/*
 *
 * 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.
 *
 */

#ifndef ALGO_H
#define ALGO_H

#include <stdlib.h>
#include <bool.h>
#include <pair.h>
#include <iterator.h>
#include <algobase.h>
#include <heap.h>
#include <tempbuf.h>

template <class T>
inline T __median(T a, T b, T c) {
    if (a < b)
        if (b < c)
            return b;
        else if (a < c)
            return c;
        else
            return a;
    else if (a < c)
        return a;
    else if (b < c)
        return c;
    else
        return b;
}

template <class T, class Compare>
inline T __median(T a, T b, T c, Compare comp) {
    if (comp(a, b))
        if (comp(b, c))
            return b;
        else if (comp(a, c))
            return c;
        else
            return a;
    else if (comp(a, c))
        return a;
    else if (comp(b, c))
        return c;
    else
        return b;
}

template <class InputIterator, class Function>
Function for_each(InputIterator first, InputIterator last, Function f) {
    while (first != last) f(*first++);
    return f;
}

template <class InputIterator, class T>
InputIterator find(InputIterator first, InputIterator last, const T& value) {
    while (first != last && *first != value) ++first;
    return first;
}

template <class InputIterator, class Predicate>
InputIterator find_if(InputIterator first, InputIterator last,
                      Predicate pred) {
    while (first != last && !pred(*first)) ++first;
    return first;
}

template <class InputIterator>
InputIterator adjacent_find(InputIterator first, InputIterator last) {
    if (first == last) return last;
    InputIterator next = first;
    while(++next != last) {
        if (*first == *next) return first;
        first = next;
    }
    return last;
}

template <class InputIterator, class BinaryPredicate>
InputIterator adjacent_find(InputIterator first, InputIterator last,
                            BinaryPredicate binary_pred) {
    if (first == last) return last;
    InputIterator next = first;
    while(++next != last) {
        if (binary_pred(*first, *next)) return first;
        first = next;
    }
    return last;
}

template <class InputIterator, class T, class Size>
void count(InputIterator first, InputIterator last, const T& value,
           Size& n) {
    while (first != last) 
        if (*first++ == value) ++n;
}

template <class InputIterator, class Predicate, class Size>
void count_if(InputIterator first, InputIterator last, Predicate pred,
              Size& n) {
    while (first != last)
        if (pred(*first++)) ++n;
}

template <class ForwardIterator1, class ForwardIterator2, class Distance>
ForwardIterator1 __search(ForwardIterator1 first1, ForwardIterator1 last1,
                          ForwardIterator2 first2, ForwardIterator2 last2,
                          Distance*) {
    Distance d1 = 0;
    distance(first1, last1, d1);
    Distance d2 = 0;
    distance(first2, last2, d2);

    if (d1 < d2) return last1;

    ForwardIterator1 current1 = first1;
    ForwardIterator2 current2 = first2;

    while (current2 != last2)
        if (*current1++ != *current2++)
            if (d1-- == d2)
                return last1;
            else {
                current1 = ++first1;
                current2 = first2;
            }
    return (current2 == last2) ? first1 : last1;
}

template <class ForwardIterator1, class ForwardIterator2>
inline ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1,
                               ForwardIterator2 first2, ForwardIterator2 last2)
{
    return __search(first1, last1, first2, last2, distance_type(first1));
}

template <class ForwardIterator1, class ForwardIterator2,
          class BinaryPredicate, class Distance>
ForwardIterator1 __search(ForwardIterator1 first1, ForwardIterator1 last1,
                          ForwardIterator2 first2, ForwardIterator2 last2,
                          BinaryPredicate binary_pred, Distance*) {
    Distance d1 = 0;
    distance(first1, last1, d1);
    Distance d2 = 0;
    distance(first2, last2, d2);

    if (d1 < d2) return last1;

    ForwardIterator1 current1 = first1;
    ForwardIterator2 current2 = first2;

    while (current2 != last2)
        if (!binary_pred(*current1++, *current2++))
            if (d1-- == d2)
                return last1;
            else {
                current1 = ++first1;
                current2 = first2;
            }
    return (current2 == last2) ? first1 : last1;
}

template <class ForwardIterator1, class ForwardIterator2,
          class BinaryPredicate>
inline ForwardIterator1 search(ForwardIterator1 first1, ForwardIterator1 last1,
                               ForwardIterator2 first2, ForwardIterator2 last2,
                               BinaryPredicate binary_pred) {
    return __search(first1, last1, first2, last2, binary_pred,
                    distance_type(first1));
}

template <class ForwardIterator1, class ForwardIterator2>
ForwardIterator2 swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1,
                             ForwardIterator2 first2) {
    while (first1 != last1) iter_swap(first1++, first2++);
    return first2;
}

template <class InputIterator, class OutputIterator, class UnaryOperation>
OutputIterator transform(InputIterator first, InputIterator last,
                         OutputIterator result, UnaryOperation op) {
    while (first != last) *result++ = op(*first++);
    return result;
}

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class BinaryOperation>
OutputIterator transform(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, OutputIterator result,
                         BinaryOperation binary_op) {
    while (first1 != last1) *result++ = binary_op(*first1++, *first2++);
    return result;
}

template <class ForwardIterator, class T>
void replace(ForwardIterator first, ForwardIterator last, const T& old_value,
             const T& new_value) {
    while (first != last) {
        if (*first == old_value) *first = new_value;
        ++first;
    }
}

template <class ForwardIterator, class Predicate, class T>
void replace_if(ForwardIterator first, ForwardIterator last, Predicate pred,
                const T& new_value) {
    while (first != last) {
        if (pred(*first)) *first = new_value;
        ++first;
    }
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator replace_copy(InputIterator first, InputIterator last,
                            OutputIterator result, const T& old_value,
                            const T& new_value) {
    while (first != last) {
        *result++ = *first == old_value ? new_value : *first;
        ++first;
    }
    return result;
}

template <class Iterator, class OutputIterator, class Predicate, class T>
OutputIterator replace_copy_if(Iterator first, Iterator last,
                               OutputIterator result, Predicate pred,
                               const T& new_value) {
    while (first != last) {
        *result++ = pred(*first) ? new_value : *first;
        ++first;
    }
    return result;
}

template <class ForwardIterator, class Generator>
void generate(ForwardIterator first, ForwardIterator last, Generator gen) {
    while (first != last) *first++ = gen();
}

template <class OutputIterator, class Size, class Generator>
void generate_n(OutputIterator first, Size n, Generator gen) {
    while (n-- > 0) *first++ = gen();
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator remove_copy(InputIterator first, InputIterator last,
                           OutputIterator result, const T& value) {
    while (first != last) {
        if (*first != value) *result++ = *first;
        ++first;
    }
    return result;
}

template <class InputIterator, class OutputIterator, class Predicate>
OutputIterator remove_copy_if(InputIterator first, InputIterator last,
                              OutputIterator result, Predicate pred) {
    while (first != last) {
        if (!pred(*first)) *result++ = *first;
        ++first;
    }
    return result;
}

template <class ForwardIterator, class T>
ForwardIterator remove(ForwardIterator first, ForwardIterator last,
                       const T& value) {
    first = find(first, last, value);
    ForwardIterator next = first;
    return first == last ? first : remove_copy(++next, last, first, value);
}

template <class ForwardIterator, class Predicate>
ForwardIterator remove_if(ForwardIterator first, ForwardIterator last,
                          Predicate pred) {
    first = find_if(first, last, pred);
    ForwardIterator next = first;
    return first == last ? first : remove_copy_if(++next, last, first, pred);
}

template <class InputIterator, class ForwardIterator>
ForwardIterator __unique_copy(InputIterator first, InputIterator last,
                              ForwardIterator result, forward_iterator_tag) {
    *result = *first;
    while (++first != last)
        if (*result != *first) *++result = *first;
    return ++result;
}

template <class InputIterator, class BidirectionalIterator>
inline BidirectionalIterator __unique_copy(InputIterator first, 
                                           InputIterator last,
                                           BidirectionalIterator result, 
                                           bidirectional_iterator_tag) {
    return __unique_copy(first, last, result, forward_iterator_tag());
}

template <class InputIterator, class RandomAccessIterator>
inline RandomAccessIterator __unique_copy(InputIterator first, 
                                          InputIterator last,
                                          RandomAccessIterator result, 
                                          random_access_iterator_tag) {
    return __unique_copy(first, last, result, forward_iterator_tag());
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator __unique_copy(InputIterator first, InputIterator last,
                             OutputIterator result, T*) {
    T value = *first;
    *result = value;
    while (++first != last)
        if (value != *first) {
            value = *first;
            *++result = value;
        }
    return ++result;
}

template <class InputIterator, class OutputIterator>
inline OutputIterator __unique_copy(InputIterator first, InputIterator last,
                                    OutputIterator result, 
                                    output_iterator_tag) {
    return __unique_copy(first, last, result, value_type(first));
}

template <class InputIterator, class OutputIterator>
inline OutputIterator unique_copy(InputIterator first, InputIterator last,
                                  OutputIterator result) {
    if (first == last) return result;
    return __unique_copy(first, last, result, iterator_category(result));
}
template <class InputIterator, class ForwardIterator, class BinaryPredicate>
ForwardIterator __unique_copy(InputIterator first, InputIterator last,
                              ForwardIterator result, 
                              BinaryPredicate binary_pred,
                              forward_iterator_tag) {
    *result = *first;
    while (++first != last)
        if (!binary_pred(*result, *first)) *++result = *first;
    return ++result;
}

