template <class _InputIter, class _RandomAccessIter, class _Distance,
          class _Tp>
_RandomAccessIter __partial_sort_copy(_InputIter __first,
                                         _InputIter __last,
                                         _RandomAccessIter __result_first,
                                         _RandomAccessIter __result_last, 
                                         _Distance*, _Tp*) {
  if (__result_first == __result_last) return __result_last;
  _RandomAccessIter __result_real_last = __result_first;
  while(__first != __last && __result_real_last != __result_last) {
    *__result_real_last = *__first;
    ++__result_real_last;
    ++__first;
  }
  make_heap(__result_first, __result_real_last);
  while (__first != __last) {
    if (*__first < *__result_first) 
      __adjust_heap(__result_first, _Distance(0),
                    _Distance(__result_real_last - __result_first),
                    _Tp(*__first));
    ++__first;
  }
  sort_heap(__result_first, __result_real_last);
  return __result_real_last;
}

template <class _InputIter, class _RandomAccessIter>
inline _RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last) {
  return __partial_sort_copy(__first, __last, __result_first, __result_last, 
                             __DISTANCE_TYPE(__result_first),
                             __VALUE_TYPE(__first));
}

template <class _InputIter, class _RandomAccessIter, class _Compare,
          class _Distance, class _Tp>
_RandomAccessIter __partial_sort_copy(_InputIter __first,
                                         _InputIter __last,
                                         _RandomAccessIter __result_first,
                                         _RandomAccessIter __result_last,
                                         _Compare __comp, _Distance*, _Tp*) {
  if (__result_first == __result_last) return __result_last;
  _RandomAccessIter __result_real_last = __result_first;
  while(__first != __last && __result_real_last != __result_last) {
    *__result_real_last = *__first;
    ++__result_real_last;
    ++__first;
  }
  make_heap(__result_first, __result_real_last, __comp);
  while (__first != __last) {
    if (__comp(*__first, *__result_first))
      __adjust_heap(__result_first, _Distance(0),
                    _Distance(__result_real_last - __result_first),
                    _Tp(*__first),
                    __comp);
    ++__first;
  }
  sort_heap(__result_first, __result_real_last, __comp);
  return __result_real_last;
}

template <class _InputIter, class _RandomAccessIter, class _Compare>
inline _RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last, _Compare __comp) {
  return __partial_sort_copy(__first, __last, __result_first, __result_last,
                             __comp,
                             __DISTANCE_TYPE(__result_first),
                             __VALUE_TYPE(__first));
}

// nth_element() and its auxiliary functions.  

template <class _RandomAccessIter, class _Tp>
void __nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                   _RandomAccessIter __last, _Tp*) {
  while (__last - __first > 3) {
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _Tp(__median(*__first,
                                         *(__first + (__last - __first)/2),
                                         *(__last - 1))));
    if (__cut <= __nth)
      __first = __cut;
    else 
      __last = __cut;
  }
  __insertion_sort(__first, __last);
}

template <class _RandomAccessIter>
inline void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                        _RandomAccessIter __last) {
  __nth_element(__first, __nth, __last, __VALUE_TYPE(__first));
}

template <class _RandomAccessIter, class _Tp, class _Compare>
void __nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                   _RandomAccessIter __last, _Tp*, _Compare __comp) {
  while (__last - __first > 3) {
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _Tp(__median(*__first,
                                         *(__first + (__last - __first)/2), 
                                         *(__last - 1),
                                         __comp)),
                            __comp);
    if (__cut <= __nth)
      __first = __cut;
    else 
      __last = __cut;
  }
  __insertion_sort(__first, __last, __comp);
}

template <class _RandomAccessIter, class _Compare>
inline void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                 _RandomAccessIter __last, _Compare __comp) {
  __nth_element(__first, __nth, __last, __VALUE_TYPE(__first), __comp);
}


// Binary search (lower_bound, upper_bound, equal_range, binary_search).

template <class _ForwardIter, class _Tp, class _Distance>
_ForwardIter __lower_bound(_ForwardIter __first, _ForwardIter __last,
                           const _Tp& __val, _Distance*) 
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle;

