include/algorithm

// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_ALGORITHM
#define _LIBCPP_ALGORITHM

/*
    algorithm synopsis

#include <initializer_list>

namespace std
{

namespace ranges {
  template <class I, class F>
    struct in_fun_result;     // since C++20

  template <class I1, class I2>
    struct in_in_result;      // since C++20

  template <class I1, class I2, class O>
    struct in_in_out_result;  // since C++20

  template <class I, class O1, class O2>
    struct in_out_out_result; // since C++20

  template <class I1, class I2>
    struct min_max_result;    // since C++20

  template <class I>
    struct in_found_result;   // since C++20

  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
    indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>             // since C++20
  constexpr I min_element(I first, S last, Comp comp = {}, Proj proj = {});

  template<forward_range R, class Proj = identity,
    indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less> // since C++20
  constexpr borrowed_iterator_t<R> min_element(R&& r, Comp comp = {}, Proj proj = {});

  template <input_iterator I1, sentinel_for<_I1> S1, input_iterator I2, sentinel_for<_I2> S2,
          class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<I1, I2, Pred, Proj1, Proj2>
  constexpr mismatch_result<_I1, _I2>
  mismatch()(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}) // since C++20

  template <input_range R1, input_range R2,
          class Pred = ranges::equal_to, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_comparable<iterator_t<R1>, iterator_t<R2>, Pred, Proj1, Proj2>
  constexpr mismatch_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
  mismatch(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {})                           // since C++20

    requires indirect_binary_predicate<ranges::equal_to, projected<I, Proj>, const T*>
    constexpr I find(I first, S last, const T& value, Proj proj = {});              // since C++20

  template<input_range R, class T, class Proj = identity>
    requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<R>, Proj>, const T*>
    constexpr borrowed_iterator_t<R>
      find(R&& r, const T& value, Proj proj = {});                                  // since C++20

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
           indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr I find_if(I first, S last, Pred pred, Proj proj = {});                // since C++20

  template<input_range R, class Proj = identity,
           indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_iterator_t<R>
      find_if(R&& r, Pred pred, Proj proj = {});                                    // since C++20

  template<input_iterator I, sentinel_for<I> S, class Proj = identity,
           indirect_unary_predicate<projected<I, Proj>> Pred>
    constexpr I find_if_not(I first, S last, Pred pred, Proj proj = {});            // since C++20

  template<input_range R, class Proj = identity,
           indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
    constexpr borrowed_iterator_t<R>
      find_if_not(R&& r, Pred pred, Proj proj = {});                                // since C++20

  template<class T, class Proj = identity,
           indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr const T& min(const T& a, const T& b, Comp comp = {}, Proj proj = {}); // since C++20

  template<copyable T, class Proj = identity,
           indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr T min(initializer_list<T> r, Comp comp = {}, Proj proj = {});         // since C++20

 template<input_range R, class Proj = identity,
          indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
   requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
   constexpr range_value_t<R>
     min(R&& r, Comp comp = {}, Proj proj = {});                                    // since C++20

  template<class T, class Proj = identity,
           indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr const T& max(const T& a, const T& b, Comp comp = {}, Proj proj = {}); // since C++20

  template<copyable T, class Proj = identity,
           indirect_strict_weak_order<projected<const T*, Proj>> Comp = ranges::less>
    constexpr T max(initializer_list<T> r, Comp comp = {}, Proj proj = {});         // since C++20

  template<input_range R, class Proj = identity,
           indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
    requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
    constexpr range_value_t<R>
      max(R&& r, Comp comp = {}, Proj proj = {});                                   // since C++20

  template<class I, class O>
    using unary_transform_result = in_out_result<I, O>;                             // since C++20

  template<class I1, class I2, class O>
    using binary_transform_result = in_in_out_result<I1, I2, O>;                    // since C++20

  template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
           copy_constructible F, class Proj = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<I, Proj>>>
    constexpr ranges::unary_transform_result<I, O>
      transform(I first1, S last1, O result, F op, Proj proj = {});                 // since C++20