template <class InputIterator, class BidirectionalIterator,
          class BinaryPredicate>
inline BidirectionalIterator __unique_copy(InputIterator first, 
                                           InputIterator last,
                                           BidirectionalIterator result, 
                                           BinaryPredicate binary_pred,
                                           bidirectional_iterator_tag) {
    return __unique_copy(first, last, result, binary_pred,
                         forward_iterator_tag());
}

template <class InputIterator, class RandomAccessIterator,
          class BinaryPredicate>
inline RandomAccessIterator __unique_copy(InputIterator first, 
                                          InputIterator last,
                                          RandomAccessIterator result, 
                                          BinaryPredicate binary_pred,
                                          random_access_iterator_tag) {
    return __unique_copy(first, last, result, binary_pred, 
                         forward_iterator_tag());
}

template <class InputIterator, class OutputIterator, class BinaryPredicate,
          class T>
OutputIterator __unique_copy(InputIterator first, InputIterator last,
                             OutputIterator result,
                             BinaryPredicate binary_pred, T*) {
    T value = *first;
    *result = value;
    while (++first != last)
        if (!binary_pred(value, *first)) {
            value = *first;
            *++result = value;
        }
    return ++result;
}

template <class InputIterator, class OutputIterator, class BinaryPredicate>
inline OutputIterator __unique_copy(InputIterator first, InputIterator last,
                                    OutputIterator result,
                                    BinaryPredicate binary_pred,
                                    output_iterator_tag) {
    return __unique_copy(first, last, result, binary_pred, value_type(first));
}

template <class InputIterator, class OutputIterator, class BinaryPredicate>
inline OutputIterator unique_copy(InputIterator first, InputIterator last,
                                  OutputIterator result,
                                  BinaryPredicate binary_pred) {
    if (first == last) return result;
    return __unique_copy(first, last, result, binary_pred,
                         iterator_category(result));
}

template <class ForwardIterator>
ForwardIterator unique(ForwardIterator first, ForwardIterator last) {
    first = adjacent_find(first, last);
    return unique_copy(first, last, first);
}

template <class ForwardIterator, class BinaryPredicate>
ForwardIterator unique(ForwardIterator first, ForwardIterator last,
                       BinaryPredicate binary_pred) {
    first = adjacent_find(first, last, binary_pred);
    return unique_copy(first, last, first, binary_pred);
}

template <class BidirectionalIterator>
void __reverse(BidirectionalIterator first, BidirectionalIterator last, 
               bidirectional_iterator_tag) {
    while (true)
        if (first == last || first == --last)
            return;
        else
            iter_swap(first++, last);
}

template <class RandomAccessIterator>
void __reverse(RandomAccessIterator first, RandomAccessIterator last,
               random_access_iterator_tag) {
    while (first < last) iter_swap(first++, --last);
}

template <class BidirectionalIterator>
inline void reverse(BidirectionalIterator first, BidirectionalIterator last) {
    __reverse(first, last, iterator_category(first));
}

template <class BidirectionalIterator, class OutputIterator>
OutputIterator reverse_copy(BidirectionalIterator first,
                            BidirectionalIterator last,
                            OutputIterator result) {
    while (first != last) *result++ = *--last;
    return result;
}

template <class ForwardIterator, class Distance>
void __rotate(ForwardIterator first, ForwardIterator middle,
              ForwardIterator last, Distance*, forward_iterator_tag) {
    for (ForwardIterator i = middle; ;) {
        iter_swap(first++, i++);
        if (first == middle) {
            if (i == last) return;
            middle = i;
        } else if (i == last)
            i = middle;
    }
}

template <class BidirectionalIterator, class Distance>
void __rotate(BidirectionalIterator first, BidirectionalIterator middle,
              BidirectionalIterator last, Distance*,
              bidirectional_iterator_tag) {
    reverse(first, middle);
    reverse(middle, last);
    reverse(first, last);
}

template <class EuclideanRingElement>
EuclideanRingElement __gcd(EuclideanRingElement m, EuclideanRingElement n)
{
    while (n != 0) {
        EuclideanRingElement t = m % n;
        m = n;
        n = t;
    }
    return m;
}

template <class RandomAccessIterator, class Distance, class T>
void __rotate_cycle(RandomAccessIterator first, RandomAccessIterator last,
                    RandomAccessIterator initial, Distance shift, T*) {
    T value = *initial;
    RandomAccessIterator ptr1 = initial;
    RandomAccessIterator ptr2 = ptr1 + shift;
    while (ptr2 != initial) {
        *ptr1 = *ptr2;
        ptr1 = ptr2;
        if (last - ptr2 > shift)
            ptr2 += shift;
        else
            ptr2 = first + (shift - (last - ptr2));
    }
    *ptr1 = value;
}

template <class RandomAccessIterator, class Distance>
void __rotate(RandomAccessIterator first, RandomAccessIterator middle,
              RandomAccessIterator last, Distance*,
              random_access_iterator_tag) {
    Distance n = __gcd(last - first, middle - first);
    while (n--)
        __rotate_cycle(first, last, first + n, middle - first,
                       value_type(first));
}

template <class ForwardIterator>
inline void rotate(ForwardIterator first, ForwardIterator middle,
                   ForwardIterator last) {
    if (first == middle || middle == last) return;
    __rotate(first, middle, last, distance_type(first),
             iterator_category(first));
}

template <class ForwardIterator, class OutputIterator>
OutputIterator rotate_copy(ForwardIterator first, ForwardIterator middle,
                           ForwardIterator last, OutputIterator result) {
    return copy(first, middle, copy(middle, last, result));
}

unsigned long __long_random(unsigned long);

template <class RandomAccessIterator, class Distance>
void __random_shuffle(RandomAccessIterator first, RandomAccessIterator last,
                      Distance*) {
    if (first == last) return;
    for (RandomAccessIterator i = first + 1; i != last; ++i)
        iter_swap(i, first + Distance(__long_random((i - first) + 1)));
}

template <class RandomAccessIterator>
inline void random_shuffle(RandomAccessIterator first,
                           RandomAccessIterator last) {
    __random_shuffle(first, last, distance_type(first));
}

template <class RandomAccessIterator, class RandomNumberGenerator>
void random_shuffle(RandomAccessIterator first, RandomAccessIterator last,
                    RandomNumberGenerator& rand) {
    if (first == last) return;
    for (RandomAccessIterator i = first + 1; i != last; ++i)
        iter_swap(i, first + rand((i - first) + 1));
}

template <class BidirectionalIterator, class Predicate>
BidirectionalIterator partition(BidirectionalIterator first,
                                BidirectionalIterator last, Predicate pred) {
    while (true) {
        while (true)
            if (first == last)
                return first;
            else if (pred(*first))
                ++first;
            else
                break;
        --last;
        while (true)
            if (first == last)
                return first;
            else if (!pred(*last))
                --last;
            else
                break;
        iter_swap(first, last);
        ++first;
    }
}

template <class ForwardIterator, class Predicate, class Distance>
ForwardIterator __inplace_stable_partition(ForwardIterator first,
                                           ForwardIterator last,
                                           Predicate pred, Distance len) {
    if (len == 1) return pred(*first) ? last : first;
    ForwardIterator middle = first;
    advance(middle, len / 2);
    ForwardIterator 
        first_cut = __inplace_stable_partition(first, middle, pred, len / 2);
    ForwardIterator 
        second_cut = __inplace_stable_partition(middle, last, pred,
                                                len - len / 2);
    rotate(first_cut, middle, second_cut);
    len = 0;
    distance(middle, second_cut, len);
    advance(first_cut, len);
    return first_cut;
}

template <class ForwardIterator, class Pointer, class Predicate,
          class Distance, class T>
ForwardIterator __stable_partition_adaptive(ForwardIterator first,
                                            ForwardIterator last,
                                            Predicate pred, Distance len,
                                            Pointer buffer,
                                            Distance buffer_size,
                                            Distance& fill_pointer, T*) {
    if (len <= buffer_size) {
        len = 0;
        ForwardIterator result1 = first;
        Pointer result2 = buffer;
        while (first != last && len < fill_pointer)
            if (pred(*first))
                *result1++ = *first++;
            else {
                *result2++ = *first++;
                ++len;
            }
        if (first != last) {
            raw_storage_iterator<Pointer, T> result3 = result2;
            while (first != last)           
                if (pred(*first))
                    *result1++ = *first++;
                else {
                    *result3++ = *first++;
                    ++len;
                }
            fill_pointer = len;
        }
        copy(buffer, buffer + len, result1);
        return result1;
    }
    ForwardIterator middle = first;
    advance(middle, len / 2);
    ForwardIterator first_cut = __stable_partition_adaptive
        (first, middle, pred, len / 2, buffer, buffer_size, fill_pointer, 
         (T*)0);
    ForwardIterator second_cut = __stable_partition_adaptive
        (middle, last, pred, len - len / 2, buffer, buffer_size, 
         fill_pointer, (T*)0);
    rotate(first_cut, middle, second_cut);
    len = 0;
    distance(middle, second_cut, len);
    advance(first_cut, len);
    return first_cut;
}

