}

template <class _ForwardIter, class _Integer, class _Tp, class _BinaryPred>
_ForwardIter search_n(_ForwardIter __first, _ForwardIter __last,
                      _Integer __count, const _Tp& __val,
                      _BinaryPred __binary_pred) {
  if (__count <= 0)
    return __first;
  else {
    while (__first != __last) {
      if (__binary_pred(*__first, __val))
        break;
      ++__first;
    }
    while (__first != __last) {
      _Integer __n = __count - 1;
      _ForwardIter __i = __first;
      ++__i;
      while (__i != __last && __n != 0 && __binary_pred(*__i, __val)) {
        ++__i;
        --__n;
      }
      if (__n == 0)
        return __first;
      else {
        while (__i != __last) {
          if (__binary_pred(*__i, __val))
            break;
          ++__i;
        }
        __first = __i;
      }
    }
    return __last;
  }
} 

// swap_ranges

template <class _ForwardIter1, class _ForwardIter2>
_ForwardIter2 swap_ranges(_ForwardIter1 __first1, _ForwardIter1 __last1,
                          _ForwardIter2 __first2) {
  for ( ; __first1 != __last1; ++__first1, ++__first2)
    iter_swap(__first1, __first2);
  return __first2;
}

// transform

template <class _InputIter, class _OutputIter, class _UnaryOperation>
_OutputIter transform(_InputIter __first, _InputIter __last,
                      _OutputIter __result, _UnaryOperation __opr) {
  for ( ; __first != __last; ++__first, ++__result)
    *__result = __opr(*__first);
  return __result;
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _BinaryOperation>
_OutputIter transform(_InputIter1 __first1, _InputIter1 __last1,
                      _InputIter2 __first2, _OutputIter __result,
                      _BinaryOperation __binary_op) {
  for ( ; __first1 != __last1; ++__first1, ++__first2, ++__result)
    *__result = __binary_op(*__first1, *__first2);
  return __result;
}

// replace, replace_if, replace_copy, replace_copy_if

template <class _ForwardIter, class _Tp>
void replace(_ForwardIter __first, _ForwardIter __last,
             const _Tp& __old_value, const _Tp& __new_value) {
  for ( ; __first != __last; ++__first)
    if (*__first == __old_value)
      *__first = __new_value;
}

template <class _ForwardIter, class _Predicate, class _Tp>
void replace_if(_ForwardIter __first, _ForwardIter __last,
                _Predicate __pred, const _Tp& __new_value) {
  for ( ; __first != __last; ++__first)
    if (__pred(*__first))
      *__first = __new_value;
}

template <class _InputIter, class _OutputIter, class _Tp>
_OutputIter replace_copy(_InputIter __first, _InputIter __last,
                         _OutputIter __result,
                         const _Tp& __old_value, const _Tp& __new_value) {
  for ( ; __first != __last; ++__first, ++__result)
    *__result = *__first == __old_value ? __new_value : *__first;
  return __result;
}

template <class Iterator, class _OutputIter, class _Predicate, class _Tp>
_OutputIter replace_copy_if(Iterator __first, Iterator __last,
                            _OutputIter __result,
                            _Predicate __pred, const _Tp& __new_value) {
  for ( ; __first != __last; ++__first, ++__result)
    *__result = __pred(*__first) ? __new_value : *__first;
  return __result;
}

// generate and generate_n

template <class _ForwardIter, class _Generator>
void generate(_ForwardIter __first, _ForwardIter __last, _Generator __gen) {
  for ( ; __first != __last; ++__first)
    *__first = __gen();
}

template <class _OutputIter, class _Size, class _Generator>
_OutputIter generate_n(_OutputIter __first, _Size __n, _Generator __gen) {
  for ( ; __n > 0; --__n, ++__first)
    *__first = __gen();
  return __first;
}