  template<input_range R, weakly_incrementable O, copy_constructible F,
           class Proj = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
    constexpr ranges::unary_transform_result<borrowed_iterator_t<R>, O>
      transform(R&& r, O result, F op, Proj proj = {});                             // since C++20

  template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2,
           weakly_incrementable O, copy_constructible F, class Proj1 = identity,
           class Proj2 = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                           projected<I2, Proj2>>>
    constexpr ranges::binary_transform_result<I1, I2, O>
      transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                        F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});           // since C++20

  template<input_range R1, input_range R2, weakly_incrementable O,
           copy_constructible F, class Proj1 = identity, class Proj2 = identity>
    requires indirectly_writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                           projected<iterator_t<R2>, Proj2>>>
    constexpr ranges::binary_transform_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
      transform(R1&& r1, R2&& r2, O result,
                        F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});           // since C++20
}

    constexpr bool     // constexpr in C++20
    all_of(InputIterator first, InputIterator last, Predicate pred);

template <class InputIterator, class Predicate>
    constexpr bool     // constexpr in C++20
    any_of(InputIterator first, InputIterator last, Predicate pred);

template <class InputIterator, class Predicate>
    constexpr bool     // constexpr in C++20
    none_of(InputIterator first, InputIterator last, Predicate pred);

template <class InputIterator, class Function>
    constexpr Function          // constexpr in C++20
    for_each(InputIterator first, InputIterator last, Function f);

template<class InputIterator, class Size, class Function>
    constexpr InputIterator     // constexpr in C++20
    for_each_n(InputIterator first, Size n, Function f); // C++17

template <class InputIterator, class T>
    constexpr InputIterator     // constexpr in C++20
    find(InputIterator first, InputIterator last, const T& value);

template <class InputIterator, class Predicate>
    constexpr InputIterator     // constexpr in C++20
    find_if(InputIterator first, InputIterator last, Predicate pred);

template<class InputIterator, class Predicate>
    constexpr InputIterator     // constexpr in C++20
    find_if_not(InputIterator first, InputIterator last, Predicate pred);

template <class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator1  // constexpr in C++20
    find_end(ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2);

template <class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr ForwardIterator1  // constexpr in C++20
    find_end(ForwardIterator1 first1, ForwardIterator1 last1,
             ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);

template <class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator1  // constexpr in C++20
    find_first_of(ForwardIterator1 first1, ForwardIterator1 last1,
                  ForwardIterator2 first2, ForwardIterator2 last2);

template <class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr ForwardIterator1  // constexpr in C++20
    find_first_of(ForwardIterator1 first1, ForwardIterator1 last1,
                  ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);

template <class ForwardIterator>
    constexpr ForwardIterator   // constexpr in C++20
    adjacent_find(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class BinaryPredicate>
    constexpr ForwardIterator   // constexpr in C++20
    adjacent_find(ForwardIterator first, ForwardIterator last, BinaryPredicate pred);

template <class InputIterator, class T>
    constexpr typename iterator_traits<InputIterator>::difference_type  // constexpr in C++20
    count(InputIterator first, InputIterator last, const T& value);

template <class InputIterator, class Predicate>
    constexpr typename iterator_traits<InputIterator>::difference_type // constexpr in C++20
    count_if(InputIterator first, InputIterator last, Predicate pred);

template <class InputIterator1, class InputIterator2>
    constexpr pair<InputIterator1, InputIterator2>   // constexpr in C++20
    mismatch(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2);

template <class InputIterator1, class InputIterator2>
    constexpr pair<InputIterator1, InputIterator2>   // constexpr in C++20
    mismatch(InputIterator1 first1, InputIterator1 last1,
             InputIterator2 first2, InputIterator2 last2); // **C++14**

template <class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr pair<InputIterator1, InputIterator2>   // constexpr in C++20
    mismatch(InputIterator1 first1, InputIterator1 last1,
             InputIterator2 first2, BinaryPredicate pred);

template <class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr pair<InputIterator1, InputIterator2>   // constexpr in C++20
    mismatch(InputIterator1 first1, InputIterator1 last1,
             InputIterator2 first2, InputIterator2 last2,
             BinaryPredicate pred); // **C++14**

template <class InputIterator1, class InputIterator2>
    constexpr bool      // constexpr in C++20
    equal(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2);