template <class ForwardIterator, class Predicate, class Pointer,
          class Distance>
ForwardIterator __stable_partition(ForwardIterator first, ForwardIterator last,
                                   Predicate pred, Distance len,
                                   pair<Pointer, Distance> p) {
    if (p.first == 0)
        return __inplace_stable_partition(first, last, pred, len);
    Distance fill_pointer = 0;
    ForwardIterator result = 
        __stable_partition_adaptive(first, last, pred, len, p.first, p.second,
                                    fill_pointer, value_type(first)); 
    destroy(p.first, p.first + fill_pointer);
    return_temporary_buffer(p.first);
    return result;
}

template <class ForwardIterator, class Predicate, class Distance>
inline ForwardIterator __stable_partition_aux(ForwardIterator first,
                                              ForwardIterator last, 
                                              Predicate pred, Distance*) {
    Distance len = 0;
    distance(first, last, len);
    return __stable_partition(first, last, pred, len,
                              get_temporary_buffer(len, value_type(first)));
}

template <class ForwardIterator, class Predicate>
inline ForwardIterator stable_partition(ForwardIterator first,
                                        ForwardIterator last, 
                                        Predicate pred) {
    return __stable_partition_aux(first, last, pred, distance_type(first));
}

template <class RandomAccessIterator, class T>
RandomAccessIterator __unguarded_partition(RandomAccessIterator first, 
                                           RandomAccessIterator last, 
                                           T pivot) {
    while (1) {
        while (*first < pivot) ++first;
        --last;
        while (pivot < *last) --last;
        if (!(first < last)) return first;
        iter_swap(first, last);
        ++first;
    }
}    

template <class RandomAccessIterator, class T, class Compare>
RandomAccessIterator __unguarded_partition(RandomAccessIterator first, 
                                           RandomAccessIterator last, 
                                           T pivot, Compare comp) {
    while (1) {
        while (comp(*first, pivot)) ++first;
        --last;
        while (comp(pivot, *last)) --last;
        if (!(first < last)) return first;
        iter_swap(first, last);
        ++first;
    }
}

const int __stl_threshold = 16;

template <class RandomAccessIterator, class T>
void __quick_sort_loop_aux(RandomAccessIterator first,
                           RandomAccessIterator last, T*) {
    while (last - first > __stl_threshold) {
        RandomAccessIterator cut = __unguarded_partition
            (first, last, T(__median(*first, *(first + (last - first)/2),
                                     *(last - 1))));
        if (cut - first >= last - cut) {
            __quick_sort_loop(cut, last);
            last = cut;
        } else {
            __quick_sort_loop(first, cut);
            first = cut;
        }
    }
}

template <class RandomAccessIterator>
inline void __quick_sort_loop(RandomAccessIterator first,
                              RandomAccessIterator last) {
    __quick_sort_loop_aux(first, last, value_type(first));
}

template <class RandomAccessIterator, class T, class Compare>
void __quick_sort_loop_aux(RandomAccessIterator first, 
                           RandomAccessIterator last, T*, Compare comp) {
    while (last - first > __stl_threshold) {
        RandomAccessIterator cut = __unguarded_partition
            (first, last, T(__median(*first, *(first + (last - first)/2), 
                                   *(last - 1), comp)), comp);
        if (cut - first >= last - cut) {
            __quick_sort_loop(cut, last, comp);
            last = cut;
        } else {
            __quick_sort_loop(first, cut, comp);
            first = cut;
        }
    }
}

template <class RandomAccessIterator, class Compare>
inline void __quick_sort_loop(RandomAccessIterator first, 
                              RandomAccessIterator last, Compare comp) {
    __quick_sort_loop_aux(first, last, value_type(first), comp);
}

template <class RandomAccessIterator, class T>
void __unguarded_linear_insert(RandomAccessIterator last, T value) {
    RandomAccessIterator next = last;
    --next;
    while (value < *next) {
        *last = *next;
        last = next--;
    }
    *last = value;
}

template <class RandomAccessIterator, class T, class Compare>
void __unguarded_linear_insert(RandomAccessIterator last, T value, 
                               Compare comp) {
    RandomAccessIterator next = last;
    --next;  
    while (comp(value , *next)) {
        *last = *next;
        last = next--;
    }
    *last = value;
}

template <class RandomAccessIterator, class T>
inline void __linear_insert(RandomAccessIterator first, 
                            RandomAccessIterator last, T*) {
    T value = *last;
    if (value < *first) {
        copy_backward(first, last, last + 1);
        *first = value;
    } else
        __unguarded_linear_insert(last, value);
}

template <class RandomAccessIterator, class T, class Compare>
inline void __linear_insert(RandomAccessIterator first, 
                            RandomAccessIterator last, T*, Compare comp) {
    T value = *last;
    if (comp(value, *first)) {
        copy_backward(first, last, last + 1);
        *first = value;
    } else
        __unguarded_linear_insert(last, value, comp);
}

template <class RandomAccessIterator>
void __insertion_sort(RandomAccessIterator first, RandomAccessIterator last) {
    if (first == last) return; 
    for (RandomAccessIterator i = first + 1; i != last; ++i)
        __linear_insert(first, i, value_type(first));
}

template <class RandomAccessIterator, class Compare>
void __insertion_sort(RandomAccessIterator first,
                      RandomAccessIterator last, Compare comp) {
    if (first == last) return;
    for (RandomAccessIterator i = first + 1; i != last; ++i)
        __linear_insert(first, i, value_type(first), comp);
}

template <class RandomAccessIterator, class T>
void __unguarded_insertion_sort_aux(RandomAccessIterator first, 
                                    RandomAccessIterator last, T*) {
    for (RandomAccessIterator i = first; i != last; ++i)
        __unguarded_linear_insert(i, T(*i));
}

template <class RandomAccessIterator>
inline void __unguarded_insertion_sort(RandomAccessIterator first, 
                                RandomAccessIterator last) {
    __unguarded_insertion_sort_aux(first, last, value_type(first));
}

template <class RandomAccessIterator, class T, class Compare>
void __unguarded_insertion_sort_aux(RandomAccessIterator first, 
                                    RandomAccessIterator last,
                                    T*, Compare comp) {
    for (RandomAccessIterator i = first; i != last; ++i)
        __unguarded_linear_insert(i, T(*i), comp);
}

template <class RandomAccessIterator, class Compare>
inline void __unguarded_insertion_sort(RandomAccessIterator first, 
                                       RandomAccessIterator last,
                                       Compare comp) {
    __unguarded_insertion_sort_aux(first, last, value_type(first), comp);
}

template <class RandomAccessIterator>
void __final_insertion_sort(RandomAccessIterator first, 
                            RandomAccessIterator last) {
    if (last - first > __stl_threshold) {
        __insertion_sort(first, first + __stl_threshold);
        __unguarded_insertion_sort(first + __stl_threshold, last);
    } else
        __insertion_sort(first, last);
}

template <class RandomAccessIterator, class Compare>
void __final_insertion_sort(RandomAccessIterator first, 
                            RandomAccessIterator last, Compare comp) {
    if (last - first > __stl_threshold) {
        __insertion_sort(first, first + __stl_threshold, comp);
        __unguarded_insertion_sort(first + __stl_threshold, last, comp);
    } else
        __insertion_sort(first, last, comp);
}

template <class RandomAccessIterator>
void sort(RandomAccessIterator first, RandomAccessIterator last) {
    __quick_sort_loop(first, last);
    __final_insertion_sort(first, last);
}

template <class RandomAccessIterator, class Compare>
void sort(RandomAccessIterator first, RandomAccessIterator last,
          Compare comp) {
   __quick_sort_loop(first, last, comp);
   __final_insertion_sort(first, last, comp);
}

template <class RandomAccessIterator>
void __inplace_stable_sort(RandomAccessIterator first,
                           RandomAccessIterator last) {
    if (last - first < 15) {
        __insertion_sort(first, last);
        return;
    }
    RandomAccessIterator middle = first + (last - first) / 2;
    __inplace_stable_sort(first, middle);
    __inplace_stable_sort(middle, last);
    __merge_without_buffer(first, middle, last, middle - first, last - middle);
}

template <class RandomAccessIterator, class Compare>
void __inplace_stable_sort(RandomAccessIterator first,
                           RandomAccessIterator last, Compare comp) {
    if (last - first < 15) {
        __insertion_sort(first, last, comp);
        return;
    }
    RandomAccessIterator middle = first + (last - first) / 2;
    __inplace_stable_sort(first, middle, comp);
    __inplace_stable_sort(middle, last, comp);
    __merge_without_buffer(first, middle, last, middle - first,
                           last - middle, comp);
}

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class RandomAccessIterator3, class Distance, class T>
RandomAccessIterator3 __merge_aux(RandomAccessIterator1 first1,
                                  RandomAccessIterator1 last1,
                                  RandomAccessIterator2 first2,
                                  RandomAccessIterator2 last2,
                                  RandomAccessIterator3 result,
                                  Distance& fill_pointer, T*){
    Distance len = 0;
    while (first1 != last1 && first2 != last2 && len < fill_pointer) {
        ++len;
        if (*first2 < *first1)
            *result++ = *first2++;
        else
            *result++ = *first1++;
    }
    if (fill_pointer == len) {
        raw_storage_iterator<RandomAccessIterator3, T> p = result;
        result += (last1 - first1) + (last2 - first2);
        fill_pointer += (last1 - first1) + (last2 - first2);
        while (first1 != last1 && first2 != last2)
            if (*first2 < *first1)
                *p++ = *first2++;
            else
                *p++ = *first1++;
        copy(first2, last2, copy(first1, last1, p));
    } else if (first2 == last2) {
        while (first1 != last1 && len < fill_pointer) { 
            ++len;
            *result++ = *first1++;
        }
        if (fill_pointer == len) {
            raw_storage_iterator<RandomAccessIterator3, T> p = result;  
            result += last1 - first1;
            fill_pointer += last1 - first1;
            while (first1 != last1) *p++ = *first1++;
        }
    } else {
        while (first2 != last2 && len < fill_pointer) { 
            ++len;
            *result++ = *first2++;
        }
        if (fill_pointer == len) {
            raw_storage_iterator<RandomAccessIterator3, T> p = result;  
            result += last2 - first2;
            fill_pointer += last2 - first2;
            while (first2 != last2) *p++ = *first2++;
        }
    }
    return result;
}       

