// Heap-manipulation functions: push_heap, pop_heap, make_heap, sort_heap,
  // + is_heap and is_heap_until in C++0x.

  template<typename _RandomAccessIterator, typename _Distance, typename _Tp>
    void
    __push_heap(_RandomAccessIterator __first,
                _Distance __holeIndex, _Distance __topIndex, _Tp __value)
    {
      _Distance __parent = (__holeIndex - 1) / 2;
      while (__holeIndex > __topIndex && *(__first + __parent) < __value)
        {
          *(__first + __holeIndex) = _GLIBCXX_MOVE(*(__first + __parent));
          __holeIndex = __parent;
          __parent = (__holeIndex - 1) / 2;
        }
      *(__first + __holeIndex) = _GLIBCXX_MOVE(__value);
    }

  /**
   *  @brief  Push an element onto a heap.
   *  @param  first  Start of heap.
   *  @param  last   End of heap + element.
   *  @ingroup heap_algorithms
   *
   *  This operation pushes the element at last-1 onto the valid heap over the
   *  range [first,last-1).  After completion, [first,last) is a valid heap.
  */
  template<typename _RandomAccessIterator>
    inline void
    push_heap(_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);
      __glibcxx_requires_heap(__first, __last - 1);

      _ValueType __value = _GLIBCXX_MOVE(*(__last - 1));
      std::__push_heap(__first, _DistanceType((__last - __first) - 1),
                       _DistanceType(0), _GLIBCXX_MOVE(__value));
    }