template <class InputIterator1, class InputIterator2>
    constexpr bool      // constexpr in C++20
    equal(InputIterator1 first1, InputIterator1 last1,
          InputIterator2 first2, InputIterator2 last2); // **C++14**

template <class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr bool      // constexpr in C++20
    equal(InputIterator1 first1, InputIterator1 last1,
          InputIterator2 first2, BinaryPredicate pred);

template <class InputIterator1, class InputIterator2, class BinaryPredicate>
    constexpr bool      // constexpr in C++20
    equal(InputIterator1 first1, InputIterator1 last1,
          InputIterator2 first2, InputIterator2 last2,
          BinaryPredicate pred); // **C++14**

template<class ForwardIterator1, class ForwardIterator2>
    constexpr bool      // constexpr in C++20
    is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2);

template<class ForwardIterator1, class ForwardIterator2>
    constexpr bool      // constexpr in C++20
    is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2, ForwardIterator2 last2); // **C++14**

template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr bool      // constexpr in C++20
    is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2, BinaryPredicate pred);

template<class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr bool      // constexpr in C++20
    is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2, ForwardIterator2 last2,
                   BinaryPredicate pred);  // **C++14**

template <class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator1      // constexpr in C++20
    search(ForwardIterator1 first1, ForwardIterator1 last1,
           ForwardIterator2 first2, ForwardIterator2 last2);

template <class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
    constexpr ForwardIterator1      // constexpr in C++20
    search(ForwardIterator1 first1, ForwardIterator1 last1,
           ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred);

template <class ForwardIterator, class Size, class T>
    constexpr ForwardIterator       // constexpr in C++20
    search_n(ForwardIterator first, ForwardIterator last, Size count, const T& value);

template <class ForwardIterator, class Size, class T, class BinaryPredicate>
    constexpr ForwardIterator       // constexpr in C++20
    search_n(ForwardIterator first, ForwardIterator last,
             Size count, const T& value, BinaryPredicate pred);

template <class InputIterator, class OutputIterator>
    constexpr OutputIterator      // constexpr in C++20
    copy(InputIterator first, InputIterator last, OutputIterator result);

template<class InputIterator, class OutputIterator, class Predicate>
    constexpr OutputIterator      // constexpr in C++20
    copy_if(InputIterator first, InputIterator last,
            OutputIterator result, Predicate pred);

template<class InputIterator, class Size, class OutputIterator>
    constexpr OutputIterator      // constexpr in C++20
    copy_n(InputIterator first, Size n, OutputIterator result);

template <class BidirectionalIterator1, class BidirectionalIterator2>
    constexpr BidirectionalIterator2      // constexpr in C++20
    copy_backward(BidirectionalIterator1 first, BidirectionalIterator1 last,
                  BidirectionalIterator2 result);

template <class ForwardIterator1, class ForwardIterator2>
    constexpr ForwardIterator2    // constexpr in C++20
    swap_ranges(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2);

template<input_iterator I1, sentinel_for<I1> S1, input_iterator I2, sentinel_for<I2> S2>
        requires indirectly_swappable<I1, I2>
    constexpr ranges::swap_ranges_result<I1, I2>
        ranges::swap_ranges(I1 first1, S1 last1, I2 first2, S2 last2);

template<input_range R1, input_range R2>
        requires indirectly_swappable<iterator_t<R1>, iterator_t<R2>>
    constexpr ranges::swap_ranges_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>>
        ranges::swap_ranges(R1&& r1, R2&& r2);

template <class ForwardIterator1, class ForwardIterator2>
    constexpr void                // constexpr in C++20
    iter_swap(ForwardIterator1 a, ForwardIterator2 b);

template <class InputIterator, class OutputIterator, class UnaryOperation>
    constexpr OutputIterator      // constexpr in C++20
    transform(InputIterator first, InputIterator last, OutputIterator result, UnaryOperation op);

template <class InputIterator1, class InputIterator2, class OutputIterator, class BinaryOperation>
    constexpr OutputIterator      // constexpr in C++20
    transform(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2,
              OutputIterator result, BinaryOperation binary_op);

