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Standard library header <algorithm>

From cppreference.com
< cpp‎ | header
 
 
 

This header is part of the algorithm library.

Contents

[edit] Functions

Non-modifying sequence operations
(C++11)(C++11)(C++11)
checks if a predicate is true for all, any or none of the elements in a range
(function template) [edit]
applies a function to a range of elements
(function template) [edit]
applies a function object to the first n elements of a sequence
(function template) [edit]
returns the number of elements satisfying specific criteria
(function template) [edit]
finds the first position where two ranges differ
(function template) [edit]
finds the first element satisfying specific criteria
(function template) [edit]
finds the last sequence of elements in a certain range
(function template) [edit]
searches for any one of a set of elements
(function template) [edit]
finds the first two adjacent items that are equal (or satisfy a given predicate)
(function template) [edit]
searches for a range of elements
(function template) [edit]
searches a range for a number of consecutive copies of an element
(function template) [edit]
Modifying sequence operations
copies a range of elements to a new location
(function template) [edit]
(C++11)
copies a number of elements to a new location
(function template) [edit]
copies a range of elements in backwards order
(function template) [edit]
(C++11)
moves a range of elements to a new location
(function template) [edit]
moves a range of elements to a new location in backwards order
(function template) [edit]
copy-assigns the given value to every element in a range
(function template) [edit]
copy-assigns the given value to N elements in a range
(function template) [edit]
applies a function to a range of elements, storing results in a destination range
(function template) [edit]
assigns the results of successive function calls to every element in a range
(function template) [edit]
assigns the results of successive function calls to N elements in a range
(function template) [edit]
removes elements satisfying specific criteria
(function template) [edit]
copies a range of elements omitting those that satisfy specific criteria
(function template) [edit]
replaces all values satisfying specific criteria with another value
(function template) [edit]
copies a range, replacing elements satisfying specific criteria with another value
(function template) [edit]
swaps the values of two objects
(function template) [edit]
swaps two ranges of elements
(function template) [edit]
swaps the elements pointed to by two iterators
(function template) [edit]
reverses the order of elements in a range
(function template) [edit]
creates a copy of a range that is reversed
(function template) [edit]
rotates the order of elements in a range
(function template) [edit]
copies and rotate a range of elements
(function template) [edit]
shifts elements in a range
(function template) [edit]
(until C++17)(C++11)
randomly re-orders elements in a range
(function template) [edit]
(C++17)
selects n random elements from a sequence
(function template) [edit]
removes consecutive duplicate elements in a range
(function template) [edit]
creates a copy of some range of elements that contains no consecutive duplicates
(function template) [edit]
Partitioning operations
determines if the range is partitioned by the given predicate
(function template) [edit]
divides a range of elements into two groups
(function template) [edit]
copies a range dividing the elements into two groups
(function template) [edit]
divides elements into two groups while preserving their relative order
(function template) [edit]
locates the partition point of a partitioned range
(function template) [edit]
Sorting operations
(C++11)
checks whether a range is sorted into ascending order
(function template) [edit]
finds the largest sorted subrange
(function template) [edit]
sorts a range into ascending order
(function template) [edit]
sorts the first N elements of a range
(function template) [edit]
copies and partially sorts a range of elements
(function template) [edit]
sorts a range of elements while preserving order between equal elements
(function template) [edit]
partially sorts the given range making sure that it is partitioned by the given element
(function template) [edit]
Binary search operations (on sorted ranges)
returns an iterator to the first element not less than the given value
(function template) [edit]
returns an iterator to the first element greater than a certain value
(function template) [edit]
determines if an element exists in a certain range
(function template) [edit]
returns range of elements matching a specific key
(function template) [edit]
Other operations on sorted ranges
merges two sorted ranges
(function template) [edit]
merges two ordered ranges in-place
(function template) [edit]
Set operations (on sorted ranges)
returns true if one set is a subset of another
(function template) [edit]
computes the difference between two sets
(function template) [edit]
computes the intersection of two sets
(function template) [edit]
computes the symmetric difference between two sets
(function template) [edit]
computes the union of two sets
(function template) [edit]
Heap operations
(C++11)
checks if the given range is a max heap
(function template) [edit]
finds the largest subrange that is a max heap
(function template) [edit]
creates a max heap out of a range of elements
(function template) [edit]
adds an element to a max heap
(function template) [edit]
removes the largest element from a max heap
(function template) [edit]
turns a max heap into a range of elements sorted in ascending order
(function template) [edit]
Minimum/maximum operations
returns the greater of the given values
(function template) [edit]
returns the largest element in a range
(function template) [edit]
returns the smaller of the given values
(function template) [edit]
returns the smallest element in a range
(function template) [edit]
(C++11)
returns the smaller and larger of two elements
(function template) [edit]
returns the smallest and the largest elements in a range
(function template) [edit]
(C++17)
clamps a value between a pair of boundary values
(function template) [edit]
Comparison operations
determines if two sets of elements are the same
(function template) [edit]
returns true if one range is lexicographically less than another
(function template) [edit]
compares two ranges using three-way comparison
(function template) [edit]
Permutation operations
determines if a sequence is a permutation of another sequence
(function template) [edit]
generates the next greater lexicographic permutation of a range of elements
(function template) [edit]
generates the next smaller lexicographic permutation of a range of elements
(function template) [edit]