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

template <class _ForwardIter, class _Tp>
inline _ForwardIter lower_bound(_ForwardIter __first, _ForwardIter __last,
                                   const _Tp& __val) {
  return __lower_bound(__first, __last, __val,
                       __DISTANCE_TYPE(__first));
}

template <class _ForwardIter, class _Tp, class _Compare, class _Distance>
_ForwardIter __lower_bound(_ForwardIter __first, _ForwardIter __last,
                              const _Tp& __val, _Compare __comp, _Distance*)
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle;

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

template <class _ForwardIter, class _Tp, class _Compare>
inline _ForwardIter lower_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val, _Compare __comp) {
  return __lower_bound(__first, __last, __val, __comp,
                       __DISTANCE_TYPE(__first));
}

template <class _ForwardIter, class _Tp, class _Distance>
_ForwardIter __upper_bound(_ForwardIter __first, _ForwardIter __last,
                           const _Tp& __val, _Distance*)
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle;

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

template <class _ForwardIter, class _Tp>
inline _ForwardIter upper_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val) {
  return __upper_bound(__first, __last, __val,
                       __DISTANCE_TYPE(__first));
}

template <class _ForwardIter, class _Tp, class _Compare, class _Distance>
_ForwardIter __upper_bound(_ForwardIter __first, _ForwardIter __last,
                           const _Tp& __val, _Compare __comp, _Distance*)
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle;

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

template <class _ForwardIter, class _Tp, class _Compare>
inline _ForwardIter upper_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val, _Compare __comp) {
  return __upper_bound(__first, __last, __val, __comp,
                       __DISTANCE_TYPE(__first));
}

template <class _ForwardIter, class _Tp, class _Distance>
pair<_ForwardIter, _ForwardIter>
__equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
              _Distance*)
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle, __left, __right;

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

template <class _ForwardIter, class _Tp>
inline pair<_ForwardIter, _ForwardIter>
equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val) {
  return __equal_range(__first, __last, __val,
                       __DISTANCE_TYPE(__first));
}

template <class _ForwardIter, class _Tp, class _Compare, class _Distance>
pair<_ForwardIter, _ForwardIter>
__equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
              _Compare __comp, _Distance*)
{
  _Distance __len = 0;
  distance(__first, __last, __len);
  _Distance __half;
  _ForwardIter __middle, __left, __right;

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

template <class _ForwardIter, class _Tp, class _Compare>
inline pair<_ForwardIter, _ForwardIter>
equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
            _Compare __comp) {
  return __equal_range(__first, __last, __val, __comp,
                       __DISTANCE_TYPE(__first));
} 

template <class _ForwardIter, class _Tp>
bool binary_search(_ForwardIter __first, _ForwardIter __last,
                   const _Tp& __val) {
  _ForwardIter __i = lower_bound(__first, __last, __val);
  return __i != __last && !(__val < *__i);
}

template <class _ForwardIter, class _Tp, class _Compare>
bool binary_search(_ForwardIter __first, _ForwardIter __last,
                   const _Tp& __val,
                   _Compare __comp) {
  _ForwardIter __i = lower_bound(__first, __last, __val, __comp);
  return __i != __last && !__comp(__val, *__i);
}

// merge, with and without an explicitly supplied comparison function.

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result) {
  while (__first1 != __last1 && __first2 != __last2) {
    if (*__first2 < *__first1) {
      *__result = *__first2;
      ++__first2;
    }
    else {
      *__result = *__first1;
      ++__first1;
    }
    ++__result;
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result, _Compare __comp) {
  while (__first1 != __last1 && __first2 != __last2) {
    if (__comp(*__first2, *__first1)) {
      *__result = *__first2;
      ++__first2;
    }
    else {
      *__result = *__first1;
      ++__first1;
    }
    ++__result;
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

// inplace_merge and its auxiliary functions. 

template <class _BidirectionalIter, class _Distance>
void __merge_without_buffer(_BidirectionalIter __first,
                            _BidirectionalIter __middle,
                            _BidirectionalIter __last,
                            _Distance __len1, _Distance __len2) {
  if (__len1 == 0 || __len2 == 0)
    return;
  if (__len1 + __len2 == 2) {
    if (*__middle < *__first)
      iter_swap(__first, __middle);
    return;
  }
  _BidirectionalIter __first