template <class ForwardIterator, class T>
    constexpr void      // constexpr in C++20
    replace(ForwardIterator first, ForwardIterator last, const T& old_value, const T& new_value);

template <class ForwardIterator, class Predicate, class T>
    constexpr void      // constexpr in C++20
    replace_if(ForwardIterator first, ForwardIterator last, Predicate pred, const T& new_value);

template <class InputIterator, class OutputIterator, class T>
    constexpr OutputIterator      // constexpr in C++20
    replace_copy(InputIterator first, InputIterator last, OutputIterator result,
                 const T& old_value, const T& new_value);

template <class InputIterator, class OutputIterator, class Predicate, class T>
    constexpr OutputIterator      // constexpr in C++20
    replace_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred, const T& new_value);

template <class ForwardIterator, class T>
    constexpr void      // constexpr in C++20
    fill(ForwardIterator first, ForwardIterator last, const T& value);

template <class OutputIterator, class Size, class T>
    constexpr OutputIterator      // constexpr in C++20
    fill_n(OutputIterator first, Size n, const T& value);

template <class ForwardIterator, class Generator>
    constexpr void      // constexpr in C++20
    generate(ForwardIterator first, ForwardIterator last, Generator gen);

template <class OutputIterator, class Size, class Generator>
    constexpr OutputIterator      // constexpr in C++20
    generate_n(OutputIterator first, Size n, Generator gen);

template <class ForwardIterator, class T>
    constexpr ForwardIterator     // constexpr in C++20
    remove(ForwardIterator first, ForwardIterator last, const T& value);

template <class ForwardIterator, class Predicate>
    constexpr ForwardIterator     // constexpr in C++20
    remove_if(ForwardIterator first, ForwardIterator last, Predicate pred);

template <class InputIterator, class OutputIterator, class T>
    constexpr OutputIterator     // constexpr in C++20
    remove_copy(InputIterator first, InputIterator last, OutputIterator result, const T& value);

template <class InputIterator, class OutputIterator, class Predicate>
    constexpr OutputIterator     // constexpr in C++20
    remove_copy_if(InputIterator first, InputIterator last, OutputIterator result, Predicate pred);

template <class ForwardIterator>
    constexpr ForwardIterator    // constexpr in C++20
    unique(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class BinaryPredicate>
    constexpr ForwardIterator    // constexpr in C++20
    unique(ForwardIterator first, ForwardIterator last, BinaryPredicate pred);

template <class InputIterator, class OutputIterator>
    constexpr OutputIterator     // constexpr in C++20
    unique_copy(InputIterator first, InputIterator last, OutputIterator result);

template <class InputIterator, class OutputIterator, class BinaryPredicate>
    constexpr OutputIterator     // constexpr in C++20
    unique_copy(InputIterator first, InputIterator last, OutputIterator result, BinaryPredicate pred);

template <class BidirectionalIterator>
    constexpr void               // constexpr in C++20
    reverse(BidirectionalIterator first, BidirectionalIterator last);

template <class BidirectionalIterator, class OutputIterator>
    constexpr OutputIterator       // constexpr in C++20
    reverse_copy(BidirectionalIterator first, BidirectionalIterator last, OutputIterator result);

template <class ForwardIterator>
    constexpr ForwardIterator      // constexpr in C++20
    rotate(ForwardIterator first, ForwardIterator middle, ForwardIterator last);

template <class ForwardIterator, class OutputIterator>
    constexpr OutputIterator       // constexpr in C++20
    rotate_copy(ForwardIterator first, ForwardIterator middle, ForwardIterator last, OutputIterator result);

template <class RandomAccessIterator>
    void
    random_shuffle(RandomAccessIterator first, RandomAccessIterator last); // deprecated in C++14, removed in C++17

template <class RandomAccessIterator, class RandomNumberGenerator>
    void
    random_shuffle(RandomAccessIterator first, RandomAccessIterator last,
                   RandomNumberGenerator& rand);  // deprecated in C++14, removed in C++17

template<class PopulationIterator, class SampleIterator,
         class Distance, class UniformRandomBitGenerator>
    SampleIterator sample(PopulationIterator first, PopulationIterator last,
                          SampleIterator out, Distance n,
                          UniformRandomBitGenerator&& g); // C++17

