1), __rlast1,
  					    _RevIterator2(__last2), __rlast2,
  					    __comp);
  
        if (__rresult == __rlast1)
  	return __last1;
        else
  	{
  	  _BidirectionalIterator1 __result = __rresult.base();
  	  std::advance(__result, -std::distance(__first2, __last2));
  	  return __result;
  	}
      }
  
    /**
     *  @brief  Find last matching subsequence in a sequence.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator1, typename _ForwardIterator2>
      inline _ForwardIterator1
      find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	     _ForwardIterator2 __first2, _ForwardIterator2 __last2)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator1>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator2>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_ForwardIterator1>::value_type,
  	    typename iterator_traits<_ForwardIterator2>::value_type>)
        __glibcxx_requires_valid_range(__first1, __last1);
        __glibcxx_requires_valid_range(__first2, __last2);
  
        return std::__find_end(__first1, __last1, __first2, __last2,
  			     std::__iterator_category(__first1),
  			     std::__iterator_category(__first2));
      }
  
    /**
     *  @brief  Find last matching subsequence in a sequence using a predicate.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator1, typename _ForwardIterator2,
  	   typename _BinaryPredicate>
      inline _ForwardIterator1
      find_end(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	     _ForwardIterator2 __first2, _ForwardIterator2 __last2,
  	     _BinaryPredicate __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator1>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	    typename iterator_traits<_ForwardIterator1>::value_type,
  	    typename iterator_traits<_ForwardIterator2>::value_type>)
        __glibcxx_requires_valid_range(__first1, __last1);
        __glibcxx_requires_valid_range(__first2, __last2);
  
        return std::__find_end(__first1, __last1, __first2, __last2,
  			     std::__iterator_category(__first1),
  			     std::__iterator_category(__first2),
  			     __comp);
      }
  
  #if __cplusplus >= 201103L
    /**
     *  @brief  Checks that a predicate is true for all the elements
     *          of a sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first   An input iterator.
     *  @param  __last    An input iterator.
     *  @param  __pred    A predicate.
     *  @return  True if the check is true, false otherwise.
     *
     *  Returns true if @p __pred is true for each element in the range
     *  @p [__first,__last), and false otherwise.
    */
    template<typename _InputIterator, typename _Predicate>
      inline bool
      all_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
      { return __last == std::find_if_not(__first, __last, __pred); }
  
    /**
     *  @brief  Checks that a predicate is false for all the elements
     *          of a sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first   An input iterator.
     *  @param  __last    An input iterator.
     *  @param  __pred    A predicate.
     *  @return  True if the check is true, false otherwise.
     *
     *  Returns true if @p __pred is false for each element in the range
     *  @p [__first,__last), and false otherwise.
    */
    template<typename _InputIterator, typename _Predicate>
      inline bool
      none_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
      { return __last == _GLIBCXX_STD_A::find_if(__first, __last, __pred); }
  
    /**
     *  @brief  Checks that a predicate is false for at least an element
     *          of a sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first   An input iterator.
     *  @param  __last    An input iterator.
     *  @param  __pred    A predicate.
     *  @return  True if the check is true, false otherwise.
     *
     *  Returns true if an element exists in the range @p
     *  [__first,__last) such that @p __pred is true, and false
     *  otherwise.
    */
    template<typename _InputIterator, typename _Predicate>
      inline bool
      any_of(_InputIterator __first, _InputIterator __last, _Predicate __pred)
      { return !std::none_of(__first, __last, __pred); }
  
    /**
     *  @brief  Find the first element in a sequence for which a
     *          predicate is false.
     *  @ingroup non_mutating_algorithms
     *  @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 false, or @p __last if no such iterator exists.
    */
    template<typename _InputIterator, typename _Predicate>
      inline _InputIterator
      find_if_not(_InputIterator __first, _InputIterator __last,
  		_Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	      typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        return std::__find_if_not(__first, __last, __pred);
      }
  
    /**
     *  @brief  Checks whether the sequence is partitioned.
     *  @ingroup mutating_algorithms
     *  @param  __first  An input iterator.
     *  @param  __last   An input iterator.
     *  @param  __pred   A predicate.
     *  @return  True if the range @p [__first,__last) is partioned by @p __pred,
     *  i.e. if all elements that satisfy @p __pred appear before those that
     *  do not.
    */
    template<typename _InputIterator, typename _Predicate>
      inline bool
      is_partitioned(_InputIterator __first, _InputIterator __last,
  		   _Predicate __pred)
      {
        __first = std::find_if_not(__first, __last, __pred);
        return std::none_of(__first, __last, __pred);
      }
  
    /**
     *  @brief  Find the partition point of a partitioned range.
     *  @ingroup mutating_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __pred    A predicate.
     *  @return  An iterator @p mid such that @p all_of(__first, mid, __pred)
     *           and @p none_of(mid, __last, __pred) are both true.
    */
    template<typename _ForwardIterator, typename _Predicate>
      _ForwardIterator
      partition_point(_ForwardIterator __first, _ForwardIterator __last,
  		    _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	      typename iterator_traits<_ForwardIterator>::value_type>)
  
        // A specific debug-mode test will be necessary...
        __glibcxx_requires_valid_range(__first, __last);
  
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        _DistanceType __len = std::distance(__first, __last);
        _DistanceType __half;
        _ForwardIterator __middle;
  
        while (__len > 0)
  	{
  	  __half = __len >> 1;
  	  __middle = __first;
  	  std::advance(__middle, __half);
  	  if (__pred(*__middle))
  	    {
  	      __first = __middle;
  	      ++__first;
  	      __len = __len - __half - 1;
  	    }
  	  else
  	    __len = __half;
  	}
        return __first;
      }
  #endif
  
  
    /**
     *  @brief Copy a sequence, removing elements of a given value.
     *  @ingroup mutating_algorithms
     *  @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<typename _InputIterator, typename _OutputIterator, typename _Tp>
      _OutputIterator
      remove_copy(_InputIterator __first, _InputIterator __last,
  		_OutputIterator __result, const _Tp& __value)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_InputIterator>::value_type, _Tp>)
        __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.
     *  @ingroup mutating_algorithms
     *  @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 false to the range beginning at @p __result.
     *
     *  remove_copy_if() is stable, so the relative order of elements that are
     *  copied is unchanged.
    */
    template<typename _InputIterator, typename _OutputIterator,
  	   typename _Predicate>
      _OutputIterator
      remove_copy_if(_InputIterator __first, _InputIterator __last,
  		   _OutputIterator __result, _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        for (; __first != __last; ++__first)
  	if (!bool(__pred(*__first)))
  	  {
  	    *__result = *__first;
  	    ++__result;
  	  }
        return __result;
      }
  
  #if __cplusplus >= 201103L
    /**
     *  @brief Copy the elements of a sequence for which a predicate is true.
     *  @ingroup mutating_algorithms
     *  @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.
     *
     *  copy_if() is stable, so the relative order of elements that are
     *  copied is unchanged.
    */
    template<typename _InputIterator, typename _OutputIterator,
  	   typename _Predicate>
      _OutputIterator
      copy_if(_InputIterator __first, _InputIterator __last,
  	    _OutputIterator __result, _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        for (; __first != __last; ++__first)
  	if (__pred(*__first))
  	  {
  	    *__result = *__first;
  	    ++__result;
  	  }
        return __result;
      }
  
  
    template<typename _InputIterator, typename _Size, typename _OutputIterator>
      _OutputIterator
      __copy_n(_InputIterator __first, _Size __n,
  	     _OutputIterator __result, input_iterator_tag)
      {
        if (__n > 0)
  	{
  	  while (true)
  	    {
  	      *__result = *__first;
  	      ++__result;
  	      if (--__n > 0)
  		++__first;
  	      else
  		break;
  	    }
  	}
        return __result;
      }
  
    template<typename _RandomAccessIterator, typename _Size,
  	   typename _OutputIterator>
      inline _OutputIterator
      __copy_n(_RandomAccessIterator __first, _Size __n,
  	     _OutputIterator __result, random_access_iterator_tag)
      { return std::copy(__first, __first + __n, __result); }
  
    /**
     *  @brief Copies the range [first,first+n) into [result,result+n).
     *  @ingroup mutating_algorithms
     *  @param  __first  An input iterator.
     *  @param  __n      The number of elements to copy.
     *  @param  __result An output iterator.
     *  @return  result+n.
     *
     *  This inline function will boil down to a call to @c memmove whenever
     *  possible.  Failing that, if random access iterators are passed, then the
     *  loop count will be known (and therefore a candidate for compiler
     *  optimizations such as unrolling).
    */
    template<typename _InputIterator, typename _Size, typename _OutputIterator>
      inline _OutputIterator
      copy_n(_InputIterator __first, _Size __n, _OutputIterator __result)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
  
        return std::__copy_n(__first, __n, __result,
  			   std::__iterator_category(__first));
      }
  
    /**
     *  @brief Copy the elements of a sequence to separate output sequences
     *         depending on the truth value of a predicate.
     *  @ingroup mutating_algorithms
     *  @param  __first   An input iterator.
     *  @param  __last    An input iterator.
     *  @param  __out_true   An output iterator.
     *  @param  __out_false  An output iterator.
     *  @param  __pred    A predicate.
     *  @return   A pair designating the ends of the resulting sequences.
     *
     *  Copies each element in the range @p [__first,__last) for which
     *  @p __pred returns true to the range beginning at @p out_true
     *  and each element for which @p __pred returns false to @p __out_false.
    */
    template<typename _InputIterator, typename _OutputIterator1,
  	   typename _OutputIterator2, typename _Predicate>
      pair<_OutputIterator1, _OutputIterator2>
      partition_copy(_InputIterator __first, _InputIterator __last,
  		   _OutputIterator1 __out_true, _OutputIterator2 __out_false,
  		   _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator1,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator2,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        
        for (; __first != __last; ++__first)
  	if (__pred(*__first))
  	  {
  	    *__out_true = *__first;
  	    ++__out_true;
  	  }
  	else
  	  {
  	    *__out_false = *__first;
  	    ++__out_false;
  	  }
  
        return pair<_OutputIterator1, _OutputIterator2>(__out_true, __out_false);
      }
  #endif
  
    /**
     *  @brief Remove elements from a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Tp>
      _ForwardIterator
      remove(_ForwardIterator __first, _ForwardIterator __last,
  	   const _Tp& __value)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type, _Tp>)
        __glibcxx_requires_valid_range(__first, __last);
  
        __first = _GLIBCXX_STD_A::find(__first, __last, __value);
        if(__first == __last)
          return __first;
        _ForwardIterator __result = __first;
        ++__first;
        for(; __first != __last; ++__first)
          if(!(*__first == __value))
            {
              *__result = _GLIBCXX_MOVE(*__first);
              ++__result;
            }
        return __result;
      }
  
    /**
     *  @brief Remove elements from a sequence using a predicate.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Predicate>
      _ForwardIterator
      remove_if(_ForwardIterator __first, _ForwardIterator __last,
  	      _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        __first = _GLIBCXX_STD_A::find_if(__first, __last, __pred);
        if(__first == __last)
          return __first;
        _ForwardIterator __result = __first;
        ++__first;
        for(; __first != __last; ++__first)
          if(!bool(__pred(*__first)))
            {
              *__result = _GLIBCXX_MOVE(*__first);
              ++__result;
            }
        return __result;
      }
  
    /**
     *  @brief Remove consecutive duplicate values from a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator>
      _ForwardIterator
      unique(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_EqualityComparableConcept<
  		     typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        // Skip the beginning, if already unique.
        __first = _GLIBCXX_STD_A::adjacent_find(__first, __last);
        if (__first == __last)
  	return __last;
  
        // Do the real copy work.
        _ForwardIterator __dest = __first;
        ++__first;
        while (++__first != __last)
  	if (!(*__dest == *__first))
  	  *++__dest = _GLIBCXX_MOVE(*__first);
        return ++__dest;
      }
  
    /**
     *  @brief Remove consecutive values from a sequence using a predicate.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _BinaryPredicate>
      _ForwardIterator
      unique(_ForwardIterator __first, _ForwardIterator __last,
             _BinaryPredicate __binary_pred)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  		typename iterator_traits<_ForwardIterator>::value_type,
  		typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        // Skip the beginning, if already unique.
        __first = _GLIBCXX_STD_A::adjacent_find(__first, __last, __binary_pred);
        if (__first == __last)
  	return __last;
  
        // Do the real copy work.
        _ForwardIterator __dest = __first;
        ++__first;
        while (++__first != __last)
  	if (!bool(__binary_pred(*__dest, *__first)))
  	  *++__dest = _GLIBCXX_MOVE(*__first);
        return ++__dest;
      }
  
    /**
     *  This is an uglified unique_copy(_InputIterator, _InputIterator,
     *                                  _OutputIterator)
     *  overloaded for forward iterators and output iterator as result.
    */
    template<typename _ForwardIterator, typename _OutputIterator>
      _OutputIterator
      __unique_copy(_ForwardIterator __first, _ForwardIterator __last,
  		  _OutputIterator __result,
  		  forward_iterator_tag, output_iterator_tag)
      {
        // concept requirements -- taken care of in dispatching function
        _ForwardIterator __next = __first;
        *__result = *__first;
        while (++__next != __last)
  	if (!(*__first == *__next))
  	  {
  	    __first = __next;
  	    *++__result = *__first;
  	  }
        return ++__result;
      }
  