// remove, remove_if, remove_copy, remove_copy_if

template <class _InputIter, class _OutputIter, class _Tp>
_OutputIter remove_copy(_InputIter __first, _InputIter __last,
                        _OutputIter __result, const _Tp& __value) {
  for ( ; __first != __last; ++__first)
    if (*__first != __value) {
      *__result = *__first;
      ++__result;
    }
  return __result;
}

template <class _InputIter, class _OutputIter, class _Predicate>
_OutputIter remove_copy_if(_InputIter __first, _InputIter __last,
                           _OutputIter __result, _Predicate __pred) {
  for ( ; __first != __last; ++__first)
    if (!__pred(*__first)) {
      *__result = *__first;
      ++__result;
    }
  return __result;
}

template <class _ForwardIter, class _Tp>
_ForwardIter remove(_ForwardIter __first, _ForwardIter __last,
                    const _Tp& __value) {
  __first = find(__first, __last, __value);
  _ForwardIter __i = __first;
  return __first == __last ? __first 
                           : remove_copy(++__i, __last, __first, __value);
}

template <class _ForwardIter, class _Predicate>
_ForwardIter remove_if(_ForwardIter __first, _ForwardIter __last,
                       _Predicate __pred) {
  __first = find_if(__first, __last, __pred);
  _ForwardIter __i = __first;
  return __first == __last ? __first 
                           : remove_copy_if(++__i, __last, __first, __pred);
}

// unique and unique_copy

template <class _InputIter, class _OutputIter, class _Tp>
_OutputIter __unique_copy(_InputIter __first, _InputIter __last,
                          _OutputIter __result, _Tp*) {
  _Tp __value = *__first;
  *__result = __value;
  while (++__first != __last)
    if (__value != *__first) {
      __value = *__first;
      *++__result = __value;
    }
  return ++__result;
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __unique_copy(_InputIter __first, _InputIter __last,
                                 _OutputIter __result, 
                                 output_iterator_tag) {
  return __unique_copy(__first, __last, __result, __VALUE_TYPE(__first));
}

template <class _InputIter, class _ForwardIter>
_ForwardIter __unique_copy(_InputIter __first, _InputIter __last,
                           _ForwardIter __result, forward_iterator_tag) {
  *__result = *__first;
  while (++__first != __last)
    if (*__result != *__first) *++__result = *__first;
  return ++__result;
}

template <class _InputIter, class _OutputIter>
inline _OutputIter unique_copy(_InputIter __first, _InputIter __last,
                               _OutputIter __result) {
  if (__first == __last) return __result;
  return __unique_copy(__first, __last, __result,
                       __ITERATOR_CATEGORY(__result));
}

template <class _InputIter, class _OutputIter, class _BinaryPredicate,
          class _Tp>
_OutputIter __unique_copy(_InputIter __first, _InputIter __last,
                          _OutputIter __result,
                          _BinaryPredicate __binary_pred, _Tp*) {
  _Tp __value = *__first;
  *__result = __value;
  while (++__first != __last)
    if (!__binary_pred(__value, *__first)) {
      __value = *__first;
      *++__result = __value;
    }
  return ++__result;
}

template <class _InputIter, class _OutputIter, class _BinaryPredicate>
inline _OutputIter __unique_copy(_InputIter __first, _InputIter __last,
                                 _OutputIter __result,
                                 _BinaryPredicate __binary_pred,
                                 output_iterator_tag) {
  return __unique_copy(__first, __last, __result, __binary_pred,
                       __VALUE_TYPE(__first));
}

template <class _InputIter, class _ForwardIter, class _BinaryPredicate>
_ForwardIter __unique_copy(_InputIter __first, _InputIter __last,
                           _ForwardIter __result, 
                           _BinaryPredicate __binary_pred,
                           forward_iterator_tag) {
  *__result = *__first;
  while (++__first != __last)
    if (!__binary_pred(*__result, *__first)) *++__result = *__first;
  return ++__result;
}

template <class _InputIter, class _OutputIter, class _BinaryPredicate>
inline _OutputIter unique_copy(_InputIter __first, _InputIter __last,
                               _OutputIter __result,
                               _BinaryPredicate __binary_pred) {
  if (__first == __last) return __result;
  return __unique_copy(__first, __last, __result, __binary_pred,
                       __ITERATOR_CATEGORY(__result));
}