template<class RandomAccessIterator, class UniformRandomNumberGenerator>
    void shuffle(RandomAccessIterator first, RandomAccessIterator last,
                 UniformRandomNumberGenerator&& g);

template<class ForwardIterator>
  constexpr ForwardIterator
    shift_left(ForwardIterator first, ForwardIterator last,
               typename iterator_traits<ForwardIterator>::difference_type n); // C++20

template<class ForwardIterator>
  constexpr ForwardIterator
    shift_right(ForwardIterator first, ForwardIterator last,
                typename iterator_traits<ForwardIterator>::difference_type n); // C++20

template <class InputIterator, class Predicate>
    constexpr bool  // constexpr in C++20
    is_partitioned(InputIterator first, InputIterator last, Predicate pred);

template <class ForwardIterator, class Predicate>
    constexpr ForwardIterator  // constexpr in C++20
    partition(ForwardIterator first, ForwardIterator last, Predicate pred);

template <class InputIterator, class OutputIterator1,
          class OutputIterator2, class Predicate>
    constexpr pair<OutputIterator1, OutputIterator2>   // constexpr in C++20
    partition_copy(InputIterator first, InputIterator last,
                   OutputIterator1 out_true, OutputIterator2 out_false,
                   Predicate pred);

template <class ForwardIterator, class Predicate>
    ForwardIterator
    stable_partition(ForwardIterator first, ForwardIterator last, Predicate pred);

template<class ForwardIterator, class Predicate>
    constexpr ForwardIterator  // constexpr in C++20
    partition_point(ForwardIterator first, ForwardIterator last, Predicate pred);

template <class ForwardIterator>
    constexpr bool  // constexpr in C++20
    is_sorted(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class Compare>
    constexpr bool  // constexpr in C++20
    is_sorted(ForwardIterator first, ForwardIterator last, Compare comp);

template<class ForwardIterator>
    constexpr ForwardIterator    // constexpr in C++20
    is_sorted_until(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class Compare>
    constexpr ForwardIterator    // constexpr in C++20
    is_sorted_until(ForwardIterator first, ForwardIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr void               // constexpr in C++20
    sort(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void               // constexpr in C++20
    sort(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    void
    stable_sort(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    void
    stable_sort(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr void                    // constexpr in C++20
    partial_sort(RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                    // constexpr in C++20
    partial_sort(RandomAccessIterator first, RandomAccessIterator middle, RandomAccessIterator last, Compare comp);

template <class InputIterator, class RandomAccessIterator>
    constexpr RandomAccessIterator    // constexpr in C++20
    partial_sort_copy(InputIterator first, InputIterator last,
                      RandomAccessIterator result_first, RandomAccessIterator result_last);

template <class InputIterator, class RandomAccessIterator, class Compare>
    constexpr RandomAccessIterator    // constexpr in C++20
    partial_sort_copy(InputIterator first, InputIterator last,
                      RandomAccessIterator result_first, RandomAccessIterator result_last, Compare comp);

template <class RandomAccessIterator>
    constexpr void                    // constexpr in C++20
    nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                    // constexpr in C++20
    nth_element(RandomAccessIterator first, RandomAccessIterator nth, RandomAccessIterator last, Compare comp);

template <class ForwardIterator, class T>
    constexpr ForwardIterator                         // constexpr in C++20
    lower_bound(ForwardIterator first, ForwardIterator last, const T& value);

template <class ForwardIterator, class T, class Compare>
    constexpr ForwardIterator                         // constexpr in C++20
    lower_bound(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);

template <class ForwardIterator, class T>
    constexpr ForwardIterator                         // constexpr in C++20
    upper_bound(ForwardIterator first, ForwardIterator last, const T& value);

template <class ForwardIterator, class T, class Compare>
    constexpr ForwardIterator                         // constexpr in C++20
    upper_bound(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);

template <class ForwardIterator, class T>
    constexpr pair<ForwardIterator, ForwardIterator>  // constexpr in C++20
    equal_range(ForwardIterator first, ForwardIterator last, const T& value);

template <class ForwardIterator, class T, class Compare>
    constexpr pair<ForwardIterator, ForwardIterator>  // constexpr in C++20
    equal_range(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);