    /**
     *  This is an uglified unique_copy(_InputIterator, _InputIterator,
     *                                  _OutputIterator)
     *  overloaded for input iterators and output iterator as result.
    */
    template<typename _InputIterator, typename _OutputIterator>
      _OutputIterator
      __unique_copy(_InputIterator __first, _InputIterator __last,
  		  _OutputIterator __result,
  		  input_iterator_tag, output_iterator_tag)
      {
        // concept requirements -- taken care of in dispatching function
        typename iterator_traits<_InputIterator>::value_type __value = *__first;
        *__result = __value;
        while (++__first != __last)
  	if (!(__value == *__first))
  	  {
  	    __value = *__first;
  	    *++__result = __value;
  	  }
        return ++__result;
      }
  
    /**
     *  This is an uglified unique_copy(_InputIterator, _InputIterator,
     *                                  _OutputIterator)
     *  overloaded for input iterators and forward iterator as result.
    */
    template<typename _InputIterator, typename _ForwardIterator>
      _ForwardIterator
      __unique_copy(_InputIterator __first, _InputIterator __last,
  		  _ForwardIterator __result,
  		  input_iterator_tag, forward_iterator_tag)
      {
        // concept requirements -- taken care of in dispatching function
        *__result = *__first;
        while (++__first != __last)
  	if (!(*__result == *__first))
  	  *++__result = *__first;
        return ++__result;
      }
  
    /**
     *  This is an uglified
     *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
     *              _BinaryPredicate)
     *  overloaded for forward iterators and output iterator as result.
    */
    template<typename _ForwardIterator, typename _OutputIterator,
  	   typename _BinaryPredicate>
      _OutputIterator
      __unique_copy(_ForwardIterator __first, _ForwardIterator __last,
  		  _OutputIterator __result, _BinaryPredicate __binary_pred,
  		  forward_iterator_tag, output_iterator_tag)
      {
        // concept requirements -- iterators already checked
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	  typename iterator_traits<_ForwardIterator>::value_type,
  	  typename iterator_traits<_ForwardIterator>::value_type>)
  
        _ForwardIterator __next = __first;
        *__result = *__first;
        while (++__next != __last)
  	if (!bool(__binary_pred(*__first, *__next)))
  	  {
  	    __first = __next;
  	    *++__result = *__first;
  	  }
        return ++__result;
      }
  
    /**
     *  This is an uglified
     *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
     *              _BinaryPredicate)
     *  overloaded for input iterators and output iterator as result.
    */
    template<typename _InputIterator, typename _OutputIterator,
  	   typename _BinaryPredicate>
      _OutputIterator
      __unique_copy(_InputIterator __first, _InputIterator __last,
  		  _OutputIterator __result, _BinaryPredicate __binary_pred,
  		  input_iterator_tag, output_iterator_tag)
      {
        // concept requirements -- iterators already checked
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	  typename iterator_traits<_InputIterator>::value_type,
  	  typename iterator_traits<_InputIterator>::value_type>)
  
        typename iterator_traits<_InputIterator>::value_type __value = *__first;
        *__result = __value;
        while (++__first != __last)
  	if (!bool(__binary_pred(__value, *__first)))
  	  {
  	    __value = *__first;
  	    *++__result = __value;
  	  }
        return ++__result;
      }
  
    /**
     *  This is an uglified
     *  unique_copy(_InputIterator, _InputIterator, _OutputIterator,
     *              _BinaryPredicate)
     *  overloaded for input iterators and forward iterator as result.
    */
    template<typename _InputIterator, typename _ForwardIterator,
  	   typename _BinaryPredicate>
      _ForwardIterator
      __unique_copy(_InputIterator __first, _InputIterator __last,
  		  _ForwardIterator __result, _BinaryPredicate __binary_pred,
  		  input_iterator_tag, forward_iterator_tag)
      {
        // concept requirements -- iterators already checked
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	  typename iterator_traits<_ForwardIterator>::value_type,
  	  typename iterator_traits<_InputIterator>::value_type>)
  
        *__result = *__first;
        while (++__first != __last)
  	if (!bool(__binary_pred(*__result, *__first)))
  	  *++__result = *__first;
        return ++__result;
      }
  
    /**
     *  This is an uglified reverse(_BidirectionalIterator,
     *                              _BidirectionalIterator)
     *  overloaded for bidirectional iterators.
    */
    template<typename _BidirectionalIterator>
      void
      __reverse(_BidirectionalIterator __first, _BidirectionalIterator __last,
  	      bidirectional_iterator_tag)
      {
        while (true)
  	if (__first == __last || __first == --__last)
  	  return;
  	else
  	  {
  	    std::iter_swap(__first, __last);
  	    ++__first;
  	  }
      }
  
    /**
     *  This is an uglified reverse(_BidirectionalIterator,
     *                              _BidirectionalIterator)
     *  overloaded for random access iterators.
    */
    template<typename _RandomAccessIterator>
      void
      __reverse(_RandomAccessIterator __first, _RandomAccessIterator __last,
  	      random_access_iterator_tag)
      {
        if (__first == __last)
  	return;
        --__last;
        while (__first < __last)
  	{
  	  std::iter_swap(__first, __last);
  	  ++__first;
  	  --__last;
  	}
      }
  
    /**
     *  @brief Reverse a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _BidirectionalIterator>
      inline void
      reverse(_BidirectionalIterator __first, _BidirectionalIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_requires_valid_range(__first, __last);
        std::__reverse(__first, __last, std::__iterator_category(__first));
      }
  
    /**
     *  @brief Copy a sequence, reversing its elements.
     *  @ingroup mutating_algorithms
     *  @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)-1-i) = *(__first+i).
     *  The ranges @p [__first,__last) and @p
     *  [__result,__result+(__last-__first)) must not overlap.
    */
    template<typename _BidirectionalIterator, typename _OutputIterator>
      _OutputIterator
      reverse_copy(_BidirectionalIterator __first, _BidirectionalIterator __last,
  		 _OutputIterator __result)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  		typename iterator_traits<_BidirectionalIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        while (__first != __last)
  	{
  	  --__last;
  	  *__result = *__last;
  	  ++__result;
  	}
        return __result;
      }
  
    /**
     *  This is a helper function for the rotate algorithm specialized on RAIs.
     *  It returns the greatest common divisor of two integer values.
    */
    template<typename _EuclideanRingElement>
      _EuclideanRingElement
      __gcd(_EuclideanRingElement __m, _EuclideanRingElement __n)
      {
        while (__n != 0)
  	{
  	  _EuclideanRingElement __t = __m % __n;
  	  __m = __n;
  	  __n = __t;
  	}
        return __m;
      }
  
    /// This is a helper function for the rotate algorithm.
    template<typename _ForwardIterator>
      void
      __rotate(_ForwardIterator __first,
  	     _ForwardIterator __middle,
  	     _ForwardIterator __last,
  	     forward_iterator_tag)
      {
        if (__first == __middle || __last  == __middle)
  	return;
  
        _ForwardIterator __first2 = __middle;
        do
  	{
  	  std::iter_swap(__first, __first2);
  	  ++__first;
  	  ++__first2;
  	  if (__first == __middle)
  	    __middle = __first2;
  	}
        while (__first2 != __last);
  
        __first2 = __middle;
  
        while (__first2 != __last)
  	{
  	  std::iter_swap(__first, __first2);
  	  ++__first;
  	  ++__first2;
  	  if (__first == __middle)
  	    __middle = __first2;
  	  else if (__first2 == __last)
  	    __first2 = __middle;
  	}
      }
  
     /// This is a helper function for the rotate algorithm.
    template<typename _BidirectionalIterator>
      void
      __rotate(_BidirectionalIterator __first,
  	     _BidirectionalIterator __middle,
  	     _BidirectionalIterator __last,
  	      bidirectional_iterator_tag)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
  
        if (__first == __middle || __last  == __middle)
  	return;
  
        std::__reverse(__first,  __middle, bidirectional_iterator_tag());
        std::__reverse(__middle, __last,   bidirectional_iterator_tag());
  
        while (__first != __middle && __middle != __last)
  	{
  	  std::iter_swap(__first, --__last);
  	  ++__first;
  	}
  
        if (__first == __middle)
  	std::__reverse(__middle, __last,   bidirectional_iterator_tag());
        else
  	std::__reverse(__first,  __middle, bidirectional_iterator_tag());
      }
  
    /// This is a helper function for the rotate algorithm.
    template<typename _RandomAccessIterator>
      void
      __rotate(_RandomAccessIterator __first,
  	     _RandomAccessIterator __middle,
  	     _RandomAccessIterator __last,
  	     random_access_iterator_tag)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  				  _RandomAccessIterator>)
  
        if (__first == __middle || __last  == __middle)
  	return;
  
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_Distance;
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        _Distance __n = __last   - __first;
        _Distance __k = __middle - __first;
  
        if (__k == __n - __k)
  	{
  	  std::swap_ranges(__first, __middle, __middle);
  	  return;
  	}
  
        _RandomAccessIterator __p = __first;
  
        for (;;)
  	{
  	  if (__k < __n - __k)
  	    {
  	      if (__is_pod(_ValueType) && __k == 1)
  		{
  		  _ValueType __t = _GLIBCXX_MOVE(*__p);
  		  _GLIBCXX_MOVE3(__p + 1, __p + __n, __p);
  		  *(__p + __n - 1) = _GLIBCXX_MOVE(__t);
  		  return;
  		}
  	      _RandomAccessIterator __q = __p + __k;
  	      for (_Distance __i = 0; __i < __n - __k; ++ __i)
  		{
  		  std::iter_swap(__p, __q);
  		  ++__p;
  		  ++__q;
  		}
  	      __n %= __k;
  	      if (__n == 0)
  		return;
  	      std::swap(__n, __k);
  	      __k = __n - __k;
  	    }
  	  else
  	    {
  	      __k = __n - __k;
  	      if (__is_pod(_ValueType) && __k == 1)
  		{
  		  _ValueType __t = _GLIBCXX_MOVE(*(__p + __n - 1));
  		  _GLIBCXX_MOVE_BACKWARD3(__p, __p + __n - 1, __p + __n);
  		  *__p = _GLIBCXX_MOVE(__t);
  		  return;
  		}
  	      _RandomAccessIterator __q = __p + __n;
  	      __p = __q - __k;
  	      for (_Distance __i = 0; __i < __n - __k; ++ __i)
  		{
  		  --__p;
  		  --__q;
  		  std::iter_swap(__p, __q);
  		}
  	      __n %= __k;
  	      if (__n == 0)
  		return;
  	      std::swap(__n, __k);
  	    }
  	}
      }
  
    /**
     *  @brief Rotate the elements of a sequence.
     *  @ingroup mutating_algorithms
     *  @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
     *  @p __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<typename _ForwardIterator>
      inline void
      rotate(_ForwardIterator __first, _ForwardIterator __middle,
  	   _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_requires_valid_range(__first, __middle);
        __glibcxx_requires_valid_range(__middle, __last);
  
        typedef typename iterator_traits<_ForwardIterator>::iterator_category
  	_IterType;
        std::__rotate(__first, __middle, __last, _IterType());
      }
  
    /**
     *  @brief Copy a sequence, rotating its elements.
     *  @ingroup mutating_algorithms
     *  @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 @p __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<typename _ForwardIterator, typename _OutputIterator>
      _OutputIterator
      rotate_copy(_ForwardIterator __first, _ForwardIterator __middle,
                  _ForwardIterator __last, _OutputIterator __result)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  		typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __middle);
        __glibcxx_requires_valid_range(__middle, __last);
  
        return std::copy(__first, __middle,
                         std::copy(__middle, __last, __result));
      }
  
    /// This is a helper function...
    template<typename _ForwardIterator, typename _Predicate>
      _ForwardIterator
      __partition(_ForwardIterator __first, _ForwardIterator __last,
  		_Predicate __pred, forward_iterator_tag)
      {
        if (__first == __last)
  	return __first;
  
        while (__pred(*__first))
  	if (++__first == __last)
  	  return __first;
  
        _ForwardIterator __next = __first;
  
        while (++__next != __last)
  	if (__pred(*__next))
  	  {
  	    std::iter_swap(__first, __next);
  	    ++__first;
  	  }
  
        return __first;
      }
  
    /// This is a helper function...
    template<typename _BidirectionalIterator, typename _Predicate>
      _BidirectionalIterator
      __partition(_BidirectionalIterator __first, _BidirectionalIterator __last,
  		_Predicate __pred, bidirectional_iterator_tag)
      {
        while (true)
  	{
  	  while (true)
  	    if (__first == __last)
  	      return __first;
  	    else if (__pred(*__first))
  	      ++__first;
  	    else
  	      break;
  	  --__last;
  	  while (true)
  	    if (__first == __last)
  	      return __first;
  	    else if (!bool(__pred(*__last)))
  	      --__last;
  	    else
  	      break;
  	  std::iter_swap(__first, __last);
  	  ++__first;
  	}
      }
  