template <class _ForwardIter>
_ForwardIter unique(_ForwardIter __first, _ForwardIter __last) {
  __first = adjacent_find(__first, __last);
  return unique_copy(__first, __last, __first);
}

template <class _ForwardIter, class _BinaryPredicate>
_ForwardIter unique(_ForwardIter __first, _ForwardIter __last,
                    _BinaryPredicate __binary_pred) {
  __first = adjacent_find(__first, __last, __binary_pred);
  return unique_copy(__first, __last, __first, __binary_pred);
}

// reverse and reverse_copy, and their auxiliary functions

template <class _BidirectionalIter>
void __reverse(_BidirectionalIter __first, _BidirectionalIter __last, 
               bidirectional_iterator_tag) {
  while (true)
    if (__first == __last || __first == --__last)
      return;
    else
      iter_swap(__first++, __last);
}

template <class _RandomAccessIter>
void __reverse(_RandomAccessIter __first, _RandomAccessIter __last,
               random_access_iterator_tag) {
  while (__first < __last)
    iter_swap(__first++, --__last);
}

template <class _BidirectionalIter>
inline void reverse(_BidirectionalIter __first, _BidirectionalIter __last) {
  __reverse(__first, __last, __ITERATOR_CATEGORY(__first));
}

template <class _BidirectionalIter, class _OutputIter>
_OutputIter reverse_copy(_BidirectionalIter __first,
                            _BidirectionalIter __last,
                            _OutputIter __result) {
  while (__first != __last) {
    --__last;
    *__result = *__last;
    ++__result;
  }
  return __result;
}

// rotate and rotate_copy, and their auxiliary functions

template <class _EuclideanRingElement>
_EuclideanRingElement __gcd(_EuclideanRingElement __m,
                            _EuclideanRingElement __n)
{
  while (__n != 0) {
    _EuclideanRingElement __t = __m % __n;
    __m = __n;
    __n = __t;
  }
  return __m;
}

template <class _ForwardIter, class _Distance>
_ForwardIter __rotate(_ForwardIter __first,
                      _ForwardIter __middle,
                      _ForwardIter __last,
                      _Distance*,
                      forward_iterator_tag) {
  if (__first == __middle)
    return __last;
  if (__last  == __middle)
    return __first;

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

  _ForwardIter __new_middle = __first;

  __first2 = __middle;

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

  return __new_middle;
}


template <class _BidirectionalIter, class _Distance>
_BidirectionalIter __rotate(_BidirectionalIter __first,
                            _BidirectionalIter __middle,
                            _BidirectionalIter __last,
                            _Distance*,
                            bidirectional_iterator_tag) {
  if (__first == __middle)
    return __last;
  if (__last  == __middle)
    return __first;

  __reverse(__first,  __middle, bidirectional_iterator_tag());
  __reverse(__middle, __last,   bidirectional_iterator_tag());

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

  if (__first == __middle) {
    __reverse(__middle, __last,   bidirectional_iterator_tag());
    return __last;
  }
  else {
    __reverse(__first,  __middle, bidirectional_iterator_tag());
    return __first;
  }
}

template <class _RandomAccessIter, class _Distance, class _Tp>
_RandomAccessIter __rotate(_RandomAccessIter __first,
                           _RandomAccessIter __middle,
                           _RandomAccessIter __last,
                           _Distance *, _Tp *) {

  _Distance __n = __last   - __first;
  _Distance __k = __middle - __first;
  _Distance __l = __n - __k;
  _RandomAccessIter __result = __first + (__last - __middle);

  if (__k == 0)
    return __last;

  else if (__k == __l) {
    swap_ranges(__first, __middle, __middle);
    return __result;
  }

  _Distance __d = __gcd(__n, __k);

  for (_Distance __i = 0; __i < __d; __i++) {
    _Tp __tmp = *__first;
    _RandomAccessIter __p = __first;

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

        *__p = *(__p + __k);