template <class ForwardIterator, class T>
    constexpr bool                                    // constexpr in C++20
    binary_search(ForwardIterator first, ForwardIterator last, const T& value);

template <class ForwardIterator, class T, class Compare>
    constexpr bool                                    // constexpr in C++20
    binary_search(ForwardIterator first, ForwardIterator last, const T& value, Compare comp);

template <class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator                          // constexpr in C++20
    merge(InputIterator1 first1, InputIterator1 last1,
          InputIterator2 first2, InputIterator2 last2, OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator                          // constexpr in C++20
    merge(InputIterator1 first1, InputIterator1 last1,
          InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp);

template <class BidirectionalIterator>
    void
    inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last);

template <class BidirectionalIterator, class Compare>
    void
    inplace_merge(BidirectionalIterator first, BidirectionalIterator middle, BidirectionalIterator last, Compare comp);

template <class InputIterator1, class InputIterator2>
    constexpr bool                                    // constexpr in C++20
    includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2);

template <class InputIterator1, class InputIterator2, class Compare>
    constexpr bool                                    // constexpr in C++20
    includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp);

template <class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator                          // constexpr in C++20
    set_union(InputIterator1 first1, InputIterator1 last1,
              InputIterator2 first2, InputIterator2 last2, OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator                          // constexpr in C++20
    set_union(InputIterator1 first1, InputIterator1 last1,
              InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp);

template <class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator                         // constexpr in C++20
    set_intersection(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2, OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator                         // constexpr in C++20
    set_intersection(InputIterator1 first1, InputIterator1 last1,
                     InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp);

template <class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator                         // constexpr in C++20
    set_difference(InputIterator1 first1, InputIterator1 last1,
                   InputIterator2 first2, InputIterator2 last2, OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator                         // constexpr in C++20
    set_difference(InputIterator1 first1, InputIterator1 last1,
                   InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp);

template <class InputIterator1, class InputIterator2, class OutputIterator>
    constexpr OutputIterator                         // constexpr in C++20
    set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
                             InputIterator2 first2, InputIterator2 last2, OutputIterator result);

template <class InputIterator1, class InputIterator2, class OutputIterator, class Compare>
    constexpr OutputIterator                         // constexpr in C++20
    set_symmetric_difference(InputIterator1 first1, InputIterator1 last1,
                             InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp);

template <class RandomAccessIterator>
    constexpr void                                   // constexpr in C++20
    push_heap(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                                   // constexpr in C++20
    push_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr void                                   // constexpr in C++20
    pop_heap(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                                   // constexpr in C++20
    pop_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr void                                   // constexpr in C++20
    make_heap(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                                   // constexpr in C++20
    make_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr void                                   // constexpr in C++20
    sort_heap(RandomAccessIterator first, RandomAccessIterator last);

template <class RandomAccessIterator, class Compare>
    constexpr void                                   // constexpr in C++20
    sort_heap(RandomAccessIterator first, RandomAccessIterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr bool   // constexpr in C++20
    is_heap(RandomAccessIterator first, RandomAccessiterator last);

template <class RandomAccessIterator, class Compare>
    constexpr bool   // constexpr in C++20
    is_heap(RandomAccessIterator first, RandomAccessiterator last, Compare comp);

template <class RandomAccessIterator>
    constexpr RandomAccessIterator   // constexpr in C++20
    is_heap_until(RandomAccessIterator first, RandomAccessiterator last);

template <class RandomAccessIterator, class Compare>
    constexpr RandomAccessIterator   // constexpr in C++20
    is_heap_until(RandomAccessIterator first, RandomAccessiterator last, Compare comp);

template <class ForwardIterator>
    constexpr ForwardIterator        // constexpr in C++14
    min_element(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class Compare>
    constexpr ForwardIterator        // constexpr in C++14
    min_element(ForwardIterator first, ForwardIterator last, Compare comp);

template <class T>
    constexpr const T&               // constexpr in C++14
    min(const T& a, const T& b);

template <class T, class Compare>
    constexpr const T&               // constexpr in C++14
    min(const T& a, const T& b, Compare comp);