    // partition
  
    /// This is a helper function...
    /// Requires __len != 0 and !__pred(*__first),
    /// same as __stable_partition_adaptive.
    template<typename _ForwardIterator, typename _Predicate, typename _Distance>
      _ForwardIterator
      __inplace_stable_partition(_ForwardIterator __first,
  			       _Predicate __pred, _Distance __len)
      {
        if (__len == 1)
  	return __first;
        _ForwardIterator __middle = __first;
        std::advance(__middle, __len / 2);
        _ForwardIterator __left_split =
  	std::__inplace_stable_partition(__first, __pred, __len / 2);
        // Advance past true-predicate values to satisfy this
        // function's preconditions.
        _Distance __right_len = __len - __len / 2;
        _ForwardIterator __right_split =
  	std::__find_if_not_n(__middle, __right_len, __pred);
        if (__right_len)
  	__right_split = std::__inplace_stable_partition(__middle,
  							__pred,
  							__right_len);
        std::rotate(__left_split, __middle, __right_split);
        std::advance(__left_split, std::distance(__middle, __right_split));
        return __left_split;
      }
  
    /// This is a helper function...
    /// Requires __first != __last and !__pred(*__first)
    /// and __len == distance(__first, __last).
    ///
    /// !__pred(*__first) allows us to guarantee that we don't
    /// move-assign an element onto itself.
    template<typename _ForwardIterator, typename _Pointer, typename _Predicate,
  	   typename _Distance>
      _ForwardIterator
      __stable_partition_adaptive(_ForwardIterator __first,
  				_ForwardIterator __last,
  				_Predicate __pred, _Distance __len,
  				_Pointer __buffer,
  				_Distance __buffer_size)
      {
        if (__len <= __buffer_size)
  	{
  	  _ForwardIterator __result1 = __first;
  	  _Pointer __result2 = __buffer;
  	  // The precondition guarantees that !__pred(*__first), so
  	  // move that element to the buffer before starting the loop.
  	  // This ensures that we only call __pred once per element.
  	  *__result2 = _GLIBCXX_MOVE(*__first);
  	  ++__result2;
  	  ++__first;
  	  for (; __first != __last; ++__first)
  	    if (__pred(*__first))
  	      {
  		*__result1 = _GLIBCXX_MOVE(*__first);
  		++__result1;
  	      }
  	    else
  	      {
  		*__result2 = _GLIBCXX_MOVE(*__first);
  		++__result2;
  	      }
  	  _GLIBCXX_MOVE3(__buffer, __result2, __result1);
  	  return __result1;
  	}
        else
  	{
  	  _ForwardIterator __middle = __first;
  	  std::advance(__middle, __len / 2);
  	  _ForwardIterator __left_split =
  	    std::__stable_partition_adaptive(__first, __middle, __pred,
  					     __len / 2, __buffer,
  					     __buffer_size);
  	  // Advance past true-predicate values to satisfy this
  	  // function's preconditions.
  	  _Distance __right_len = __len - __len / 2;
  	  _ForwardIterator __right_split =
  	    std::__find_if_not_n(__middle, __right_len, __pred);
  	  if (__right_len)
  	    __right_split =
  	      std::__stable_partition_adaptive(__right_split, __last, __pred,
  					       __right_len,
  					       __buffer, __buffer_size);
  	  std::rotate(__left_split, __middle, __right_split);
  	  std::advance(__left_split, std::distance(__middle, __right_split));
  	  return __left_split;
  	}
      }
  
    /**
     *  @brief Move elements for which a predicate is true to the beginning
     *         of a sequence, preserving relative ordering.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Predicate>
      _ForwardIterator
      stable_partition(_ForwardIterator __first, _ForwardIterator __last,
  		     _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        __first = std::__find_if_not(__first, __last, __pred);
  
        if (__first == __last)
  	return __first;
        else
  	{
  	  typedef typename iterator_traits<_ForwardIterator>::value_type
  	    _ValueType;
  	  typedef typename iterator_traits<_ForwardIterator>::difference_type
  	    _DistanceType;
  
  	  _Temporary_buffer<_ForwardIterator, _ValueType> __buf(__first,
  								__last);
  	if (__buf.size() > 0)
  	  return
  	    std::__stable_partition_adaptive(__first, __last, __pred,
  					  _DistanceType(__buf.requested_size()),
  					  __buf.begin(),
  					  _DistanceType(__buf.size()));
  	else
  	  return
  	    std::__inplace_stable_partition(__first, __pred,
  					 _DistanceType(__buf.requested_size()));
  	}
      }
  
    /// This is a helper function for the sort routines.
    template<typename _RandomAccessIterator>
      void
      __heap_select(_RandomAccessIterator __first,
  		  _RandomAccessIterator __middle,
  		  _RandomAccessIterator __last)
      {
        std::make_heap(__first, __middle);
        for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
  	if (*__i < *__first)
  	  std::__pop_heap(__first, __middle, __i);
      }
  
    /// This is a helper function for the sort routines.
    template<typename _RandomAccessIterator, typename _Compare>
      void
      __heap_select(_RandomAccessIterator __first,
  		  _RandomAccessIterator __middle,
  		  _RandomAccessIterator __last, _Compare __comp)
      {
        std::make_heap(__first, __middle, __comp);
        for (_RandomAccessIterator __i = __middle; __i < __last; ++__i)
  	if (__comp(*__i, *__first))
  	  std::__pop_heap(__first, __middle, __i, __comp);
      }
  
    // partial_sort
  
    /**
     *  @brief Copy the smallest elements of a sequence.
     *  @ingroup sorting_algorithms
     *  @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 @e i and @e j are iterators in the range
     *  @p [__result_first,__result_first+N) such that i precedes j then
     *  *j<*i is false.
     *  The value returned is @p __result_first+N.
    */
    template<typename _InputIterator, typename _RandomAccessIterator>
      _RandomAccessIterator
      partial_sort_copy(_InputIterator __first, _InputIterator __last,
  		      _RandomAccessIterator __result_first,
  		      _RandomAccessIterator __result_last)
      {
        typedef typename iterator_traits<_InputIterator>::value_type
  	_InputValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_OutputValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_ConvertibleConcept<_InputValueType,
  				  _OutputValueType>)
        __glibcxx_function_requires(_LessThanOpConcept<_InputValueType,
  				                     _OutputValueType>)
        __glibcxx_function_requires(_LessThanComparableConcept<_OutputValueType>)
        __glibcxx_requires_valid_range(__first, __last);
        __glibcxx_requires_valid_range(__result_first, __result_last);
  
        if (__result_first == __result_last)
  	return __result_last;
        _RandomAccessIterator __result_real_last = __result_first;
        while(__first != __last && __result_real_last != __result_last)
  	{
  	  *__result_real_last = *__first;
  	  ++__result_real_last;
  	  ++__first;
  	}
        std::make_heap(__result_first, __result_real_last);
        while (__first != __last)
  	{
  	  if (*__first < *__result_first)
  	    std::__adjust_heap(__result_first, _DistanceType(0),
  			       _DistanceType(__result_real_last
  					     - __result_first),
  			       _InputValueType(*__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.
     *  @ingroup sorting_algorithms
     *  @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 @e i and @e 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<typename _InputIterator, typename _RandomAccessIterator, typename _Compare>
      _RandomAccessIterator
      partial_sort_copy(_InputIterator __first, _InputIterator __last,
  		      _RandomAccessIterator __result_first,
  		      _RandomAccessIterator __result_last,
  		      _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator>::value_type
  	_InputValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_OutputValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  				  _RandomAccessIterator>)
        __glibcxx_function_requires(_ConvertibleConcept<_InputValueType,
  				  _OutputValueType>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _InputValueType, _OutputValueType>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _OutputValueType, _OutputValueType>)
        __glibcxx_requires_valid_range(__first, __last);
        __glibcxx_requires_valid_range(__result_first, __result_last);
  
        if (__result_first == __result_last)
  	return __result_last;
        _RandomAccessIterator __result_real_last = __result_first;
        while(__first != __last && __result_real_last != __result_last)
  	{
  	  *__result_real_last = *__first;
  	  ++__result_real_last;
  	  ++__first;
  	}
        std::make_heap(__result_first, __result_real_last, __comp);
        while (__first != __last)
  	{
  	  if (__comp(*__first, *__result_first))
  	    std::__adjust_heap(__result_first, _DistanceType(0),
  			       _DistanceType(__result_real_last
  					     - __result_first),
  			       _InputValueType(*__first),
  			       __comp);
  	  ++__first;
  	}
        std::sort_heap(__result_first, __result_real_last, __comp);
        return __result_real_last;
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator>
      void
      __unguarded_linear_insert(_RandomAccessIterator __last)
      {
        typename iterator_traits<_RandomAccessIterator>::value_type
  	__val = _GLIBCXX_MOVE(*__last);
        _RandomAccessIterator __next = __last;
        --__next;
        while (__val < *__next)
  	{
  	  *__last = _GLIBCXX_MOVE(*__next);
  	  __last = __next;
  	  --__next;
  	}
        *__last = _GLIBCXX_MOVE(__val);
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Compare>
      void
      __unguarded_linear_insert(_RandomAccessIterator __last,
  			      _Compare __comp)
      {
        typename iterator_traits<_RandomAccessIterator>::value_type
  	__val = _GLIBCXX_MOVE(*__last);
        _RandomAccessIterator __next = __last;
        --__next;
        while (__comp(__val, *__next))
  	{
  	  *__last = _GLIBCXX_MOVE(*__next);
  	  __last = __next;
  	  --__next;
  	}
        *__last = _GLIBCXX_MOVE(__val);
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator>
      void
      __insertion_sort(_RandomAccessIterator __first,
  		     _RandomAccessIterator __last)
      {
        if (__first == __last)
  	return;
  
        for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
  	{
  	  if (*__i < *__first)
  	    {
  	      typename iterator_traits<_RandomAccessIterator>::value_type
  		__val = _GLIBCXX_MOVE(*__i);
  	      _GLIBCXX_MOVE_BACKWARD3(__first, __i, __i + 1);
  	      *__first = _GLIBCXX_MOVE(__val);
  	    }
  	  else
  	    std::__unguarded_linear_insert(__i);
  	}
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Compare>
      void
      __insertion_sort(_RandomAccessIterator __first,
  		     _RandomAccessIterator __last, _Compare __comp)
      {
        if (__first == __last) return;
  
        for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
  	{
  	  if (__comp(*__i, *__first))
  	    {
  	      typename iterator_traits<_RandomAccessIterator>::value_type
  		__val = _GLIBCXX_MOVE(*__i);
  	      _GLIBCXX_MOVE_BACKWARD3(__first, __i, __i + 1);
  	      *__first = _GLIBCXX_MOVE(__val);
  	    }
  	  else
  	    std::__unguarded_linear_insert(__i, __comp);
  	}
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator>
      inline void
      __unguarded_insertion_sort(_RandomAccessIterator __first,
  			       _RandomAccessIterator __last)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        for (_RandomAccessIterator __i = __first; __i != __last; ++__i)
  	std::__unguarded_linear_insert(__i);
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Compare>
      inline void
      __unguarded_insertion_sort(_RandomAccessIterator __first,
  			       _RandomAccessIterator __last, _Compare __comp)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        for (_RandomAccessIterator __i = __first; __i != __last; ++__i)
  	std::__unguarded_linear_insert(__i, __comp);
      }
  
    /**
     *  @doctodo
     *  This controls some aspect of the sort routines.
    */
    enum { _S_threshold = 16 };
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator>
      void
      __final_insertion_sort(_RandomAccessIterator __first,
  			   _RandomAccessIterator __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);
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Compare>
      void
      __final_insertion_sort(_RandomAccessIterator __first,
  			   _RandomAccessIterator __last, _Compare __comp)
      {
        if (__last - __first > int(_S_threshold))
  	{
  	  std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
  	  std::__unguarded_insertion_sort(__first + int(_S_threshold), __last,
  					  __comp);
  	}
        else
  	std::__insertion_sort(__first, __last, __comp);
      }
  
    /// This is a helper function...
    template<typename _RandomAccessIterator, typename _Tp>
      _RandomAccessIterator
      __unguarded_partition(_RandomAccessIterator __first,
  			  _RandomAccessIterator __last, const _Tp& __pivot)
      {
        while (true)
  	{
  	  while (*__first < __pivot)
  	    ++__first;
  	  --__last;
  	  while (__pivot < *__last)
  	    --__last;
  	  if (!(__first < __last))
  	    return __first;
  	  std::iter_swap(__first, __last);
  	  ++__first;
  	}
      }
  
    /// This is a helper function...
    template<typename _RandomAccessIterator, typename _Tp, typename _Compare>
      _RandomAccessIterator
      __unguarded_partition(_RandomAccessIterator __first,
  			  _RandomAccessIterator __last,
  			  const _Tp& __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;
  	}
      }
  
    /// This is a helper function...
    template<typename _RandomAccessIterator>
      inline _RandomAccessIterator
      __unguarded_partition_pivot(_RandomAccessIterator __first,
  				_RandomAccessIterator __last)
      {
        _RandomAccessIterator __mid = __first + (__last - __first) / 2;
        std::__move_median_to_first(__first, __first + 1, __mid, (__last - 2));
        return std::__unguarded_partition(__first + 1, __last, *__first);
      }
  