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class RandomAccessIterator3, class Distance, class T, class Compare>
RandomAccessIterator3 __merge_aux(RandomAccessIterator1 first1,
                                  RandomAccessIterator1 last1,
                                  RandomAccessIterator2 first2,
                                  RandomAccessIterator2 last2,
                                  RandomAccessIterator3 result,
                                  Distance& fill_pointer, T*, Compare comp){
    Distance len = 0;
    while (first1 != last1 && first2 != last2 && len < fill_pointer) {
        ++len;
        if (comp(*first2, *first1))
            *result++ = *first2++;
        else
            *result++ = *first1++;
    }
    if (fill_pointer <= len) {
        raw_storage_iterator<RandomAccessIterator3, T> p = result;
        result += (last1 - first1) + (last2 - first2);
        fill_pointer += (last1 - first1) + (last2 - first2);
        while (first1 != last1 && first2 != last2)
            if (comp(*first2, *first1))
                *p++ = *first2++;
            else
                *p++ = *first1++;
        copy(first2, last2, copy(first1, last1, p));
    } else if (first2 == last2) {
        while (first1 != last1 && len < fill_pointer) { 
            ++len;
            *result++ = *first1++;
        }
        if (fill_pointer == len) {
            raw_storage_iterator<RandomAccessIterator3, T> p = result;  
            result += last1 - first1;
            fill_pointer += last1 - first1;
            while (first1 != last1) *p++ = *first1++;
        }
    } else {
        while (first2 != last2 && len < fill_pointer) { 
            ++len;
            *result++ = *first2++;
        }
        if (fill_pointer == len) {
            raw_storage_iterator<RandomAccessIterator3, T> p = result;  
            result += last2 - first2;
            fill_pointer += last2 - first2;
            while (first2 != last2) *p++ = *first2++;
        }
    }
    return result;
}       

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class Distance, class T>
void __merge_sort_loop_aux(RandomAccessIterator1 first,
                           RandomAccessIterator1 last, 
                           RandomAccessIterator2 result, Distance step_size,
                           Distance& fill_pointer, T*) {
    Distance two_step = 2 * step_size;

    while (last - first >= two_step) {
        result = __merge_aux(first, first + step_size, first + step_size,
                             first + two_step, result, fill_pointer, (T*)0);
        first += two_step;
    }
    step_size = min(Distance(last - first), step_size);

    __merge_aux(first, first + step_size, first + step_size, last, result,
                fill_pointer, (T*)0);
}

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class Distance, class T, class Compare>
void __merge_sort_loop_aux(RandomAccessIterator1 first,
                       RandomAccessIterator1 last, 
                       RandomAccessIterator2 result, Distance step_size,
                       Distance& fill_pointer, T*, Compare comp) {
    Distance two_step = 2 * step_size;

    while (last - first >= two_step) {
        result = __merge_aux(first, first + step_size, first + step_size, 
                             first + two_step, result, fill_pointer, (T*)0,
                             comp);
        first += two_step;
    }
    step_size = min(Distance(last - first), step_size);

    __merge_aux(first, first + step_size, first + step_size, last, result, 
                fill_pointer, (T*)0, comp);
}

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class Distance>
void __merge_sort_loop(RandomAccessIterator1 first,
                       RandomAccessIterator1 last, 
                       RandomAccessIterator2 result, Distance step_size) {
    Distance two_step = 2 * step_size;

    while (last - first >= two_step) {
        result = merge(first, first + step_size,
                       first + step_size, first + two_step, result);
        first += two_step;
    }
    step_size = min(Distance(last - first), step_size);

    merge(first, first + step_size, first + step_size, last, result);
}

template <class RandomAccessIterator1, class RandomAccessIterator2,
          class Distance, class Compare>
void __merge_sort_loop(RandomAccessIterator1 first,
                       RandomAccessIterator1 last, 
                       RandomAccessIterator2 result, Distance step_size,
                       Compare comp) {
    Distance two_step = 2 * step_size;

    while (last - first >= two_step) {
        result = merge(first, first + step_size,
                       first + step_size, first + two_step, result, comp);
        first += two_step;
    }
    step_size = min(Distance(last - first), step_size);

    merge(first, first + step_size, first + step_size, last, result, comp);
}

const int __stl_chunk_size = 7;
        
template <class RandomAccessIterator, class Distance>
void __chunk_insertion_sort(RandomAccessIterator first, 
                              RandomAccessIterator last, Distance chunk_size) {
    while (last - first >= chunk_size) {
        __insertion_sort(first, first + chunk_size);
        first += chunk_size;
    }
    __insertion_sort(first, last);
}

template <class RandomAccessIterator, class Distance, class Compare>
void __chunk_insertion_sort(RandomAccessIterator first, 
                            RandomAccessIterator last,
                            Distance chunk_size, Compare comp) {
    while (last - first >= chunk_size) {
        __insertion_sort(first, first + chunk_size, comp);
        first += chunk_size;
    }
    __insertion_sort(first, last, comp);
}

template <class RandomAccessIterator, class Pointer, class Distance, class T>
void __merge_sort_with_buffer(RandomAccessIterator first, 
                               RandomAccessIterator last,
                               Pointer buffer, Distance& fill_pointer, T*) {
    Distance len = last - first;
    Pointer buffer_last = buffer + len;

    Distance step_size = __stl_chunk_size;
    __chunk_insertion_sort(first, last, step_size);
    while (step_size < len) {
        __merge_sort_loop_aux(first, last, buffer, step_size, fill_pointer,
                              (T*)0);
        step_size *= 2;
        __merge_sort_loop(buffer, buffer_last, first, step_size);
        step_size *= 2;
    }
}

template <class RandomAccessIterator, class Pointer, class Distance, class T,
          class Compare>
void __merge_sort_with_buffer(RandomAccessIterator first, 
                              RandomAccessIterator last,
                              Pointer buffer, Distance& fill_pointer,
                              T*, Compare comp) {
    Distance len = last - first;
    Pointer buffer_last = buffer + len;

    Distance step_size = __stl_chunk_size;
    __chunk_insertion_sort(first, last, step_size, comp);

    while (step_size < len) {
        __merge_sort_loop_aux(first, last, buffer, step_size, fill_pointer,
                              (T*)0, comp);
        step_size *= 2;
        __merge_sort_loop(buffer, buffer_last, first, step_size, comp);
        step_size *= 2;
    }
}

template <class RandomAccessIterator, class Pointer, class Distance, class T>
void __stable_sort_adaptive(RandomAccessIterator first, 
                            RandomAccessIterator last, Pointer buffer,
                            Distance buffer_size, Distance& fill_pointer, T*) {
    Distance len = (last - first + 1) / 2;
    RandomAccessIterator middle = first + len;
    if (len > buffer_size) {
        __stable_sort_adaptive(first, middle, buffer, buffer_size,
                               fill_pointer, (T*)0);
        __stable_sort_adaptive(middle, last, buffer, buffer_size,
                               fill_pointer, (T*)0);
    } else {
        __merge_sort_with_buffer(first, middle, buffer, fill_pointer, (T*)0);
        __merge_sort_with_buffer(middle, last, buffer, fill_pointer, (T*)0);
    }
    __merge_adaptive(first, middle, last, Distance(middle - first), 
                     Distance(last - middle), buffer, buffer_size,
                     fill_pointer, (T*)0);
}

template <class RandomAccessIterator, class Pointer, class Distance, class T,
          class Compare>
void __stable_sort_adaptive(RandomAccessIterator first, 
                            RandomAccessIterator last, Pointer buffer,
                            Distance buffer_size, Distance& fill_pointer, 
                            T*, Compare comp) {
    Distance len = (last - first + 1) / 2;
    RandomAccessIterator middle = first + len;
    if (len > buffer_size) {
        __stable_sort_adaptive(first, middle, buffer, buffer_size,
                               fill_pointer, (T*)0, comp);
        __stable_sort_adaptive(middle, last, buffer, buffer_size,
                               fill_pointer, (T*)0, comp);
    } else {
        __merge_sort_with_buffer(first, middle, buffer, fill_pointer,
                                 (T*)0, comp);
        __merge_sort_with_buffer(middle, last, buffer, fill_pointer,
                                 (T*)0, comp);
    }
    __merge_adaptive(first, middle, last, Distance(middle - first), 
                     Distance(last - middle), buffer, buffer_size,
                     fill_pointer, (T*)0, comp);
}

template <class RandomAccessIterator, class Pointer, class Distance>
inline void __stable_sort(RandomAccessIterator first,
                          RandomAccessIterator last,
                          pair<Pointer, Distance> p) {
    if (p.first == 0) {
        __inplace_stable_sort(first, last);
        return;
    }
    Distance fill_pointer = 0;
    __stable_sort_adaptive(first, last, p.first, p.second, fill_pointer,
                           value_type(first));
    destroy(p.first, p.first + fill_pointer);
    return_temporary_buffer(p.first);
}