template<class T>
    constexpr T                      // constexpr in C++14
    min(initializer_list<T> t);

template<class T, class Compare>
    constexpr T                      // constexpr in C++14
    min(initializer_list<T> t, Compare comp);

template<class T>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi);               // C++17

template<class T, class Compare>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi, Compare comp); // C++17

template <class ForwardIterator>
    constexpr ForwardIterator        // constexpr in C++14
    max_element(ForwardIterator first, ForwardIterator last);

template <class ForwardIterator, class Compare>
    constexpr ForwardIterator        // constexpr in C++14
    max_element(ForwardIterator first, ForwardIterator last, Compare comp);

template <class T>
    constexpr const T&               // constexpr in C++14
    max(const T& a, const T& b);

template <class T, class Compare>
    constexpr const T&               // constexpr in C++14
    max(const T& a, const T& b, Compare comp);

template<class T>
    constexpr T                      // constexpr in C++14
    max(initializer_list<T> t);

template<class T, class Compare>
    constexpr T                      // constexpr in C++14
    max(initializer_list<T> t, Compare comp);

template<class ForwardIterator>
    constexpr pair<ForwardIterator, ForwardIterator>  // constexpr in C++14
    minmax_element(ForwardIterator first, ForwardIterator last);

template<class ForwardIterator, class Compare>
    constexpr pair<ForwardIterator, ForwardIterator>  // constexpr in C++14
    minmax_element(ForwardIterator first, ForwardIterator last, Compare comp);

template<class T>
    constexpr pair<const T&, const T&>  // constexpr in C++14
    minmax(const T& a, const T& b);

template<class T, class Compare>
    constexpr pair<const T&, const T&>  // constexpr in C++14
    minmax(const T& a, const T& b, Compare comp);

template<class T>
    constexpr pair<T, T>                // constexpr in C++14
    minmax(initializer_list<T> t);

template<class T, class Compare>
    constexpr pair<T, T>                // constexpr in C++14
    minmax(initializer_list<T> t, Compare comp);

template <class InputIterator1, class InputIterator2>
    constexpr bool     // constexpr in C++20
    lexicographical_compare(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2);

template <class InputIterator1, class InputIterator2, class Compare>
    constexpr bool     // constexpr in C++20
    lexicographical_compare(InputIterator1 first1, InputIterator1 last1,
                            InputIterator2 first2, InputIterator2 last2, Compare comp);

template <class BidirectionalIterator>
    constexpr bool     // constexpr in C++20
    next_permutation(BidirectionalIterator first, BidirectionalIterator last);

template <class BidirectionalIterator, class Compare>
    constexpr bool     // constexpr in C++20
    next_permutation(BidirectionalIterator first, BidirectionalIterator last, Compare comp);

template <class BidirectionalIterator>
    constexpr bool     // constexpr in C++20
    prev_permutation(BidirectionalIterator first, BidirectionalIterator last);

template <class BidirectionalIterator, class Compare>
    constexpr bool     // constexpr in C++20
    prev_permutation(BidirectionalIterator first, BidirectionalIterator last, Compare comp);
}  // std

*/

#include <__assert> // all public C++ headers provide the assertion handler
#include <__bits>
#include <__config>
#include <__debug>
#include <cstddef>
#include <cstring>
#include <functional>
#include <initializer_list>
#include <iterator>
#include <memory>
#include <type_traits>
#include <version>