  
    /// This is a helper function...
    template<typename _RandomAccessIterator, typename _Compare>
      inline _RandomAccessIterator
      __unguarded_partition_pivot(_RandomAccessIterator __first,
  				_RandomAccessIterator __last, _Compare __comp)
      {
        _RandomAccessIterator __mid = __first + (__last - __first) / 2;
        std::__move_median_to_first(__first, __first + 1, __mid, (__last - 2),
  				  __comp);
        return std::__unguarded_partition(__first + 1, __last, *__first, __comp);
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Size>
      void
      __introsort_loop(_RandomAccessIterator __first,
  		     _RandomAccessIterator __last,
  		     _Size __depth_limit)
      {
        while (__last - __first > int(_S_threshold))
  	{
  	  if (__depth_limit == 0)
  	    {
  	      _GLIBCXX_STD_A::partial_sort(__first, __last, __last);
  	      return;
  	    }
  	  --__depth_limit;
  	  _RandomAccessIterator __cut =
  	    std::__unguarded_partition_pivot(__first, __last);
  	  std::__introsort_loop(__cut, __last, __depth_limit);
  	  __last = __cut;
  	}
      }
  
    /// This is a helper function for the sort routine.
    template<typename _RandomAccessIterator, typename _Size, typename _Compare>
      void
      __introsort_loop(_RandomAccessIterator __first,
  		     _RandomAccessIterator __last,
  		     _Size __depth_limit, _Compare __comp)
      {
        while (__last - __first > int(_S_threshold))
  	{
  	  if (__depth_limit == 0)
  	    {
  	      _GLIBCXX_STD_A::partial_sort(__first, __last, __last, __comp);
  	      return;
  	    }
  	  --__depth_limit;
  	  _RandomAccessIterator __cut =
  	    std::__unguarded_partition_pivot(__first, __last, __comp);
  	  std::__introsort_loop(__cut, __last, __depth_limit, __comp);
  	  __last = __cut;
  	}
      }
  
    // sort
  
    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_pivot(__first, __last);
  	  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_pivot(__first, __last, __comp);
  	  if (__cut <= __nth)
  	    __first = __cut;
  	  else
  	    __last = __cut;
  	}
        std::__insertion_sort(__first, __last, __comp);
      }
  
    // nth_element
  
    // lower_bound moved to stl_algobase.h
  
    /**
     *  @brief Finds the first position in which @p __val could be inserted
     *         without changing the ordering.
     *  @ingroup binary_search_algorithms
     *  @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 <em>not less
     *           than</em> @p __val, or end() if every element is less
     *           than @p __val.
     *  @ingroup binary_search_algorithms
     *
     *  The comparison function should have the same effects on ordering as
     *  the function used for the initial sort.
    */
    template<typename _ForwardIterator, typename _Tp, typename _Compare>
      _ForwardIterator
      lower_bound(_ForwardIterator __first, _ForwardIterator __last,
  		const _Tp& __val, _Compare __comp)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType, _Tp>)
        __glibcxx_requires_partitioned_lower_pred(__first, __last,
  						__val, __comp);
  
        _DistanceType __len = std::distance(__first, __last);
  
        while (__len > 0)
  	{
  	  _DistanceType __half = __len >> 1;
  	  _ForwardIterator __middle = __first;
  	  std::advance(__middle, __half);
  	  if (__comp(*__middle, __val))
  	    {
  	      __first = __middle;
  	      ++__first;
  	      __len = __len - __half - 1;
  	    }
  	  else
  	    __len = __half;
  	}
        return __first;
      }
  
    /**
     *  @brief Finds the last position in which @p __val could be inserted
     *         without changing the ordering.
     *  @ingroup binary_search_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __val     The search term.
     *  @return  An iterator pointing to the first element greater than @p __val,
     *           or end() if no elements are greater than @p __val.
     *  @ingroup binary_search_algorithms
    */
    template<typename _ForwardIterator, typename _Tp>
      _ForwardIterator
      upper_bound(_ForwardIterator __first, _ForwardIterator __last,
  		const _Tp& __val)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)
        __glibcxx_requires_partitioned_upper(__first, __last, __val);
  
        _DistanceType __len = std::distance(__first, __last);
  
        while (__len > 0)
  	{
  	  _DistanceType __half = __len >> 1;
  	  _ForwardIterator __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 @p __val could be inserted
     *         without changing the ordering.
     *  @ingroup binary_search_algorithms
     *  @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 @p __val,
     *           or end() if no elements are greater than @p __val.
     *  @ingroup binary_search_algorithms
     *
     *  The comparison function should have the same effects on ordering as
     *  the function used for the initial sort.
    */
    template<typename _ForwardIterator, typename _Tp, typename _Compare>
      _ForwardIterator
      upper_bound(_ForwardIterator __first, _ForwardIterator __last,
  		const _Tp& __val, _Compare __comp)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _Tp, _ValueType>)
        __glibcxx_requires_partitioned_upper_pred(__first, __last,
  						__val, __comp);
  
        _DistanceType __len = std::distance(__first, __last);
  
        while (__len > 0)
  	{
  	  _DistanceType __half = __len >> 1;
  	  _ForwardIterator __middle = __first;
  	  std::advance(__middle, __half);
  	  if (__comp(__val, *__middle))
  	    __len = __half;
  	  else
  	    {
  	      __first = __middle;
  	      ++__first;
  	      __len = __len - __half - 1;
  	    }
  	}
        return __first;
      }
  
    /**
     *  @brief Finds the largest subrange in which @p __val could be inserted
     *         at any place in it without changing the ordering.
     *  @ingroup binary_search_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __val     The search term.
     *  @return  An pair of iterators defining the subrange.
     *  @ingroup binary_search_algorithms
     *
     *  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<typename _ForwardIterator, typename _Tp>
      pair<_ForwardIterator, _ForwardIterator>
      equal_range(_ForwardIterator __first, _ForwardIterator __last,
  		const _Tp& __val)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType, _Tp>)
        __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)	
        __glibcxx_requires_partitioned_lower(__first, __last, __val);
        __glibcxx_requires_partitioned_upper(__first, __last, __val);      
  
        _DistanceType __len = std::distance(__first, __last);
   
        while (__len > 0)
  	{
  	  _DistanceType __half = __len >> 1;
  	  _ForwardIterator __middle = __first;
  	  std::advance(__middle, __half);
  	  if (*__middle < __val)
  	    {
  	      __first = __middle;
  	      ++__first;
  	      __len = __len - __half - 1;
  	    }
  	  else if (__val < *__middle)
  	    __len = __half;
  	  else
  	    {
  	      _ForwardIterator __left = std::lower_bound(__first, __middle,
  							 __val);
  	      std::advance(__first, __len);
  	      _ForwardIterator __right = std::upper_bound(++__middle, __first,
  							  __val);
  	      return pair<_ForwardIterator, _ForwardIterator>(__left, __right);
  	    }
  	}
        return pair<_ForwardIterator, _ForwardIterator>(__first, __first);
      }
  
    /**
     *  @brief Finds the largest subrange in which @p __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 binary_search_algorithms
     *
     *  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<typename _ForwardIterator, typename _Tp, typename _Compare>
      pair<_ForwardIterator, _ForwardIterator>
      equal_range(_ForwardIterator __first, _ForwardIterator __last,
  		const _Tp& __val, _Compare __comp)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_ForwardIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType, _Tp>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _Tp, _ValueType>)
        __glibcxx_requires_partitioned_lower_pred(__first, __last,
  						__val, __comp);
        __glibcxx_requires_partitioned_upper_pred(__first, __last,
  						__val, __comp);
  
        _DistanceType __len = std::distance(__first, __last);
  
        while (__len > 0)
  	{
  	  _DistanceType __half = __len >> 1;
  	  _ForwardIterator __middle = __first;
  	  std::advance(__middle, __half);
  	  if (__comp(*__middle, __val))
  	    {
  	      __first = __middle;
  	      ++__first;
  	      __len = __len - __half - 1;
  	    }
  	  else if (__comp(__val, *__middle))
  	    __len = __half;
  	  else
  	    {
  	      _ForwardIterator __left = std::lower_bound(__first, __middle,
  							 __val, __comp);
  	      std::advance(__first, __len);
  	      _ForwardIterator __right = std::upper_bound(++__middle, __first,
  							  __val, __comp);
  	      return pair<_ForwardIterator, _ForwardIterator>(__left, __right);
  	    }
  	}
        return pair<_ForwardIterator, _ForwardIterator>(__first, __first);
      }
  
    /**
     *  @brief Determines whether an element exists in a range.
     *  @ingroup binary_search_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __val     The search term.
     *  @return True if @p __val (or its equivalent) is in [@p
     *  __first,@p __last ].
     *
     *  Note that this does not actually return an iterator to @p __val.  For
     *  that, use std::find or a container's specialized find member functions.
    */
    template<typename _ForwardIterator, typename _Tp>
      bool
      binary_search(_ForwardIterator __first, _ForwardIterator __last,
                    const _Tp& __val)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanOpConcept<_Tp, _ValueType>)
        __glibcxx_requires_partitioned_lower(__first, __last, __val);
        __glibcxx_requires_partitioned_upper(__first, __last, __val);
  
        _ForwardIterator __i = std::lower_bound(__first, __last, __val);
        return __i != __last && !(__val < *__i);
      }
  
    /**
     *  @brief Determines whether an element exists in a range.
     *  @ingroup binary_search_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __val     The search term.
     *  @param  __comp    A functor to use for comparisons.
     *  @return  True if @p __val (or its equivalent) is in @p [__first,__last].
     *
     *  Note that this does not actually return an iterator to @p __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<typename _ForwardIterator, typename _Tp, typename _Compare>
      bool
      binary_search(_ForwardIterator __first, _ForwardIterator __last,
                    const _Tp& __val, _Compare __comp)
      {
        typedef typename iterator_traits<_ForwardIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _Tp, _ValueType>)
        __glibcxx_requires_partitioned_lower_pred(__first, __last,
  						__val, __comp);
        __glibcxx_requires_partitioned_upper_pred(__first, __last,
  						__val, __comp);
  
        _ForwardIterator __i = std::lower_bound(__first, __last, __val, __comp);
        return __i != __last && !bool(__comp(__val, *__i));
      }
  
    // merge
  
    /// This is a helper function for the __merge_adaptive routines.
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      void
      __move_merge_adaptive(_InputIterator1 __first1, _InputIterator1 __last1,
  			  _InputIterator2 __first2, _InputIterator2 __last2,
  			  _OutputIterator __result)
      {
        while (__first1 != __last1 && __first2 != __last2)
  	{
  	  if (*__first2 < *__first1)
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first2);
  	      ++__first2;
  	    }
  	  else
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first1);
  	      ++__first1;
  	    }
  	  ++__result;
  	}
        if (__first1 != __last1)
  	_GLIBCXX_MOVE3(__first1, __last1, __result);
      }
  
    /// This is a helper function for the __merge_adaptive routines.
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      void
      __move_merge_adaptive(_InputIterator1 __first1, _InputIterator1 __last1,
  			  _InputIterator2 __first2, _InputIterator2 __last2,
  			  _OutputIterator __result, _Compare __comp)
      {
        while (__first1 != __last1 && __first2 != __last2)
  	{
  	  if (__comp(*__first2, *__first1))
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first2);
  	      ++__first2;
  	    }
  	  else
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first1);
  	      ++__first1;
  	    }
  	  ++__result;
  	}
        if (__first1 != __last1)
  	_GLIBCXX_MOVE3(__first1, __last1, __result);
      }
  
    /// This is a helper function for the __merge_adaptive routines.
    template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
  	   typename _BidirectionalIterator3>
      void
      __move_merge_adaptive_backward(_BidirectionalIterator1 __first1,
  				   _BidirectionalIterator1 __last1,
  				   _BidirectionalIterator2 __first2,
  				   _BidirectionalIterator2 __last2,
  				   _BidirectionalIterator3 __result)
      {
        if (__first1 == __last1)
  	{
  	  _GLIBCXX_MOVE_BACKWARD3(__first2, __last2, __result);
  	  return;
  	}
        else if (__first2 == __last2)
  	return;
  
        --__last1;
        --__last2;
        while (true)
  	{
  	  if (*__last2 < *__last1)
  	    {
  	      *--__result = _GLIBCXX_MOVE(*__last1);
  	      if (__first1 == __last1)
  		{
  		  _GLIBCXX_MOVE_BACKWARD3(__first2, ++__last2, __result);
  		  return;
  		}
  	      --__last1;
  	    }
  	  else
  	    {
  	      *--__result = _GLIBCXX_MOVE(*__last2);
  	      if (__first2 == __last2)
  		return;
  	      --__last2;
  	    }
  	}
      }
  
    /// This is a helper function for the __merge_adaptive routines.
    template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
  	   typename _BidirectionalIterator3, typename _Compare>
      void
      __move_merge_adaptive_backward(_BidirectionalIterator1 __first1,
  				   _BidirectionalIterator1 __last1,
  				   _BidirectionalIterator2 __first2,
  				   _BidirectionalIterator2 __last2,
  				   _BidirectionalIterator3 __result,
  				   _Compare __comp)
      {
        if (__first1 == __last1)
  	{
  	  _GLIBCXX_MOVE_BACKWARD3(__first2, __last2, __result);
  	  return;
  	}
        else if (__first2 == __last2)
  	return;
  