template <class RandomAccessIterator, class Pointer, class Distance,
          class Compare>
inline void __stable_sort(RandomAccessIterator first,
                          RandomAccessIterator last,
                          pair<Pointer, Distance> p, Compare comp) {
    if (p.first == 0) {
        __inplace_stable_sort(first, last, comp);
        return;
    }
    Distance fill_pointer = 0;
    __stable_sort_adaptive(first, last, p.first, p.second, fill_pointer,
                           value_type(first), comp);
    destroy(p.first, p.first + fill_pointer);
    return_temporary_buffer(p.first);
}

template <class RandomAccessIterator, class Distance>
inline void __stable_sort_aux(RandomAccessIterator first,
                              RandomAccessIterator last, Distance*) {
    __stable_sort(first, last, get_temporary_buffer(Distance(last - first),
                                                    value_type(first)));
}

template <class RandomAccessIterator, class Distance, class Compare>
inline void __stable_sort_aux(RandomAccessIterator first,
                              RandomAccessIterator last, Distance*,
                              Compare comp) {
    __stable_sort(first, last, get_temporary_buffer(Distance(last - first),
                                                    value_type(first)), comp);
}

template <class RandomAccessIterator>
inline void stable_sort(RandomAccessIterator first,
                        RandomAccessIterator last) {
    __stable_sort_aux(first, last, distance_type(first));
}

template <class RandomAccessIterator, class Compare>
inline void stable_sort(RandomAccessIterator first,
                        RandomAccessIterator last, Compare comp) {
    __stable_sort_aux(first, last, distance_type(first), comp);
}

template <class RandomAccessIterator, class T>
void __partial_sort(RandomAccessIterator first, RandomAccessIterator middle,
                    RandomAccessIterator last, T*) {
    make_heap(first, middle);
    for (RandomAccessIterator i = middle; i < last; ++i)
        if (*i < *first) 
          __pop_heap(first, middle, i, T(*i), distance_type(first));
    sort_heap(first, middle);
}

template <class RandomAccessIterator>
inline void partial_sort(RandomAccessIterator first,
                         RandomAccessIterator middle,
                         RandomAccessIterator last) {
    __partial_sort(first, middle, last, value_type(first));
}

template <class RandomAccessIterator, class T, class Compare>
void __partial_sort(RandomAccessIterator first, RandomAccessIterator middle,
                    RandomAccessIterator last, T*, Compare comp) {
    make_heap(first, middle, comp);
    for (RandomAccessIterator i = middle; i < last; ++i)
        if (*i < *first) 
          __pop_heap(first, middle, i, T(*i), comp, distance_type(first));
    sort_heap(first, middle, comp);
}

template <class RandomAccessIterator, class Compare>
inline void partial_sort(RandomAccessIterator first,
                         RandomAccessIterator middle,
                         RandomAccessIterator last, Compare comp) {
    __partial_sort(first, middle, last, value_type(first), comp);
}

template <class InputIterator, class RandomAccessIterator, class Distance,
          class T>
RandomAccessIterator __partial_sort_copy(InputIterator first,
                                         InputIterator last,
                                         RandomAccessIterator result_first,
                                         RandomAccessIterator result_last, 
                                         Distance*, T*) {
    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++;
    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), T(*first));
        ++first;
    }
    sort_heap(result_first, result_real_last);
    return result_real_last;
}

template <class InputIterator, class RandomAccessIterator>
inline RandomAccessIterator
partial_sort_copy(InputIterator first, InputIterator last,
                  RandomAccessIterator result_first,
                  RandomAccessIterator result_last) {
    return __partial_sort_copy(first, last, result_first, result_last, 
                               distance_type(result_first), value_type(first));
}

template <class InputIterator, class RandomAccessIterator, class Compare,
          class Distance, class T>
RandomAccessIterator __partial_sort_copy(InputIterator first,
                                         InputIterator last,
                                         RandomAccessIterator result_first,
                                         RandomAccessIterator result_last,
                                         Compare comp, Distance*, T*) {
    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++;
    make_heap(result_first, result_real_last, comp);
    while (first != last) {
        if (*first < *result_first) 
            __adjust_heap(result_first, Distance(0),
                          Distance(result_real_last - result_first), T(*first),
                          comp);
        ++first;
    }
    sort_heap(result_first, result_real_last, comp);
    return result_real_last;
}

template <class InputIterator, class RandomAccessIterator, class Compare>
inline RandomAccessIterator
partial_sort_copy(InputIterator first, InputIterator last,
                  RandomAccessIterator result_first,
                  RandomAccessIterator result_last, Compare comp) {
    return __partial_sort_copy(first, last, result_first, result_last, comp,
                               distance_type(result_first), value_type(first));
}

template <class RandomAccessIterator, class T>
void __nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last, T*) {
    while (last - first > 3) {
        RandomAccessIterator cut = __unguarded_partition
            (first, last, T(__median(*first, *(first + (last - first)/2),
                                     *(last - 1))));
        if (cut <= nth)
            first = cut;
        else 
            last = cut;
    }
    __insertion_sort(first, last);
}

template <class RandomAccessIterator>
inline void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                        RandomAccessIterator last) {
    __nth_element(first, nth, last, value_type(first));
}

template <class RandomAccessIterator, class T, class Compare>
void __nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                   RandomAccessIterator last, T*, Compare comp) {
    while (last - first > 3) {
        RandomAccessIterator cut = __unguarded_partition
            (first, last, T(__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 RandomAccessIterator, class Compare>
inline void nth_element(RandomAccessIterator first, RandomAccessIterator nth,
                 RandomAccessIterator last, Compare comp) {
    __nth_element(first, nth, last, value_type(first), comp);
}

template <class ForwardIterator, class T, class Distance>
ForwardIterator __lower_bound(ForwardIterator first, ForwardIterator last,
                              const T& value, Distance*,
                              forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (*middle < value) {
            first = middle;
            ++first;
            len = len - half - 1;
        } else
            len = half;
    }
    return first;
}

template <class ForwardIterator, class T, class Distance>
inline ForwardIterator __lower_bound(ForwardIterator first,
                                     ForwardIterator last,
                                     const T& value, Distance*,
                                     bidirectional_iterator_tag) {
    return __lower_bound(first, last, value, (Distance*)0,
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Distance>
RandomAccessIterator __lower_bound(RandomAccessIterator first,
                                   RandomAccessIterator last, const T& value,
                                   Distance*, random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (*middle < value) {
            first = middle + 1;
            len = len - half - 1;
        } else
            len = half;
    }
    return first;
}

template <class ForwardIterator, class T>
inline ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last,
                                   const T& value) {
    return __lower_bound(first, last, value, distance_type(first),
                         iterator_category(first));
}

template <class ForwardIterator, class T, class Compare, class Distance>
ForwardIterator __lower_bound(ForwardIterator first, ForwardIterator last,
                              const T& value, Compare comp, Distance*,
                              forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (comp(*middle, value)) {
            first = middle;
            ++first;
            len = len - half - 1;
        } else
            len = half;
    }
    return first;
}

template <class ForwardIterator, class T, class Compare, class Distance>
inline ForwardIterator __lower_bound(ForwardIterator first,
                                     ForwardIterator last,
                                     const T& value, Compare comp, Distance*,
                                     bidirectional_iterator_tag) {
    return __lower_bound(first, last, value, comp, (Distance*)0,
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Compare, class Distance>
RandomAccessIterator __lower_bound(RandomAccessIterator first,
                                   RandomAccessIterator last,
                                   const T& value, Compare comp, Distance*,
                                   random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (comp(*middle, value)) {
            first = middle + 1;
            len = len - half - 1;
        } else
            len = half;
    }
    return first;
}

template <class ForwardIterator, class T, class Compare>
inline ForwardIterator lower_bound(ForwardIterator first, ForwardIterator last,
                                   const T& value, Compare comp) {
    return __lower_bound(first, last, value, comp, distance_type(first),
                         iterator_category(first));
}

template <class ForwardIterator, class T, class Distance>
ForwardIterator __upper_bound(ForwardIterator first, ForwardIterator last,
                              const T& value, Distance*,
                              forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (value < *middle)
            len = half;
        else {
            first = middle;
            ++first;
            len = len - half - 1;
        }
    }
    return first;
}

template <class ForwardIterator, class T, class Distance>
inline ForwardIterator __upper_bound(ForwardIterator first,
                                     ForwardIterator last,
                                     const T& value, Distance*,
                                     bidirectional_iterator_tag) {
    return __upper_bound(first, last, value, (Distance*)0,
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Distance>
RandomAccessIterator __upper_bound(RandomAccessIterator first,
                                   RandomAccessIterator last, const T& value,
                                   Distance*, random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (value < *middle)
            len = half;
        else {
            first = middle + 1;
            len = len - half - 1;
        }
    }
    return first;
}

template <class ForwardIterator, class T>
inline ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
                                   const T& value) {
    return __upper_bound(first, last, value, distance_type(first),
                         iterator_category(first));
}

template <class ForwardIterator, class T, class Compare, class Distance>
ForwardIterator __upper_bound(ForwardIterator first, ForwardIterator last,
                              const T& value, Compare comp, Distance*,
                              forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (comp(value, *middle))
            len = half;
        else {
            first = middle;
            ++first;
            len = len - half - 1;
        }
    }
    return first;
}