#include <__algorithm/adjacent_find.h>
#include <__algorithm/all_of.h>
#include <__algorithm/any_of.h>
#include <__algorithm/binary_search.h>
#include <__algorithm/clamp.h>
#include <__algorithm/comp.h>
#include <__algorithm/comp_ref_type.h>
#include <__algorithm/copy.h>
#include <__algorithm/copy_backward.h>
#include <__algorithm/copy_if.h>
#include <__algorithm/copy_n.h>
#include <__algorithm/count.h>
#include <__algorithm/count_if.h>
#include <__algorithm/equal.h>
#include <__algorithm/equal_range.h>
#include <__algorithm/fill.h>
#include <__algorithm/fill_n.h>
#include <__algorithm/find.h>
#include <__algorithm/find_end.h>
#include <__algorithm/find_first_of.h>
#include <__algorithm/find_if.h>
#include <__algorithm/find_if_not.h>
#include <__algorithm/for_each.h>
#include <__algorithm/for_each_n.h>
#include <__algorithm/generate.h>
#include <__algorithm/generate_n.h>
#include <__algorithm/half_positive.h>
#include <__algorithm/in_found_result.h>
#include <__algorithm/in_fun_result.h>
#include <__algorithm/in_in_out_result.h>
#include <__algorithm/in_in_result.h>
#include <__algorithm/in_out_out_result.h>
#include <__algorithm/in_out_result.h>
#include <__algorithm/includes.h>
#include <__algorithm/inplace_merge.h>
#include <__algorithm/is_heap.h>
#include <__algorithm/is_heap_until.h>
#include <__algorithm/is_partitioned.h>
#include <__algorithm/is_permutation.h>
#include <__algorithm/is_sorted.h>
#include <__algorithm/is_sorted_until.h>
#include <__algorithm/iter_swap.h>
#include <__algorithm/lexicographical_compare.h>
#include <__algorithm/lower_bound.h>
#include <__algorithm/make_heap.h>
#include <__algorithm/max.h>
#include <__algorithm/max_element.h>
#include <__algorithm/merge.h>
#include <__algorithm/min.h>
#include <__algorithm/min_element.h>
#include <__algorithm/min_max_result.h>
#include <__algorithm/minmax.h>
#include <__algorithm/minmax_element.h>
#include <__algorithm/mismatch.h>
#include <__algorithm/move.h>
#include <__algorithm/move_backward.h>
#include <__algorithm/next_permutation.h>
#include <__algorithm/none_of.h>
#include <__algorithm/nth_element.h>
#include <__algorithm/partial_sort.h>
#include <__algorithm/partial_sort_copy.h>
#include <__algorithm/partition.h>
#include <__algorithm/partition_copy.h>
#include <__algorithm/partition_point.h>
#include <__algorithm/pop_heap.h>
#include <__algorithm/prev_permutation.h>
#include <__algorithm/push_heap.h>
#include <__algorithm/ranges_find.h>
#include <__algorithm/ranges_find_if.h>
#include <__algorithm/ranges_find_if_not.h>
#include <__algorithm/ranges_max.h>
#include <__algorithm/ranges_max_element.h>
#include <__algorithm/ranges_min.h>
#include <__algorithm/ranges_min_element.h>
#include <__algorithm/ranges_mismatch.h>
#include <__algorithm/ranges_swap_ranges.h>
#include <__algorithm/ranges_transform.h>
#include <__algorithm/remove.h>
#include <__algorithm/remove_copy.h>
#include <__algorithm/remove_copy_if.h>
#include <__algorithm/remove_if.h>
#include <__algorithm/replace.h>
#include <__algorithm/replace_copy.h>
#include <__algorithm/replace_copy_if.h>
#include <__algorithm/replace_if.h>
#include <__algorithm/reverse.h>
#include <__algorithm/reverse_copy.h>
#include <__algorithm/rotate.h>
#include <__algorithm/rotate_copy.h>
#include <__algorithm/sample.h>
#include <__algorithm/search.h>
#include <__algorithm/search_n.h>
#include <__algorithm/set_difference.h>
#include <__algorithm/set_intersection.h>
#include <__algorithm/set_symmetric_difference.h>
#include <__algorithm/set_union.h>
#include <__algorithm/shift_left.h>
#include <__algorithm/shift_right.h>
#include <__algorithm/shuffle.h>
#include <__algorithm/sift_down.h>
#include <__algorithm/sort.h>
#include <__algorithm/sort_heap.h>
#include <__algorithm/stable_partition.h>
#include <__algorithm/stable_sort.h>
#include <__algorithm/swap_ranges.h>
#include <__algorithm/transform.h>
#include <__algorithm/unique.h>
#include <__algorithm/unique_copy.h>
#include <__algorithm/unwrap_iter.h>
#include <__algorithm/upper_bound.h>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#  pragma GCC system_header
#endif

#if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17
#   include <__pstl_algorithm>
#endif

#endif // _LIBCPP_ALGORITHM