        --__last1;
        --__last2;
        while (true)
  	{
  	  if (__comp(*__last2, *__last1))
  	    {
  	      *--__result = _GLIBCXX_MOVE(*__last1);
  	      if (__first1 == __last1)
  		{
  		  _GLIBCXX_MOVE_BACKWARD3(__first2, ++__last2, __result);
  		  return;
  		}
  	      --__last1;
  	    }
  	  else
  	    {
  	      *--__result = _GLIBCXX_MOVE(*__last2);
  	      if (__first2 == __last2)
  		return;
  	      --__last2;
  	    }
  	}
      }
  
    /// This is a helper function for the merge routines.
    template<typename _BidirectionalIterator1, typename _BidirectionalIterator2,
  	   typename _Distance>
      _BidirectionalIterator1
      __rotate_adaptive(_BidirectionalIterator1 __first,
  		      _BidirectionalIterator1 __middle,
  		      _BidirectionalIterator1 __last,
  		      _Distance __len1, _Distance __len2,
  		      _BidirectionalIterator2 __buffer,
  		      _Distance __buffer_size)
      {
        _BidirectionalIterator2 __buffer_end;
        if (__len1 > __len2 && __len2 <= __buffer_size)
  	{
  	  if (__len2)
  	    {
  	      __buffer_end = _GLIBCXX_MOVE3(__middle, __last, __buffer);
  	      _GLIBCXX_MOVE_BACKWARD3(__first, __middle, __last);
  	      return _GLIBCXX_MOVE3(__buffer, __buffer_end, __first);
  	    }
  	  else
  	    return __first;
  	}
        else if (__len1 <= __buffer_size)
  	{
  	  if (__len1)
  	    {
  	      __buffer_end = _GLIBCXX_MOVE3(__first, __middle, __buffer);
  	      _GLIBCXX_MOVE3(__middle, __last, __first);
  	      return _GLIBCXX_MOVE_BACKWARD3(__buffer, __buffer_end, __last);
  	    }
  	  else
  	    return __last;
  	}
        else
  	{
  	  std::rotate(__first, __middle, __last);
  	  std::advance(__first, std::distance(__middle, __last));
  	  return __first;
  	}
      }
  
    /// This is a helper function for the merge routines.
    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 = _GLIBCXX_MOVE3(__first, __middle, __buffer);
  	  std::__move_merge_adaptive(__buffer, __buffer_end, __middle, __last,
  				     __first);
  	}
        else if (__len2 <= __buffer_size)
  	{
  	  _Pointer __buffer_end = _GLIBCXX_MOVE3(__middle, __last, __buffer);
  	  std::__move_merge_adaptive_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);
  	}
      }
  
    /// This is a helper function for the merge routines.
    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 = _GLIBCXX_MOVE3(__first, __middle, __buffer);
  	  std::__move_merge_adaptive(__buffer, __buffer_end, __middle, __last,
  				     __first, __comp);
  	}
        else if (__len2 <= __buffer_size)
  	{
  	  _Pointer __buffer_end = _GLIBCXX_MOVE3(__middle, __last, __buffer);
  	  std::__move_merge_adaptive_backward(__first, __middle, __buffer,
  					      __buffer_end, __last, __comp);
  	}
        else
  	{
  	  _BidirectionalIterator __first_cut = __first;
  	  _BidirectionalIterator __second_cut = __middle;
  	  _Distance __len11 = 0;
  	  _Distance __len22 = 0;
  	  if (__len1 > __len2)
  	    {
  	      __len11 = __len1 / 2;
  	      std::advance(__first_cut, __len11);
  	      __second_cut = std::lower_bound(__middle, __last, *__first_cut,
  					      __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);
  	}
      }
  
    /// This is a helper function for the merge routines.
    template<typename _BidirectionalIterator, typename _Distance>
      void
      __merge_without_buffer(_BidirectionalIterator __first,
  			   _BidirectionalIterator __middle,
  			   _BidirectionalIterator __last,
  			   _Distance __len1, _Distance __len2)
      {
        if (__len1 == 0 || __len2 == 0)
  	return;
        if (__len1 + __len2 == 2)
  	{
  	  if (*__middle < *__first)
  	    std::iter_swap(__first, __middle);
  	  return;
  	}
        _BidirectionalIterator __first_cut = __first;
        _BidirectionalIterator __second_cut = __middle;
        _Distance __len11 = 0;
        _Distance __len22 = 0;
        if (__len1 > __len2)
  	{
  	  __len11 = __len1 / 2;
  	  std::advance(__first_cut, __len11);
  	  __second_cut = std::lower_bound(__middle, __last, *__first_cut);
  	  __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);
  	}
        std::rotate(__first_cut, __middle, __second_cut);
        _BidirectionalIterator __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);
      }
  
    /// This is a helper function for the merge routines.
    template<typename _BidirectionalIterator, typename _Distance,
  	   typename _Compare>
      void
      __merge_without_buffer(_BidirectionalIterator __first,
                             _BidirectionalIterator __middle,
  			   _BidirectionalIterator __last,
  			   _Distance __len1, _Distance __len2,
  			   _Compare __comp)
      {
        if (__len1 == 0 || __len2 == 0)
  	return;
        if (__len1 + __len2 == 2)
  	{
  	  if (__comp(*__middle, *__first))
  	    std::iter_swap(__first, __middle);
  	  return;
  	}
        _BidirectionalIterator __first_cut = __first;
        _BidirectionalIterator __second_cut = __middle;
        _Distance __len11 = 0;
        _Distance __len22 = 0;
        if (__len1 > __len2)
  	{
  	  __len11 = __len1 / 2;
  	  std::advance(__first_cut, __len11);
  	  __second_cut = std::lower_bound(__middle, __last, *__first_cut,
  					  __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);
  	}
        std::rotate(__first_cut, __middle, __second_cut);
        _BidirectionalIterator __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);
      }
  
    /**
     *  @brief Merges two sorted ranges in place.
     *  @ingroup sorting_algorithms
     *  @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<typename _BidirectionalIterator>
      void
      inplace_merge(_BidirectionalIterator __first,
  		  _BidirectionalIterator __middle,
  		  _BidirectionalIterator __last)
      {
        typedef typename iterator_traits<_BidirectionalIterator>::value_type
            _ValueType;
        typedef typename iterator_traits<_BidirectionalIterator>::difference_type
            _DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
  	    _BidirectionalIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
        __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<_BidirectionalIterator, _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.
     *  @ingroup sorting_algorithms
     *  @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<typename _BidirectionalIterator, typename _Compare>
      void
      inplace_merge(_BidirectionalIterator __first,
  		  _BidirectionalIterator __middle,
  		  _BidirectionalIterator __last,
  		  _Compare __comp)
      {
        typedef typename iterator_traits<_BidirectionalIterator>::value_type
            _ValueType;
        typedef typename iterator_traits<_BidirectionalIterator>::difference_type
            _DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_BidirectionalIteratorConcept<
  	    _BidirectionalIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    _ValueType, _ValueType>)
        __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<_BidirectionalIterator, _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);
      }
  
  
    /// This is a helper function for the __merge_sort_loop routines.
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      __move_merge(_InputIterator1 __first1, _InputIterator1 __last1,
  		 _InputIterator2 __first2, _InputIterator2 __last2,
  		 _OutputIterator __result)
      {
        while (__first1 != __last1 && __first2 != __last2)
  	{
  	  if (*__first2 < *__first1)
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first2);
  	      ++__first2;
  	    }
  	  else
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first1);
  	      ++__first1;
  	    }
  	  ++__result;
  	}
        return _GLIBCXX_MOVE3(__first2, __last2,
  			    _GLIBCXX_MOVE3(__first1, __last1,
  					   __result));
      }
  
    /// This is a helper function for the __merge_sort_loop routines.
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      __move_merge(_InputIterator1 __first1, _InputIterator1 __last1,
  		 _InputIterator2 __first2, _InputIterator2 __last2,
  		 _OutputIterator __result, _Compare __comp)
      {
        while (__first1 != __last1 && __first2 != __last2)
  	{
  	  if (__comp(*__first2, *__first1))
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first2);
  	      ++__first2;
  	    }
  	  else
  	    {
  	      *__result = _GLIBCXX_MOVE(*__first1);
  	      ++__first1;
  	    }
  	  ++__result;
  	}
        return _GLIBCXX_MOVE3(__first2, __last2,
  			    _GLIBCXX_MOVE3(__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::__move_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::__move_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::__move_merge(__first, __first + __step_size,
  				       __first + __step_size,
  				       __first + __two_step,
  				       __result, __comp);
  	  __first += __two_step;
  	}
        __step_size = std::min(_Distance(__last - __first), __step_size);
  
        std::__move_merge(__first,__first + __step_size,
  			__first + __step_size, __last, __result, __comp);
      }
  
    template<typename _RandomAccessIterator, typename _Distance>
      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);
      }
  
    enum { _S_chunk_size = 7 };
  
    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;
  	}
      }
  
    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);
      }
  
    /// This is a helper function for the stable sorting routines.
    template<typename _RandomAccessIterator>
      void
      __inplace_stable_sort(_RandomAccessIterator __first,
  			  _RandomAccessIterator __last)
      {
        if (__last - __first < 15)
  	{
  	  std::__insertion_sort(__first, __last);
  	  return;
  	}
        _RandomAccessIterator __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);
      }
  
    /// This is a helper function for the stable sorting routines.
    template<typename _RandomAccessIterator, typename _Compare>
      void
      __inplace_stable_sort(_RandomAccessIterator __first,
  			  _RandomAccessIterator __last, _Compare __comp)
      {
        if (__last - __first < 15)
  	{
  	  std::__insertion_sort(__first, __last, __comp);
  	  return;
  	}
        _RandomAccessIterator __middle = __first + (__last - __first) / 2;
        std::__inplace_stable_sort(__first, __middle, __comp);
        std::__inplace_stable_sort(__middle, __last, __comp);
        std::__merge_without_buffer(__first, __middle, __last,
  				  __middle - __first,
  				  __last - __middle,
  				  __comp);
      }
  
    // stable_sort
  
    // 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 set_algorithms
     *
     *  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 @p __last2, false is
     *  returned.
    */
    template<typename _InputIterator1, typename _InputIterator2>
      bool
      includes(_InputIterator1 __first1, _InputIterator1 __last1,
  	     _InputIterator2 __first2, _InputIterator2 __last2)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType1, _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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 @p __last2, false is returned.
    */
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _Compare>
      bool
      includes(_InputIterator1 __first1, _InputIterator1 __last1,
  	     _InputIterator2 __first2, _InputIterator2 __last2,
  	     _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType1, _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __comp);
  
        while (__first1 != __last1 && __first2 != __last2)
  	if (__comp(*__first2, *__first1))
  	  return false;
  	else if(__comp(*__first1, *__first2))
  	  ++__first1;
  	else
  	  ++__first1, ++__first2;
  
        return __first2 == __last2;
      }
  
    // nth_element
    // merge
    // set_difference
    // set_intersection
    // set_union
    // stable_sort
    // set_symmetric_difference
    // min_element
    // max_element
  
    /**
     *  @brief  Permute range into the next @e dictionary ordering.
     *  @ingroup sorting_algorithms
     *  @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 @e 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<typename _BidirectionalIterator>
      bool
      next_permutation(_BidirectionalIterator __first,
  		     _BidirectionalIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_BidirectionalIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return false;
        _BidirectionalIterator __i = __first;
        ++__i;
        if (__i == __last)
  	return false;
        __i = __last;
        --__i;
  
        for(;;)
  	{
  	  _BidirectionalIterator __ii = __i;
  	  --__i;
  	  if (*__i < *__ii)
  	    {
  	      _BidirectionalIterator __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 @e dictionary ordering using
     *          comparison functor.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @param  __comp   A comparison functor.
     *  @return  False if wrapped to first permutation, true otherwise.
     *
     *  Treats all permutations of the range [__first,__last) as a set of
     *  @e dictionary sorted sequences ordered by @p __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<typename _BidirectionalIterator, typename _Compare>
      bool
      next_permutation(_BidirectionalIterator __first,
  		     _BidirectionalIterator __last, _Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_BidirectionalIterator>::value_type,
  	    typename iterator_traits<_BidirectionalIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return false;
        _BidirectionalIterator __i = __first;
        ++__i;
        if (__i == __last)
  	return false;
        __i = __last;
        --__i;
  
        for(;;)
  	{
  	  _BidirectionalIterator __ii = __i;
  	  --__i;
  	  if (__comp(*__i, *__ii))
  	    {
  	      _BidirectionalIterator __j = __last;
  	      while (!bool(__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 @e dictionary ordering.
     *  @ingroup sorting_algorithms
     *  @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 @e 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<typename _BidirectionalIterator>
      bool
      prev_permutation(_BidirectionalIterator __first,
  		     _BidirectionalIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_BidirectionalIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return false;
        _BidirectionalIterator __i = __first;
        ++__i;
        if (__i == __last)
  	return false;
        __i = __last;
        --__i;
  
        for(;;)
  	{
  	  _BidirectionalIterator __ii = __i;
  	  --__i;
  	  if (*__ii < *__i)
  	    {
  	      _BidirectionalIterator __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 @e dictionary ordering using
     *          comparison functor.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @param  __comp   A comparison functor.
     *  @return  False if wrapped to last permutation, true otherwise.
     *
     *  Treats all permutations of the range [__first,__last) as a set of
     *  @e dictionary sorted sequences ordered by @p __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<typename _BidirectionalIterator, typename _Compare>
      bool
      prev_permutation(_BidirectionalIterator __first,
  		     _BidirectionalIterator __last, _Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_BidirectionalIteratorConcept<
  				  _BidirectionalIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_BidirectionalIterator>::value_type,
  	    typename iterator_traits<_BidirectionalIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return false;
        _BidirectionalIterator __i = __first;
        ++__i;
        if (__i == __last)
  	return false;
        __i = __last;
        --__i;
  
        for(;;)
  	{
  	  _BidirectionalIterator __ii = __i;
  	  --__i;
  	  if (__comp(*__ii, *__i))
  	    {
  	      _BidirectionalIterator __j = __last;
  	      while (!bool(__comp(*--__j, *__i)))
  		{}
  	      std::iter_swap(__i, __j);
  	      std::reverse(__ii, __last);
  	      return true;
  	    }
  	  if (__i == __first)
  	    {
  	      std::reverse(__first, __last);
  	      return false;
  	    }
  	}
      }
  