template <class ForwardIterator, class T, class Compare, class Distance>
inline ForwardIterator __upper_bound(ForwardIterator first,
                                     ForwardIterator last,
                                     const T& value, Compare comp, Distance*,
                                     bidirectional_iterator_tag) {
    return __upper_bound(first, last, value, comp, (Distance*)0,
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Compare, class Distance>
RandomAccessIterator __upper_bound(RandomAccessIterator first,
                                   RandomAccessIterator last,
                                   const T& value, Compare comp, Distance*,
                                   random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (comp(value, *middle))
            len = half;
        else {
            first = middle + 1;
            len = len - half - 1;
        }
    }
    return first;
}

template <class ForwardIterator, class T, class Compare>
inline ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
                                   const T& value, Compare comp) {
    return __upper_bound(first, last, value, comp, distance_type(first),
                         iterator_category(first));
}

template <class ForwardIterator, class T, class Distance>
pair<ForwardIterator, ForwardIterator>
__equal_range(ForwardIterator first, ForwardIterator last, const T& value,
              Distance*, forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle, left, right;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (*middle < value) {
            first = middle;
            ++first;
            len = len - half - 1;
        } else if (value < *middle)
            len = half;
        else {
            left = lower_bound(first, middle, value);
            advance(first, len);
            right = upper_bound(++middle, first, value);
            return pair<ForwardIterator, ForwardIterator>(left, right);
        }
    }
    return pair<ForwardIterator, ForwardIterator>(first, first);
}

template <class ForwardIterator, class T, class Distance>
inline pair<ForwardIterator, ForwardIterator>
__equal_range(ForwardIterator first, ForwardIterator last, const T& value,
              Distance*, bidirectional_iterator_tag) {
    return __equal_range(first, last, value, (Distance*)0, 
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Distance>
pair<RandomAccessIterator, RandomAccessIterator>
__equal_range(RandomAccessIterator first, RandomAccessIterator last,
              const T& value, Distance*, random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle, left, right;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (*middle < value) {
            first = middle + 1;
            len = len - half - 1;
        } else if (value < *middle)
            len = half;
        else {
            left = lower_bound(first, middle, value);
            right = upper_bound(++middle, first + len, value);
            return pair<RandomAccessIterator, RandomAccessIterator>(left,
                                                                    right);
        }
    }
    return pair<RandomAccessIterator, RandomAccessIterator>(first, first);
}

template <class ForwardIterator, class T>
inline pair<ForwardIterator, ForwardIterator>
equal_range(ForwardIterator first, ForwardIterator last, const T& value) {
    return __equal_range(first, last, value, distance_type(first),
                         iterator_category(first));
}

template <class ForwardIterator, class T, class Compare, class Distance>
pair<ForwardIterator, ForwardIterator>
__equal_range(ForwardIterator first, ForwardIterator last, const T& value,
              Compare comp, Distance*, forward_iterator_tag) {
    Distance len = 0;
    distance(first, last, len);
    Distance half;
    ForwardIterator middle, left, right;

    while (len > 0) {
        half = len / 2;
        middle = first;
        advance(middle, half);
        if (comp(*middle, value)) {
            first = middle;
            ++first;
            len = len - half - 1;
        } else if (comp(value, *middle))
            len = half;
        else {
            left = lower_bound(first, middle, value, comp);
            advance(first, len);
            right = upper_bound(++middle, first, value, comp);
            return pair<ForwardIterator, ForwardIterator>(left, right);
        }
    }
    return pair<ForwardIterator, ForwardIterator>(first, first);
}           

template <class ForwardIterator, class T, class Compare, class Distance>
inline pair<ForwardIterator, ForwardIterator>
__equal_range(ForwardIterator first, ForwardIterator last, const T& value,
              Compare comp, Distance*, bidirectional_iterator_tag) {
    return __equal_range(first, last, value, comp, (Distance*)0, 
                         forward_iterator_tag());
}

template <class RandomAccessIterator, class T, class Compare, class Distance>
pair<RandomAccessIterator, RandomAccessIterator>
__equal_range(RandomAccessIterator first, RandomAccessIterator last,
              const T& value, Compare comp, Distance*,
              random_access_iterator_tag) {
    Distance len = last - first;
    Distance half;
    RandomAccessIterator middle, left, right;

    while (len > 0) {
        half = len / 2;
        middle = first + half;
        if (comp(*middle, value)) {
            first = middle + 1;
            len = len - half - 1;
        } else if (comp(value, *middle))
            len = half;
        else {
            left = lower_bound(first, middle, value, comp);
            right = upper_bound(++middle, first + len, value, comp);
            return pair<RandomAccessIterator, RandomAccessIterator>(left,
                                                                    right);
        }
    }
    return pair<RandomAccessIterator, RandomAccessIterator>(first, first);
}           

template <class ForwardIterator, class T, class Compare>
inline pair<ForwardIterator, ForwardIterator>
equal_range(ForwardIterator first, ForwardIterator last, const T& value,
            Compare comp) {
    return __equal_range(first, last, value, comp, distance_type(first),
                         iterator_category(first));
}    

template <class ForwardIterator, class T>
bool binary_search(ForwardIterator first, ForwardIterator last,
                   const T& value) {
    ForwardIterator i = lower_bound(first, last, value);
    return i != last && !(value < *i);
}

template <class ForwardIterator, class T, class Compare>
bool binary_search(ForwardIterator first, ForwardIterator last, const T& value,
                   Compare comp) {
    ForwardIterator i = lower_bound(first, last, value, comp);
    return i != last && !comp(value, *i);
}

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator merge(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2,
                     OutputIterator result) {
    while (first1 != last1 && first2 != last2)
        if (*first2 < *first1)
            *result++ = *first2++;
        else
            *result++ = *first1++;
    return copy(first2, last2, copy(first1, last1, result));
}

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class Compare>
OutputIterator merge(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2,
                     OutputIterator result, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first2, *first1))
            *result++ = *first2++;
        else
            *result++ = *first1++;
    return copy(first2, last2, copy(first1, last1, result));
}

template <class BidirectionalIterator, class 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) 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;
        advance(first_cut, len11);
        second_cut = lower_bound(middle, last, *first_cut);
        distance(middle, second_cut, len22);
    } else {
        len22 = len2 / 2;
        advance(second_cut, len22);
        first_cut = upper_bound(first, middle, *second_cut);
        distance(first, first_cut, len11);
    }
    rotate(first_cut, middle, second_cut);
    BidirectionalIterator new_middle = first_cut;
    advance(new_middle, len22);
    __merge_without_buffer(first, first_cut, new_middle, len11, len22);
    __merge_without_buffer(new_middle, second_cut, last, len1 - len11,
                           len2 - len22);
}

template <class BidirectionalIterator, class Distance, class 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)) 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;
        advance(first_cut, len11);
        second_cut = lower_bound(middle, last, *first_cut, comp);
        distance(middle, second_cut, len22);
    } else {
        len22 = len2 / 2;
        advance(second_cut, len22);
        first_cut = upper_bound(first, middle, *second_cut, comp);
        distance(first, first_cut, len11);
    }
    rotate(first_cut, middle, second_cut);
    BidirectionalIterator new_middle = first_cut;
    advance(new_middle, len22);
    __merge_without_buffer(first, first_cut, new_middle, len11, len22, comp);
    __merge_without_buffer(new_middle, second_cut, last, len1 - len11,
                           len2 - len22, comp);
}


template <class InputIterator, class OutputIterator>
OutputIterator __borland_bugfix_copy(InputIterator first, InputIterator last,
                    OutputIterator result) {
// this is used in __rotate_adaptive to work around some obscure Borland
// bug. It is the same as copy, but with a different (and appropriate) name.
    while (first != last) *result++ = *first++;
    return result;
}

template <class BidirectionalIterator1, class BidirectionalIterator2,
          class Distance>
BidirectionalIterator1 __rotate_adaptive(BidirectionalIterator1 first,
                                         BidirectionalIterator1 middle,
                                         BidirectionalIterator1 last,
                                         Distance len1, Distance len2,
                                         BidirectionalIterator2 buffer,
                                         Distance buffer_size) {
    BidirectionalIterator2 buffer_end;
    if (len1 > len2 && len2 <= buffer_size) {
        buffer_end = __borland_bugfix_copy(middle, last, buffer);
        copy_backward(first, middle, last);
        return copy(buffer, buffer_end, first);
    } else if (len1 <= buffer_size) {
        buffer_end = __borland_bugfix_copy(first, middle, buffer);
        copy(middle, last, first);
        return copy_backward(buffer, buffer_end, last);
    } else  {
        rotate(first, middle, last);
        advance(first, len2);
        return first;
    }
}

template <class BidirectionalIterator1, class BidirectionalIterator2,
          class BidirectionalIterator3>
BidirectionalIterator3 __merge_backward(BidirectionalIterator1 first1,
                                        BidirectionalIterator1 last1,
                                        BidirectionalIterator2 first2,
                                        BidirectionalIterator2 last2,
                                        BidirectionalIterator3 result) {
    if (first1 == last1) return copy_backward(first2, last2, result);
    if (first2 == last2) return copy_backward(first1, last1, result);
    --last1;
    --last2;
    while (true) {
        if (*last2 < *last1) {
            *--result = *last1;
            if (first1 == last1) return copy_backward(first2, ++last2, result);
            --last1;
        } else {
            *--result = *last2;
            if (first2 == last2) return copy_backward(first1, ++last1, result);
            --last2;
        }
    }
}