    // replace
    // replace_if
  
    /**
     *  @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<typename _InputIterator, typename _OutputIterator, typename _Tp>
      _OutputIterator
      replace_copy(_InputIterator __first, _InputIterator __last,
  		 _OutputIterator __result,
  		 const _Tp& __old_value, const _Tp& __new_value)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_InputIterator>::value_type, _Tp>)
        __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.
     *  @ingroup mutating_algorithms
     *  @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<typename _InputIterator, typename _OutputIterator,
  	   typename _Predicate, typename _Tp>
      _OutputIterator
      replace_copy_if(_InputIterator __first, _InputIterator __last,
  		    _OutputIterator __result,
  		    _Predicate __pred, const _Tp& __new_value)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        for (; __first != __last; ++__first, ++__result)
  	if (__pred(*__first))
  	  *__result = __new_value;
  	else
  	  *__result = *__first;
        return __result;
      }
  
  #if __cplusplus >= 201103L
    /**
     *  @brief  Determines whether the elements of a sequence are sorted.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @return  True if the elements are sorted, false otherwise.
    */
    template<typename _ForwardIterator>
      inline bool
      is_sorted(_ForwardIterator __first, _ForwardIterator __last)
      { return std::is_sorted_until(__first, __last) == __last; }
  
    /**
     *  @brief  Determines whether the elements of a sequence are sorted
     *          according to a comparison functor.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __comp    A comparison functor.
     *  @return  True if the elements are sorted, false otherwise.
    */
    template<typename _ForwardIterator, typename _Compare>
      inline bool
      is_sorted(_ForwardIterator __first, _ForwardIterator __last,
  	      _Compare __comp)
      { return std::is_sorted_until(__first, __last, __comp) == __last; }
  
    /**
     *  @brief  Determines the end of a sorted sequence.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @return  An iterator pointing to the last iterator i in [__first, __last)
     *           for which the range [__first, i) is sorted.
    */
    template<typename _ForwardIterator>
      _ForwardIterator
      is_sorted_until(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __last;
  
        _ForwardIterator __next = __first;
        for (++__next; __next != __last; __first = __next, ++__next)
  	if (*__next < *__first)
  	  return __next;
        return __next;
      }
  
    /**
     *  @brief  Determines the end of a sorted sequence using comparison functor.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @param  __comp    A comparison functor.
     *  @return  An iterator pointing to the last iterator i in [__first, __last)
     *           for which the range [__first, i) is sorted.
    */
    template<typename _ForwardIterator, typename _Compare>
      _ForwardIterator
      is_sorted_until(_ForwardIterator __first, _ForwardIterator __last,
  		    _Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_ForwardIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __last;
  
        _ForwardIterator __next = __first;
        for (++__next; __next != __last; __first = __next, ++__next)
  	if (__comp(*__next, *__first))
  	  return __next;
        return __next;
      }
  
    /**
     *  @brief  Determines min and max at once as an ordered pair.
     *  @ingroup sorting_algorithms
     *  @param  __a  A thing of arbitrary type.
     *  @param  __b  Another thing of arbitrary type.
     *  @return A pair(__b, __a) if __b is smaller than __a, pair(__a,
     *  __b) otherwise.
    */
    template<typename _Tp>
      inline pair<const _Tp&, const _Tp&>
      minmax(const _Tp& __a, const _Tp& __b)
      {
        // concept requirements
        __glibcxx_function_requires(_LessThanComparableConcept<_Tp>)
  
        return __b < __a ? pair<const _Tp&, const _Tp&>(__b, __a)
  	               : pair<const _Tp&, const _Tp&>(__a, __b);
      }
  
    /**
     *  @brief  Determines min and max at once as an ordered pair.
     *  @ingroup sorting_algorithms
     *  @param  __a  A thing of arbitrary type.
     *  @param  __b  Another thing of arbitrary type.
     *  @param  __comp  A @link comparison_functors comparison functor @endlink.
     *  @return A pair(__b, __a) if __b is smaller than __a, pair(__a,
     *  __b) otherwise.
    */
    template<typename _Tp, typename _Compare>
      inline pair<const _Tp&, const _Tp&>
      minmax(const _Tp& __a, const _Tp& __b, _Compare __comp)
      {
        return __comp(__b, __a) ? pair<const _Tp&, const _Tp&>(__b, __a)
  	                      : pair<const _Tp&, const _Tp&>(__a, __b);
      }
  
    /**
     *  @brief  Return a pair of iterators pointing to the minimum and maximum
     *          elements in a range.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @return  make_pair(m, M), where m is the first iterator i in 
     *           [__first, __last) such that no other element in the range is
     *           smaller, and where M is the last iterator i in [__first, __last)
     *           such that no other element in the range is larger.
    */
    template<typename _ForwardIterator>
      pair<_ForwardIterator, _ForwardIterator>
      minmax_element(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        _ForwardIterator __next = __first;
        if (__first == __last
  	  || ++__next == __last)
  	return std::make_pair(__first, __first);
  
        _ForwardIterator __min, __max;
        if (*__next < *__first)
  	{
  	  __min = __next;
  	  __max = __first;
  	}
        else
  	{
  	  __min = __first;
  	  __max = __next;
  	}
  
        __first = __next;
        ++__first;
  
        while (__first != __last)
  	{
  	  __next = __first;
  	  if (++__next == __last)
  	    {
  	      if (*__first < *__min)
  		__min = __first;
  	      else if (!(*__first < *__max))
  		__max = __first;
  	      break;
  	    }
  
  	  if (*__next < *__first)
  	    {
  	      if (*__next < *__min)
  		__min = __next;
  	      if (!(*__first < *__max))
  		__max = __first;
  	    }
  	  else
  	    {
  	      if (*__first < *__min)
  		__min = __first;
  	      if (!(*__next < *__max))
  		__max = __next;
  	    }
  
  	  __first = __next;
  	  ++__first;
  	}
  
        return std::make_pair(__min, __max);
      }
  
    /**
     *  @brief  Return a pair of iterators pointing to the minimum and maximum
     *          elements in a range.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @param  __comp   Comparison functor.
     *  @return  make_pair(m, M), where m is the first iterator i in 
     *           [__first, __last) such that no other element in the range is
     *           smaller, and where M is the last iterator i in [__first, __last)
     *           such that no other element in the range is larger.
    */
    template<typename _ForwardIterator, typename _Compare>
      pair<_ForwardIterator, _ForwardIterator>
      minmax_element(_ForwardIterator __first, _ForwardIterator __last,
  		   _Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_ForwardIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        _ForwardIterator __next = __first;
        if (__first == __last
  	  || ++__next == __last)
  	return std::make_pair(__first, __first);
  
        _ForwardIterator __min, __max;
        if (__comp(*__next, *__first))
  	{
  	  __min = __next;
  	  __max = __first;
  	}
        else
  	{
  	  __min = __first;
  	  __max = __next;
  	}
  
        __first = __next;
        ++__first;
  
        while (__first != __last)
  	{
  	  __next = __first;
  	  if (++__next == __last)
  	    {
  	      if (__comp(*__first, *__min))
  		__min = __first;
  	      else if (!__comp(*__first, *__max))
  		__max = __first;
  	      break;
  	    }
  
  	  if (__comp(*__next, *__first))
  	    {
  	      if (__comp(*__next, *__min))
  		__min = __next;
  	      if (!__comp(*__first, *__max))
  		__max = __first;
  	    }
  	  else
  	    {
  	      if (__comp(*__first, *__min))
  		__min = __first;
  	      if (!__comp(*__next, *__max))
  		__max = __next;
  	    }
  
  	  __first = __next;
  	  ++__first;
  	}
  
        return std::make_pair(__min, __max);
      }
  
    // N2722 + DR 915.
    template<typename _Tp>
      inline _Tp
      min(initializer_list<_Tp> __l)
      { return *std::min_element(__l.begin(), __l.end()); }
  
    template<typename _Tp, typename _Compare>
      inline _Tp
      min(initializer_list<_Tp> __l, _Compare __comp)
      { return *std::min_element(__l.begin(), __l.end(), __comp); }
  
    template<typename _Tp>
      inline _Tp
      max(initializer_list<_Tp> __l)
      { return *std::max_element(__l.begin(), __l.end()); }
  
    template<typename _Tp, typename _Compare>
      inline _Tp
      max(initializer_list<_Tp> __l, _Compare __comp)
      { return *std::max_element(__l.begin(), __l.end(), __comp); }
  
    template<typename _Tp>
      inline pair<_Tp, _Tp>
      minmax(initializer_list<_Tp> __l)
      {
        pair<const _Tp*, const _Tp*> __p =
  	std::minmax_element(__l.begin(), __l.end());
        return std::make_pair(*__p.first, *__p.second);
      }
  
    template<typename _Tp, typename _Compare>
      inline pair<_Tp, _Tp>
      minmax(initializer_list<_Tp> __l, _Compare __comp)
      {
        pair<const _Tp*, const _Tp*> __p =
  	std::minmax_element(__l.begin(), __l.end(), __comp);
        return std::make_pair(*__p.first, *__p.second);
      }
  
    /**
     *  @brief  Checks whether a permutaion of the second sequence is equal
     *          to the first sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first1  Start of first range.
     *  @param  __last1   End of first range.
     *  @param  __first2  Start of second range.
     *  @return true if there exists a permutation of the elements in the range
     *          [__first2, __first2 + (__last1 - __first1)), beginning with 
     *          ForwardIterator2 begin, such that equal(__first1, __last1, begin)
     *          returns true; otherwise, returns false.
    */
    template<typename _ForwardIterator1, typename _ForwardIterator2>
      bool
      is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  		   _ForwardIterator2 __first2)
      {
        // Efficiently compare identical prefixes:  O(N) if sequences
        // have the same elements in the same order.
        for (; __first1 != __last1; ++__first1, ++__first2)
  	if (!(*__first1 == *__first2))
  	  break;
  
        if (__first1 == __last1)
  	return true;
  
        // Establish __last2 assuming equal ranges by iterating over the
        // rest of the list.
        _ForwardIterator2 __last2 = __first2;
        std::advance(__last2, std::distance(__first1, __last1));
        for (_ForwardIterator1 __scan = __first1; __scan != __last1; ++__scan)
  	{
  	  if (__scan != _GLIBCXX_STD_A::find(__first1, __scan, *__scan))
  	    continue; // We've seen this one before.
  
  	  auto __matches = std::count(__first2, __last2, *__scan);
  	  if (0 == __matches
  	      || std::count(__scan, __last1, *__scan) != __matches)
  	    return false;
  	}
        return true;
      }
  
    /**
     *  @brief  Checks whether a permutation of the second sequence is equal
     *          to the first sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first1  Start of first range.
     *  @param  __last1   End of first range.
     *  @param  __first2  Start of second range.
     *  @param  __pred    A binary predicate.
     *  @return true if there exists a permutation of the elements in
     *          the range [__first2, __first2 + (__last1 - __first1)),
     *          beginning with ForwardIterator2 begin, such that
     *          equal(__first1, __last1, __begin, __pred) returns true;
     *          otherwise, returns false.
    */
    template<typename _ForwardIterator1, typename _ForwardIterator2,
  	   typename _BinaryPredicate>
      bool
      is_permutation(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  		   _ForwardIterator2 __first2, _BinaryPredicate __pred)
      {
        // Efficiently compare identical prefixes:  O(N) if sequences
        // have the same elements in the same order.
        for (; __first1 != __last1; ++__first1, ++__first2)
  	if (!bool(__pred(*__first1, *__first2)))
  	  break;
  
        if (__first1 == __last1)
  	return true;
  