template <class BidirectionalIterator1, class BidirectionalIterator2,
          class BidirectionalIterator3, class Compare>
BidirectionalIterator3 __merge_backward(BidirectionalIterator1 first1,
                                        BidirectionalIterator1 last1,
                                        BidirectionalIterator2 first2,
                                        BidirectionalIterator2 last2,
                                        BidirectionalIterator3 result,
                                        Compare comp) {
    if (first1 == last1) return copy_backward(first2, last2, result);
    if (first2 == last2) return copy_backward(first1, last1, result);
    --last1;
    --last2;
    while (true) {
        if (comp(*last2, *last1)) {
            *--result = *last1;
            if (first1 == last1) return copy_backward(first2, ++last2, result);
            --last1;
        } else {
            *--result = *last2;
            if (first2 == last2) return copy_backward(first1, ++last1, result);
            --last2;
        }
    }
}

template <class BidirectionalIterator, class Distance, class Pointer, class T>
void __merge_adaptive(BidirectionalIterator first, 
                      BidirectionalIterator middle, 
                      BidirectionalIterator last, Distance len1, Distance len2,
                      Pointer buffer, Distance buffer_size,
                      Distance& fill_pointer, T*) {
    if (len1 <= len2 && len1 <= buffer_size) {
        BidirectionalIterator i = first;
        Pointer j = buffer;
        len2 = 0;
        while (len2 < len1 && len2 < fill_pointer) {
            *buffer++ = *first++;
            ++len2;
        }
        raw_storage_iterator<Pointer, T> end_buffer = buffer;
        while (len2++ < len1) {
            *end_buffer++ = *first++;
            ++fill_pointer;
        }
        merge(j, j + len1, middle, last, i);
    } else if (len2 <= buffer_size) {
        BidirectionalIterator i = middle;
        Pointer j = buffer;
        len1 = 0;
        while (len1 < len2 && len1 < fill_pointer) {
            *buffer++ = *middle++;
            ++len1;
        }
        raw_storage_iterator<Pointer, T> end_buffer = buffer;
        while (len1++ < len2) {
            *end_buffer++ = *middle++;
            ++fill_pointer;
        }
        __merge_backward(first, i, j, j + len2, last);
    } else {
        BidirectionalIterator first_cut = first;
        BidirectionalIterator second_cut = middle;
        Distance len11 = 0;
        Distance len22 = 0;
        if (len1 > len2) {
            len11 = len1 / 2;
            advance(first_cut, len11);
            second_cut = lower_bound(middle, last, *first_cut);
            distance(middle, second_cut, len22);   
        } else {
            len22 = len2 / 2;
            advance(second_cut, len22);
            first_cut = upper_bound(first, middle, *second_cut);
            distance(first, first_cut, len11);
        }
        BidirectionalIterator new_middle =
            __rotate_adaptive(first_cut, middle, second_cut, len1 - len11,
                              len22, buffer, buffer_size);
        __merge_adaptive(first, first_cut, new_middle, len11, len22, buffer,
                         buffer_size, fill_pointer, (T*)0);
        __merge_adaptive(new_middle, second_cut, last, len1 - len11,
                         len2 - len22, buffer, buffer_size, fill_pointer,
                         (T*)0);
    }
}

template <class BidirectionalIterator, class Distance, class Pointer, class T,
          class Compare>
void __merge_adaptive(BidirectionalIterator first, 
                      BidirectionalIterator middle, 
                      BidirectionalIterator last, Distance len1, Distance len2,
                      Pointer buffer, Distance buffer_size,
                      Distance& fill_pointer, T*, Compare comp) {
    if (len1 <= len2 && len1 <= buffer_size) {
        BidirectionalIterator i = first;
        Pointer j = buffer;
        len2 = 0;
        while (len2 < len1 && len2 < fill_pointer) {
            *buffer++ = *first++;
            ++len2;
        }
        raw_storage_iterator<Pointer, T> end_buffer = buffer;
        while (len2++ < len1) {
            *end_buffer++ = *first++;
            ++fill_pointer;
        }
        merge(j, j + len1, middle, last, i, comp);
    } else if (len2 <= buffer_size) {
        BidirectionalIterator i = middle;
        Pointer j = buffer;
        len1 = 0;
        while (len1 < len2 && len1 < fill_pointer) {
            *buffer++ = *middle++;
            ++len1;
        }
        raw_storage_iterator<Pointer, T> end_buffer = buffer;
        while (len1++ < len2) {
            *end_buffer++ = *middle++;
            ++fill_pointer;
        }
        __merge_backward(first, i, j, j + len2, last, comp);
    } else {
        BidirectionalIterator first_cut = first;
        BidirectionalIterator second_cut = middle;
        Distance len11 = 0;
        Distance len22 = 0;
        if (len1 > len2) {
            len11 = len1 / 2;
            advance(first_cut, len11);
            second_cut = lower_bound(middle, last, *first_cut, comp);
            distance(middle, second_cut, len22);   
        } else {
            len22 = len2 / 2;
            advance(second_cut, len22);
            first_cut = upper_bound(first, middle, *second_cut, comp);
            distance(first, first_cut, len11);
        }
        BidirectionalIterator new_middle =
            __rotate_adaptive(first_cut, middle, second_cut, len1 - len11,
                              len22, buffer, buffer_size);
        __merge_adaptive(first, first_cut, new_middle, len11, len22, buffer,
                         buffer_size, fill_pointer, (T*)0, comp);
        __merge_adaptive(new_middle, second_cut, last, len1 - len11,
                         len2 - len22, buffer, buffer_size, fill_pointer,
                         (T*)0, comp);
    }
}

template <class BidirectionalIterator, class Distance, class Pointer>
void __inplace_merge(BidirectionalIterator first,
                     BidirectionalIterator middle, 
                     BidirectionalIterator last, Distance len1, Distance len2,
                     pair<Pointer, Distance> p) {
    if (p.first == 0) {
        __merge_without_buffer(first, middle, last, len1, len2);
        return;
    }
    Distance fill_pointer = 0;
    __merge_adaptive(first, middle, last, len1, len2, p.first, p.second,
                     fill_pointer, value_type(first)); 
    destroy(p.first, p.first + fill_pointer);
    return_temporary_buffer(p.first);
}

template <class BidirectionalIterator, class Distance, class Pointer, 
          class Compare>
void __inplace_merge(BidirectionalIterator first,
                     BidirectionalIterator middle, 
                     BidirectionalIterator last, Distance len1, Distance len2,
                     pair<Pointer, Distance> p, Compare comp) {
    if (p.first == 0) {
        __merge_without_buffer(first, middle, last, len1, len2, comp);
        return;
    }
    Distance fill_pointer = 0;
    __merge_adaptive(first, middle, last, len1, len2, p.first, p.second,
                     fill_pointer, value_type(first), comp); 
    destroy(p.first, p.first + fill_pointer);
    return_temporary_buffer(p.first);
}

template <class BidirectionalIterator, class Distance>
inline void __inplace_merge_aux(BidirectionalIterator first,
                                BidirectionalIterator middle,
                                BidirectionalIterator last, Distance*) {
    Distance len1 = 0;
    distance(first, middle, len1);
    Distance len2 = 0;
    distance(middle, last, len2);
    __inplace_merge(first, middle, last, len1, len2,
                    get_temporary_buffer(len1 + len2, value_type(first)));
}

template <class BidirectionalIterator, class Distance, class Compare>
inline void __inplace_merge_aux(BidirectionalIterator first,
                                BidirectionalIterator middle,
                                BidirectionalIterator last, Distance*,
                                Compare comp) {
    Distance len1 = 0;
    distance(first, middle, len1);
    Distance len2 = 0;
    distance(middle, last, len2);
    __inplace_merge(first, middle, last, len1, len2,
                    get_temporary_buffer(len1 + len2, value_type(first)),
                    comp);
}

template <class BidirectionalIterator>
inline void inplace_merge(BidirectionalIterator first,
                          BidirectionalIterator middle,
                          BidirectionalIterator last) {
    __inplace_merge_aux(first, middle, last, distance_type(first));
}

template <class BidirectionalIterator, class Compare>
inline void inplace_merge(BidirectionalIterator first,
                          BidirectionalIterator middle,
                          BidirectionalIterator last, Compare comp) {
    __inplace_merge_aux(first, middle, last, distance_type(first), comp);
}

template <class InputIterator1, class InputIterator2>
bool includes(InputIterator1 first1, InputIterator1 last1,
              InputIterator2 first2, InputIterator2 last2) {
    while (first1 != last1 && first2 != last2)
        if (*first2 < *first1)
            return false;
        else if(*first1 < *first2) 
            ++first1;
        else
            ++first1, ++first2;

    return first2 == last2;
}

template <class InputIterator1, class InputIterator2, class Compare>
bool includes(InputIterator1 first1, InputIterator1 last1,
              InputIterator2 first2, InputIterator2 last2, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first2, *first1))
            return false;
        else if(comp(*first1, *first2)) 
            ++first1;
        else
            ++first1, ++first2;

    return first2 == last2;
}

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_union(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, InputIterator2 last2,
                         OutputIterator result) {
    while (first1 != last1 && first2 != last2)
        if (*first1 < *first2)
            *result++ = *first1++;
        else if (*first2 < *first1)
            *result++ = *first2++;
        else {
            *result++ = *first1++;
            first2++;
        }
    return copy(first2, last2, copy(first1, last1, result));
}