        // Establish __last2 assuming equal ranges by iterating over the
        // rest of the list.
        _ForwardIterator2 __last2 = __first2;
        std::advance(__last2, std::distance(__first1, __last1));
        for (_ForwardIterator1 __scan = __first1; __scan != __last1; ++__scan)
  	{
  	  using std::placeholders::_1;
  
  	  if (__scan != _GLIBCXX_STD_A::find_if(__first1, __scan,
  						std::bind(__pred, _1, *__scan)))
  	    continue; // We've seen this one before.
  	  
  	  auto __matches = std::count_if(__first2, __last2,
  					 std::bind(__pred, _1, *__scan));
  	  if (0 == __matches
  	      || std::count_if(__scan, __last1,
  			       std::bind(__pred, _1, *__scan)) != __matches)
  	    return false;
  	}
        return true;
      }
  
  #ifdef _GLIBCXX_USE_C99_STDINT_TR1
    /**
     *  @brief Shuffle the elements of a sequence using a uniform random
     *         number generator.
     *  @ingroup mutating_algorithms
     *  @param  __first   A forward iterator.
     *  @param  __last    A forward iterator.
     *  @param  __g       A UniformRandomNumberGenerator (26.5.1.3).
     *  @return  Nothing.
     *
     *  Reorders the elements in the range @p [__first,__last) using @p __g to
     *  provide random numbers.
    */
    template<typename _RandomAccessIterator,
  	   typename _UniformRandomNumberGenerator>
      void
      shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last,
  	    _UniformRandomNumberGenerator&& __g)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return;
  
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_DistanceType;
  
        typedef typename std::make_unsigned<_DistanceType>::type __ud_type;
        typedef typename std::uniform_int_distribution<__ud_type> __distr_type;
        typedef typename __distr_type::param_type __p_type;
        __distr_type __d;
  
        for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
  	std::iter_swap(__i, __first + __d(__g, __p_type(0, __i - __first)));
      }
  #endif
  
  #endif // C++11
  
  _GLIBCXX_END_NAMESPACE_VERSION
  
  _GLIBCXX_BEGIN_NAMESPACE_ALGO
  
    /**
     *  @brief Apply a function to every element of a sequence.
     *  @ingroup non_mutating_algorithms
     *  @param  __first  An input iterator.
     *  @param  __last   An input iterator.
     *  @param  __f      A unary function object.
     *  @return   @p __f (std::move(@p __f) in C++0x).
     *
     *  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<typename _InputIterator, typename _Function>
      _Function
      for_each(_InputIterator __first, _InputIterator __last, _Function __f)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_requires_valid_range(__first, __last);
        for (; __first != __last; ++__first)
  	__f(*__first);
        return _GLIBCXX_MOVE(__f);
      }
  
    /**
     *  @brief Find the first occurrence of a value in a sequence.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _InputIterator, typename _Tp>
      inline _InputIterator
      find(_InputIterator __first, _InputIterator __last,
  	 const _Tp& __val)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  		typename iterator_traits<_InputIterator>::value_type, _Tp>)
        __glibcxx_requires_valid_range(__first, __last);
        return std::__find(__first, __last, __val,
  		         std::__iterator_category(__first));
      }
  
    /**
     *  @brief Find the first element in a sequence for which a
     *         predicate is true.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _InputIterator, typename _Predicate>
      inline _InputIterator
      find_if(_InputIterator __first, _InputIterator __last,
  	    _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	      typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        return std::__find_if(__first, __last, __pred,
  			    std::__iterator_category(__first));
      }
  
    /**
     *  @brief  Find element from a set in a sequence.
     *  @ingroup non_mutating_algorithms
     *  @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
     *  iterator 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<typename _InputIterator, typename _ForwardIterator>
      _InputIterator
      find_first_of(_InputIterator __first1, _InputIterator __last1,
  		  _ForwardIterator __first2, _ForwardIterator __last2)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_InputIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first1, __last1);
        __glibcxx_requires_valid_range(__first2, __last2);
  
        for (; __first1 != __last1; ++__first1)
  	for (_ForwardIterator __iter = __first2; __iter != __last2; ++__iter)
  	  if (*__first1 == *__iter)
  	    return __first1;
        return __last1;
      }
  
    /**
     *  @brief  Find element from a set in a sequence using a predicate.
     *  @ingroup non_mutating_algorithms
     *  @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 iterator 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<typename _InputIterator, typename _ForwardIterator,
  	   typename _BinaryPredicate>
      _InputIterator
      find_first_of(_InputIterator __first1, _InputIterator __last1,
  		  _ForwardIterator __first2, _ForwardIterator __last2,
  		  _BinaryPredicate __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	    typename iterator_traits<_InputIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first1, __last1);
        __glibcxx_requires_valid_range(__first2, __last2);
  
        for (; __first1 != __last1; ++__first1)
  	for (_ForwardIterator __iter = __first2; __iter != __last2; ++__iter)
  	  if (__comp(*__first1, *__iter))
  	    return __first1;
        return __last1;
      }
  
    /**
     *  @brief Find two adjacent values in a sequence that are equal.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator>
      _ForwardIterator
      adjacent_find(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_EqualityComparableConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        if (__first == __last)
  	return __last;
        _ForwardIterator __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.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator, typename _BinaryPredicate>
      _ForwardIterator
      adjacent_find(_ForwardIterator __first, _ForwardIterator __last,
  		  _BinaryPredicate __binary_pred)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	    typename iterator_traits<_ForwardIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        if (__first == __last)
  	return __last;
        _ForwardIterator __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.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _InputIterator, typename _Tp>
      typename iterator_traits<_InputIterator>::difference_type
      count(_InputIterator __first, _InputIterator __last, const _Tp& __value)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  	typename iterator_traits<_InputIterator>::value_type, _Tp>)
        __glibcxx_requires_valid_range(__first, __last);
        typename iterator_traits<_InputIterator>::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.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _InputIterator, typename _Predicate>
      typename iterator_traits<_InputIterator>::difference_type
      count_if(_InputIterator __first, _InputIterator __last, _Predicate __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
        typename iterator_traits<_InputIterator>::difference_type __n = 0;
        for (; __first != __last; ++__first)
  	if (__pred(*__first))
  	  ++__n;
        return __n;
      }
  
    /**
     *  @brief Search a sequence for a matching sub-sequence.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator1, typename _ForwardIterator2>
      _ForwardIterator1
      search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	   _ForwardIterator2 __first2, _ForwardIterator2 __last2)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator1>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator2>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_ForwardIterator1>::value_type,
  	    typename iterator_traits<_ForwardIterator2>::value_type>)
        __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.
        _ForwardIterator2 __p1(__first2);
        if (++__p1 == __last2)
  	return _GLIBCXX_STD_A::find(__first1, __last1, *__first2);
  
        // General case.
        _ForwardIterator2 __p;
        _ForwardIterator1 __current = __first1;
  
        for (;;)
  	{
  	  __first1 = _GLIBCXX_STD_A::find(__first1, __last1, *__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.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator1, typename _ForwardIterator2,
  	   typename _BinaryPredicate>
      _ForwardIterator1
      search(_ForwardIterator1 __first1, _ForwardIterator1 __last1,
  	   _ForwardIterator2 __first2, _ForwardIterator2 __last2,
  	   _BinaryPredicate  __predicate)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator1>)
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	    typename iterator_traits<_ForwardIterator1>::value_type,
  	    typename iterator_traits<_ForwardIterator2>::value_type>)
        __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.
        _ForwardIterator2 __p1(__first2);
        if (++__p1 == __last2)
  	{
  	  while (__first1 != __last1
  		 && !bool(__predicate(*__first1, *__first2)))
  	    ++__first1;
  	  return __first1;
  	}
  
        // General case.
        _ForwardIterator2 __p;
        _ForwardIterator1 __current = __first1;
  
        for (;;)
  	{
  	  while (__first1 != __last1
  		 && !bool(__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.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Integer, typename _Tp>
      _ForwardIterator
      search_n(_ForwardIterator __first, _ForwardIterator __last,
  	     _Integer __count, const _Tp& __val)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  	typename iterator_traits<_ForwardIterator>::value_type, _Tp>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__count <= 0)
  	return __first;
        if (__count == 1)
  	return _GLIBCXX_STD_A::find(__first, __last, __val);
        return std::__search_n(__first, __last, __count, __val,
  			     std::__iterator_category(__first));
      }
  
  
    /**
     *  @brief Search a sequence for a number of consecutive values using a
     *         predicate.
     *  @ingroup non_mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Integer, typename _Tp,
             typename _BinaryPredicate>
      _ForwardIterator
      search_n(_ForwardIterator __first, _ForwardIterator __last,
  	     _Integer __count, const _Tp& __val,
  	     _BinaryPredicate __binary_pred)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_BinaryPredicate,
  	    typename iterator_traits<_ForwardIterator>::value_type, _Tp>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__count <= 0)
  	return __first;
        if (__count == 1)
  	{
  	  while (__first != __last && !bool(__binary_pred(*__first, __val)))
  	    ++__first;
  	  return __first;
  	}
        return std::__search_n(__first, __last, __count, __val, __binary_pred,
  			     std::__iterator_category(__first));
      }
  
  
    /**
     *  @brief Perform an operation on a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _InputIterator, typename _OutputIterator,
  	   typename _UnaryOperation>
      _OutputIterator
      transform(_InputIterator __first, _InputIterator __last,
  	      _OutputIterator __result, _UnaryOperation __unary_op)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
              // "the type returned by a _UnaryOperation"
              __typeof__(__unary_op(*__first))>)
        __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.
     *  @ingroup mutating_algorithms
     *  @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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _BinaryOperation>
      _OutputIterator
      transform(_InputIterator1 __first1, _InputIterator1 __last1,
  	      _InputIterator2 __first2, _OutputIterator __result,
  	      _BinaryOperation __binary_op)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
              // "the type returned by a _BinaryOperation"
              __typeof__(__binary_op(*__first1,*__first2))>)
        __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.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Tp>
      void
      replace(_ForwardIterator __first, _ForwardIterator __last,
  	    const _Tp& __old_value, const _Tp& __new_value)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_EqualOpConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type, _Tp>)
        __glibcxx_function_requires(_ConvertibleConcept<_Tp,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __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.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Predicate, typename _Tp>
      void
      replace_if(_ForwardIterator __first, _ForwardIterator __last,
  	       _Predicate __pred, const _Tp& __new_value)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_ConvertibleConcept<_Tp,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        for (; __first != __last; ++__first)
  	if (__pred(*__first))
  	  *__first = __new_value;
      }
  
    /**
     *  @brief Assign the result of a function object to each value in a
     *         sequence.
     *  @ingroup mutating_algorithms
     *  @param  __first  A forward iterator.
     *  @param  __last   A forward iterator.
     *  @param  __gen    A function object taking no arguments and returning
     *                 std::iterator_traits<_ForwardIterator>::value_type
     *  @return   generate() returns no value.
     *
     *  Performs the assignment @c *i = @p __gen() for each @c i in the range
     *  @p [__first,__last).
    */
    template<typename _ForwardIterator, typename _Generator>
      void
      generate(_ForwardIterator __first, _ForwardIterator __last,
  	     _Generator __gen)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_GeneratorConcept<_Generator,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __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.
     *  @ingroup mutating_algorithms
     *  @param  __first  A forward iterator.
     *  @param  __n      The length of the sequence.
     *  @param  __gen    A function object taking no arguments and returning
     *                 std::iterator_traits<_ForwardIterator>::value_type
     *  @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).
     *
     *  _GLIBCXX_RESOLVE_LIB_DEFECTS
     *  DR 865. More algorithms that throw away information
    */
    template<typename _OutputIterator, typename _Size, typename _Generator>
      _OutputIterator
      generate_n(_OutputIterator __first, _Size __n, _Generator __gen)
      {
        // concept requirements
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
              // "the type returned by a _Generator"
              __typeof__(__gen())>)
  
        for (__decltype(__n + 0) __niter = __n;
  	   __niter > 0; --__niter, ++__first)
  	*__first = __gen();
        return __first;
      }
  
  
    /**
     *  @brief Copy a sequence, removing consecutive duplicate values.
     *  @ingroup mutating_algorithms
     *  @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.
     *
     *  _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?
    */
    template<typename _InputIterator, typename _OutputIterator>
      inline _OutputIterator
      unique_copy(_InputIterator __first, _InputIterator __last,
  		_OutputIterator __result)
      {
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_function_requires(_EqualityComparableConcept<
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __result;
        return std::__unique_copy(__first, __last, __result,
  				std::__iterator_category(__first),
  				std::__iterator_category(__result));
      }
  
    /**
     *  @brief Copy a sequence, removing consecutive values using a predicate.
     *  @ingroup mutating_algorithms
     *  @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.
     *
     *  _GLIBCXX_RESOLVE_LIB_DEFECTS
     *  DR 241. Does unique_copy() require CopyConstructible and Assignable?
    */
    template<typename _InputIterator, typename _OutputIterator,
  	   typename _BinaryPredicate>
      inline _OutputIterator
      unique_copy(_InputIterator __first, _InputIterator __last,
  		_OutputIterator __result,
  		_BinaryPredicate __binary_pred)
      {
        // concept requirements -- predicates checked later
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  	    typename iterator_traits<_InputIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __result;
        return std::__unique_copy(__first, __last, __result, __binary_pred,
  				std::__iterator_category(__first),
  				std::__iterator_category(__result));
      }
  
  
    /**
     *  @brief Randomly shuffle the elements of a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _RandomAccessIterator>
      inline void
      random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first != __last)
  	for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
  	  std::iter_swap(__i, __first + (std::rand() % ((__i - __first) + 1)));
      }
  
    /**
     *  @brief Shuffle the elements of a sequence using a random number
     *         generator.
     *  @ingroup mutating_algorithms
     *  @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<typename _RandomAccessIterator, typename _RandomNumberGenerator>
      void
      random_shuffle(_RandomAccessIterator __first, _RandomAccessIterator __last,
  #if __cplusplus >= 201103L
  		   _RandomNumberGenerator&& __rand)
  #else
  		   _RandomNumberGenerator& __rand)
  #endif
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return;
        for (_RandomAccessIterator __i = __first + 1; __i != __last; ++__i)
  	std::iter_swap(__i, __first + __rand((__i - __first) + 1));
      }
  
  
    /**
     *  @brief Move elements for which a predicate is true to the beginning
     *         of a sequence.
     *  @ingroup mutating_algorithms
     *  @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<typename _ForwardIterator, typename _Predicate>
      inline _ForwardIterator
      partition(_ForwardIterator __first, _ForwardIterator __last,
  	      _Predicate   __pred)
      {
        // concept requirements
        __glibcxx_function_requires(_Mutable_ForwardIteratorConcept<
  				  _ForwardIterator>)
        __glibcxx_function_requires(_UnaryPredicateConcept<_Predicate,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        return std::__partition(__first, __last, __pred,
  			      std::__iterator_category(__first));
      }
  
  
  
    /**
     *  @brief Sort the smallest elements of a sequence.
     *  @ingroup sorting_algorithms
     *  @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 @e i and @e j are iterators in the range
     *  @p [__first,__middle) such that i precedes j and @e k is an iterator in
     *  the range @p [__middle,__last) then *j<*i and *k<*i are both false.
    */
    template<typename _RandomAccessIterator>
      inline void
      partial_sort(_RandomAccessIterator __first,
  		 _RandomAccessIterator __middle,
  		 _RandomAccessIterator __last)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
        __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.
     *  @ingroup sorting_algorithms
     *  @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 @e i and @e j are iterators in the range
     *  @p [__first,__middle) such that i precedes j and @e k is an iterator in
     *  the range @p [__middle,__last) then @p *__comp(j,*i) and @p __comp(*k,*i)
     *  are both false.
    */
    template<typename _RandomAccessIterator, typename _Compare>
      inline void
      partial_sort(_RandomAccessIterator __first,
  		 _RandomAccessIterator __middle,
  		 _RandomAccessIterator __last,
  		 _Compare __comp)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType, _ValueType>)
        __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 Sort a sequence just enough to find a particular position.
     *  @ingroup sorting_algorithms
     *  @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. The elements either side of @p *__nth are
     *  not completely sorted, but for any iterator @e i in the range
     *  @p [__first,__nth) and any iterator @e j in the range @p [__nth,__last) it
     *  holds that *j < *i is false.
    */
    template<typename _RandomAccessIterator>
      inline void
      nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth,
  		_RandomAccessIterator __last)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  				  _RandomAccessIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
        __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.
     *  @ingroup sorting_algorithms
     *  @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 @e i in the range
     *  @p [__first,__nth) and any iterator @e j in the range @p [__nth,__last) it
     *  holds that @p __comp(*j,*i) is false.
    */
    template<typename _RandomAccessIterator, typename _Compare>
      inline void
      nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth,
  		_RandomAccessIterator __last, _Compare __comp)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  				  _RandomAccessIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType, _ValueType>)
        __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 Sort the elements of a sequence.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @return  Nothing.
     *
     *  Sorts the elements in the range @p [__first,__last) in ascending order,
     *  such that for each iterator @e i in the range @p [__first,__last-1),  
     *  *(i+1)<*i is false.
     *
     *  The relative ordering of equivalent elements is not preserved, use
     *  @p stable_sort() if this is needed.
    */
    template<typename _RandomAccessIterator>
      inline void
      sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first != __last)
  	{
  	  std::__introsort_loop(__first, __last,
  				std::__lg(__last - __first) * 2);
  	  std::__final_insertion_sort(__first, __last);
  	}
      }
  
    /**
     *  @brief Sort the elements of a sequence using a predicate for comparison.
     *  @ingroup sorting_algorithms
     *  @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 @e 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<typename _RandomAccessIterator, typename _Compare>
      inline void
      sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
  	 _Compare __comp)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare, _ValueType,
  				  _ValueType>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first != __last)
  	{
  	  std::__introsort_loop(__first, __last,
  				std::__lg(__last - __first) * 2, __comp);
  	  std::__final_insertion_sort(__first, __last, __comp);
  	}
      }
  
    /**
     *  @brief Merges two sorted ranges.
     *  @ingroup sorting_algorithms
     *  @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 <em>not less
     *                  than</em> @e val.
     *
     *  Merges the ranges @p [__first1,__last1) and @p [__first2,__last2) into
     *  the sorted range @p [__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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      merge(_InputIterator1 __first1, _InputIterator1 __last1,
  	  _InputIterator2 __first2, _InputIterator2 __last2,
  	  _OutputIterator __result)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)	
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup sorting_algorithms
     *  @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" @e val.
     *
     *  Merges the ranges @p [__first1,__last1) and @p [__first2,__last2) into
     *  the sorted range @p [__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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      merge(_InputIterator1 __first1, _InputIterator1 __last1,
  	  _InputIterator2 __first2, _InputIterator2 __last2,
  	  _OutputIterator __result, _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __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));
      }
  
  
    /**
     *  @brief Sort the elements of a sequence, preserving the relative order
     *         of equivalent elements.
     *  @ingroup sorting_algorithms
     *  @param  __first   An iterator.
     *  @param  __last    Another iterator.
     *  @return  Nothing.
     *
     *  Sorts the elements in the range @p [__first,__last) in ascending order,
     *  such that for each iterator @p i in the range @p [__first,__last-1),
     *  @p *(i+1)<*i is false.
     *
     *  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<typename _RandomAccessIterator>
      inline void
      stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<_ValueType>)
        __glibcxx_requires_valid_range(__first, __last);
  
        _Temporary_buffer<_RandomAccessIterator, _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.
     *  @ingroup sorting_algorithms
     *  @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 for each iterator @p i in the range @p [__first,__last-1),
     *  @p __comp(*(i+1),*i) is false.
     *
     *  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<typename _RandomAccessIterator, typename _Compare>
      inline void
      stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last,
  		_Compare __comp)
      {
        typedef typename iterator_traits<_RandomAccessIterator>::value_type
  	_ValueType;
        typedef typename iterator_traits<_RandomAccessIterator>::difference_type
  	_DistanceType;
  
        // concept requirements
        __glibcxx_function_requires(_Mutable_RandomAccessIteratorConcept<
  	    _RandomAccessIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType,
  				  _ValueType>)
        __glibcxx_requires_valid_range(__first, __last);
  
        _Temporary_buffer<_RandomAccessIterator, _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);
      }
  
  
    /**
     *  @brief Return the union of two sorted ranges.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      set_union(_InputIterator1 __first1, _InputIterator1 __last1,
  	      _InputIterator2 __first2, _InputIterator2 __last2,
  	      _OutputIterator __result)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType1, _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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 @p __comp, that element is copied and the iterator advanced.
     *  If an equivalent element according to @p __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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      set_union(_InputIterator1 __first1, _InputIterator1 __last1,
  	      _InputIterator2 __first2, _InputIterator2 __last2,
  	      _OutputIterator __result, _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType1, _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      set_intersection(_InputIterator1 __first1, _InputIterator1 __last1,
  		     _InputIterator2 __first2, _InputIterator2 __last2,
  		     _OutputIterator __result)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType1, _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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 @p __comp, that iterator advances.  If an element is
     *  contained in both ranges according to @p __comp, the element from the
     *  first range is copied and both ranges advance.  The output range may not
     *  overlap either input range.
    */
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      set_intersection(_InputIterator1 __first1, _InputIterator1 __last1,
  		     _InputIterator2 __first2, _InputIterator2 __last2,
  		     _OutputIterator __result, _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType1, _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      set_difference(_InputIterator1 __first1, _InputIterator1 __last1,
  		   _InputIterator2 __first2, _InputIterator2 __last2,
  		   _OutputIterator __result)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType1, _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)	
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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 @p __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 @p __comp, no
     *  elements are copied and both ranges advance.  The output range may not
     *  overlap either input range.
    */
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      set_difference(_InputIterator1 __first1, _InputIterator1 __last1,
  		   _InputIterator2 __first2, _InputIterator2 __last2,
  		   _OutputIterator __result, _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType1, _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator>
      _OutputIterator
      set_symmetric_difference(_InputIterator1 __first1, _InputIterator1 __last1,
  			     _InputIterator2 __first2, _InputIterator2 __last2,
  			     _OutputIterator __result)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType1, _ValueType2>)
        __glibcxx_function_requires(_LessThanOpConcept<_ValueType2, _ValueType1>)	
        __glibcxx_requires_sorted_set(__first1, __last1, __first2);
        __glibcxx_requires_sorted_set(__first2, __last2, __first1);
  
        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.
     *  @ingroup set_algorithms
     *  @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 set_algorithms
     *
     *  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 @p comp, that element is copied and the
     *  iterator advances.  If an element is contained in both ranges according
     *  to @p __comp, no elements are copied and both ranges advance.  The output
     *  range may not overlap either input range.
    */
    template<typename _InputIterator1, typename _InputIterator2,
  	   typename _OutputIterator, typename _Compare>
      _OutputIterator
      set_symmetric_difference(_InputIterator1 __first1, _InputIterator1 __last1,
  			     _InputIterator2 __first2, _InputIterator2 __last2,
  			     _OutputIterator __result,
  			     _Compare __comp)
      {
        typedef typename iterator_traits<_InputIterator1>::value_type
  	_ValueType1;
        typedef typename iterator_traits<_InputIterator2>::value_type
  	_ValueType2;
  
        // concept requirements
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator1>)
        __glibcxx_function_requires(_InputIteratorConcept<_InputIterator2>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType1>)
        __glibcxx_function_requires(_OutputIteratorConcept<_OutputIterator,
  				  _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType1, _ValueType2>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  				  _ValueType2, _ValueType1>)
        __glibcxx_requires_sorted_set_pred(__first1, __last1, __first2, __comp);
        __glibcxx_requires_sorted_set_pred(__first2, __last2, __first1, __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));
      }
  
  
    /**
     *  @brief  Return the minimum element in a range.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @return  Iterator referencing the first instance of the smallest value.
    */
    template<typename _ForwardIterator>
      _ForwardIterator
      min_element(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __first;
        _ForwardIterator __result = __first;
        while (++__first != __last)
  	if (*__first < *__result)
  	  __result = __first;
        return __result;
      }
  
    /**
     *  @brief  Return the minimum element in a range using comparison functor.
     *  @ingroup sorting_algorithms
     *  @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<typename _ForwardIterator, typename _Compare>
      _ForwardIterator
      min_element(_ForwardIterator __first, _ForwardIterator __last,
  		_Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_ForwardIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __first;
        _ForwardIterator __result = __first;
        while (++__first != __last)
  	if (__comp(*__first, *__result))
  	  __result = __first;
        return __result;
      }
  
    /**
     *  @brief  Return the maximum element in a range.
     *  @ingroup sorting_algorithms
     *  @param  __first  Start of range.
     *  @param  __last   End of range.
     *  @return  Iterator referencing the first instance of the largest value.
    */
    template<typename _ForwardIterator>
      _ForwardIterator
      max_element(_ForwardIterator __first, _ForwardIterator __last)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_LessThanComparableConcept<
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last)
  	return __first;
        _ForwardIterator __result = __first;
        while (++__first != __last)
  	if (*__result < *__first)
  	  __result = __first;
        return __result;
      }
  
    /**
     *  @brief  Return the maximum element in a range using comparison functor.
     *  @ingroup sorting_algorithms
     *  @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<typename _ForwardIterator, typename _Compare>
      _ForwardIterator
      max_element(_ForwardIterator __first, _ForwardIterator __last,
  		_Compare __comp)
      {
        // concept requirements
        __glibcxx_function_requires(_ForwardIteratorConcept<_ForwardIterator>)
        __glibcxx_function_requires(_BinaryPredicateConcept<_Compare,
  	    typename iterator_traits<_ForwardIterator>::value_type,
  	    typename iterator_traits<_ForwardIterator>::value_type>)
        __glibcxx_requires_valid_range(__first, __last);
  
        if (__first == __last) return __first;
        _ForwardIterator __result = __first;
        while (++__first != __last)
  	if (__comp(*__result, *__first))
  	  __result = __first;
        return __result;
      }
  
  _GLIBCXX_END_NAMESPACE_ALGO
  } // namespace std
  
  #endif /* _STL_ALGO_H */
  