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class Compare>
OutputIterator set_union(InputIterator1 first1, InputIterator1 last1,
                         InputIterator2 first2, InputIterator2 last2,
                         OutputIterator result, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first1, *first2))
            *result++ = *first1++;
        else if (comp(*first2, *first1))
            *result++ = *first2++;
        else {
            *result++ = *first1++;
            ++first2;
        }
    return copy(first2, last2, copy(first1, last1, result));
}

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1,
                                InputIterator2 first2, InputIterator2 last2,
                                OutputIterator result) {
    while (first1 != last1 && first2 != last2)
        if (*first1 < *first2)
            ++first1;
        else if (*first2 < *first1)
            ++first2;
        else {
            *result++ = *first1++;
            ++first2;
        }
    return result;
}

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class Compare>
OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1,
                                InputIterator2 first2, InputIterator2 last2,
                                OutputIterator result, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first1, *first2))
            ++first1;
        else if (comp(*first2, *first1))
            ++first2;
        else {
            *result++ = *first1++;
            ++first2;
        }
    return result;
}

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1,
                              InputIterator2 first2, InputIterator2 last2,
                              OutputIterator result) {
    while (first1 != last1 && first2 != last2)
        if (*first1 < *first2)
            *result++ = *first1++;
        else if (*first2 < *first1)
            ++first2;
        else {
            ++first1;
            ++first2;
        }
    return copy(first1, last1, result);
}

template <class InputIterator1, class InputIterator2, class OutputIterator, 
          class Compare>
OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1,
                              InputIterator2 first2, InputIterator2 last2, 
                              OutputIterator result, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first1, *first2))
            *result++ = *first1++;
        else if (comp(*first2, *first1))
            ++first2;
        else {
            ++first1;
            ++first2;
        }
    return copy(first1, last1, result);
}

template <class InputIterator1, class InputIterator2, class OutputIterator>
OutputIterator set_symmetric_difference(InputIterator1 first1,
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result) {
    while (first1 != last1 && first2 != last2)
        if (*first1 < *first2)
            *result++ = *first1++;
        else if (*first2 < *first1)
            *result++ = *first2++;
        else {
            ++first1;
            ++first2;
        }
    return copy(first2, last2, copy(first1, last1, result));
}

template <class InputIterator1, class InputIterator2, class OutputIterator,
          class Compare>
OutputIterator set_symmetric_difference(InputIterator1 first1,
                                        InputIterator1 last1,
                                        InputIterator2 first2,
                                        InputIterator2 last2,
                                        OutputIterator result, Compare comp) {
    while (first1 != last1 && first2 != last2)
        if (comp(*first1, *first2))
            *result++ = *first1++;
        else if (comp(*first2, *first1))
            *result++ = *first2++;
        else {
            ++first1;
            ++first2;
        }
    return copy(first2, last2, copy(first1, last1, result));
}

template <class InputIterator>
InputIterator max_element(InputIterator first, InputIterator last) {
    if (first == last) return first;
    InputIterator result = first;
    while (++first != last) 
        if (*result < *first) result = first;
    return result;
}

template <class InputIterator, class Compare>
InputIterator max_element(InputIterator first, InputIterator last,
                          Compare comp) {
    if (first == last) return first;
    InputIterator result = first;
    while (++first != last) 
        if (comp(*result, *first)) result = first;
    return result;
}

template <class InputIterator>
InputIterator min_element(InputIterator first, InputIterator last) {
    if (first == last) return first;
    InputIterator result = first;
    while (++first != last) 
        if (*first < *result) result = first;
    return result;
}

template <class InputIterator, class Compare>
InputIterator min_element(InputIterator first, InputIterator last,
                          Compare comp) {
    if (first == last) return first;
    InputIterator result = first;
    while (++first != last) 
        if (comp(*first, *result)) result = first;
    return result;
}

template <class BidirectionalIterator>
bool next_permutation(BidirectionalIterator first,
                      BidirectionalIterator last) {
    if (first == last) return false;
    BidirectionalIterator i = first;
    ++i;
    if (i == last) return false;
    i = last;
    --i;

    for(;;) {
        BidirectionalIterator ii = i--;
        if (*i < *ii) {
            BidirectionalIterator j = last;
            while (!(*i < *--j));
            iter_swap(i, j);
            reverse(ii, last);
            return true;
        }
        if (i == first) {
            reverse(first, last);
            return false;
        }
    }
}

template <class BidirectionalIterator, class Compare>
bool next_permutation(BidirectionalIterator first, BidirectionalIterator last,
                      Compare comp) {
    if (first == last) return false;
    BidirectionalIterator i = first;
    ++i;
    if (i == last) return false;
    i = last;
    --i;

    for(;;) {
        BidirectionalIterator ii = i--;
        if (comp(*i, *ii)) {
            BidirectionalIterator j = last;
            while (!comp(*i, *--j));
            iter_swap(i, j);
            reverse(ii, last);
            return true;
        }
        if (i == first) {
            reverse(first, last);
            return false;
        }
    }
}

template <class BidirectionalIterator>
bool prev_permutation(BidirectionalIterator first,
                      BidirectionalIterator last) {
    if (first == last) return false;
    BidirectionalIterator i = first;
    ++i;
    if (i == last) return false;
    i = last;
    --i;

    for(;;) {
        BidirectionalIterator ii = i--;
        if (!(*i < *ii)) {
            BidirectionalIterator j = last;
            while (*i < *--j);
            iter_swap(i, j);
            reverse(ii, last);
            return true;
        }
        if (i == first) {
            reverse(first, last);
            return false;
        }
    }
}

template <class BidirectionalIterator, class Compare>
bool prev_permutation(BidirectionalIterator first, BidirectionalIterator last,
                      Compare comp) {
    if (first == last) return false;
    BidirectionalIterator i = first;
    ++i;
    if (i == last) return false;
    i = last;
    --i;

    for(;;) {
        BidirectionalIterator ii = i--;
        if (!comp(*i, *ii)) {
            BidirectionalIterator j = last;
            while (comp(*i, *--j));
            iter_swap(i, j);
            reverse(ii, last);
            return true;
        }
        if (i == first) {
            reverse(first, last);
            return false;
        }
    }
}

template <class InputIterator, class T>
T accumulate(InputIterator first, InputIterator last, T init) {
    while (first != last) 
        init = init + *first++;
    return init;
}

template <class InputIterator, class T, class BinaryOperation>
T accumulate(InputIterator first, InputIterator last, T init,
             BinaryOperation binary_op) {
    while (first != last) 
        init = binary_op(init, *first++);
    return init;
}

template <class InputIterator1, class InputIterator2, class T>
T inner_product(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, T init) {
    while (first1 != last1) 
        init = init + (*first1++ * *first2++);
    return init;
}

template <class InputIterator1, class InputIterator2, class T,
          class BinaryOperation1, class BinaryOperation2>
T inner_product(InputIterator1 first1, InputIterator1 last1,
                InputIterator2 first2, T init, BinaryOperation1 binary_op1,
                BinaryOperation2 binary_op2) {
    while (first1 != last1) 
        init = binary_op1(init, binary_op2(*first1++, *first2++));
    return init;
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator __partial_sum(InputIterator first, InputIterator last,
                             OutputIterator result, T*) {
    T value = *first;
    while (++first != last) {
        value = value + *first;
        *++result = value;
    }
    return ++result;
}

template <class InputIterator, class OutputIterator>
OutputIterator partial_sum(InputIterator first, InputIterator last,
                           OutputIterator result) {
    if (first == last) return result;
    *result = *first;
    return __partial_sum(first, last, result, value_type(first));
}

template <class InputIterator, class OutputIterator, class T,
          class BinaryOperation>
OutputIterator __partial_sum(InputIterator first, InputIterator last,
                             OutputIterator result, T*,
                             BinaryOperation binary_op) {
    T value = *first;
    while (++first != last) {
        value = binary_op(value, *first);
        *++result = value;
    }
    return ++result;
}

template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator partial_sum(InputIterator first, InputIterator last,
                           OutputIterator result, BinaryOperation binary_op) {
    if (first == last) return result;
    *result = *first;
    return __partial_sum(first, last, result, value_type(first), binary_op);
}

template <class InputIterator, class OutputIterator, class T>
OutputIterator __adjacent_difference(InputIterator first, InputIterator last, 
                                     OutputIterator result, T*) {
    T value = *first;
    while (++first != last) {
        T tmp = *first;
        *++result = tmp - value;
        value = tmp;
    }
    return ++result;
}

template <class InputIterator, class OutputIterator>
OutputIterator adjacent_difference(InputIterator first, InputIterator last, 
                                   OutputIterator result) {
    if (first == last) return result;
    *result = *first;
    return __adjacent_difference(first, last, result, value_type(first));
}

template <class InputIterator, class OutputIterator, class T, 
          class BinaryOperation>
OutputIterator __adjacent_difference(InputIterator first, InputIterator last, 
                                     OutputIterator result, T*,
                                     BinaryOperation binary_op) {
    T value = *first;
    while (++first != last) {
        T tmp = *first;
        *++result = binary_op(tmp, value);
        value = tmp;
    }
    return ++result;
}

template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator adjacent_difference(InputIterator first, InputIterator last,
                                   OutputIterator result,
                                   BinaryOperation binary_op) {
    if (first == last) return result;
    *result = *first;
    return __adjacent_difference(first, last, result, value_type(first),
                                 binary_op);
}

template <class ForwardIterator, class T>
void iota(ForwardIterator first, ForwardIterator last, T value) {
    while (first != last) *first++ = value++;
}

#endif