[edit] Niebloids

Defined in namespace std::ranges
Non-modifying sequence operations
checks if a predicate is true for all, any or none of the elements in a range
(niebloid) [edit]
applies a function to a range of elements
(niebloid) [edit]
returns the number of elements satisfying specific criteria
(niebloid) [edit]
finds the first position where two ranges differ
(niebloid) [edit]
finds the first element satisfying specific criteria
(niebloid) [edit]
finds the last sequence of elements in a certain range
(niebloid) [edit]
searches for any one of a set of elements
(niebloid) [edit]
finds the first two adjacent items that are equal (or satisfy a given predicate)
(niebloid) [edit]
searches for a range of elements
(niebloid) [edit]
searches for a number consecutive copies of an element in a range
(niebloid) [edit]
Modifying sequence operations
copies a range of elements to a new location
(niebloid) [edit]
copies a number of elements to a new location
(niebloid) [edit]
copies a range of elements in backwards order
(niebloid) [edit]
moves a range of elements to a new location
(niebloid) [edit]
moves a range of elements to a new location in backwards order
(niebloid) [edit]
assigns a range of elements a certain value
(niebloid) [edit]
assigns a value to a number of elements
(niebloid) [edit]
applies a function to a range of elements
(niebloid) [edit]
saves the result of a function in a range
(niebloid) [edit]
saves the result of N applications of a function
(niebloid) [edit]
removes elements satisfying specific criteria
(niebloid) [edit]
copies a range of elements omitting those that satisfy specific criteria
(niebloid) [edit]
replaces all values satisfying specific criteria with another value
(niebloid) [edit]
copies a range, replacing elements satisfying specific criteria with another value
(niebloid) [edit]
swaps two ranges of elements
(niebloid) [edit]
reverses the order of elements in a range
(niebloid) [edit]
creates a copy of a range that is reversed
(niebloid) [edit]
rotates the order of elements in a range
(niebloid) [edit]
copies and rotate a range of elements
(niebloid) [edit]
randomly re-orders elements in a range
(niebloid) [edit]
removes consecutive duplicate elements in a range
(niebloid) [edit]
creates a copy of some range of elements that contains no consecutive duplicates
(niebloid) [edit]
Partitioning operations
determines if the range is partitioned by the given predicate
(niebloid) [edit]
divides a range of elements into two groups
(niebloid) [edit]
copies a range dividing the elements into two groups
(niebloid) [edit]
divides elements into two groups while preserving their relative order
(niebloid) [edit]
locates the partition point of a partitioned range
(niebloid) [edit]
Sorting operations
checks whether a range is sorted into ascending order
(niebloid) [edit]
finds the largest sorted subrange
(niebloid) [edit]
sorts a range into ascending order
(niebloid) [edit]
sorts the first N elements of a range
(niebloid) [edit]
copies and partially sorts a range of elements
(niebloid) [edit]
sorts a range of elements while preserving order between equal elements
(niebloid) [edit]
partially sorts the given range making sure that it is partitioned by the given element
(niebloid) [edit]
Binary search operations (on sorted ranges)
returns an iterator to the first element not less than the given value
(niebloid) [edit]
returns an iterator to the first element greater than a certain value
(niebloid) [edit]
determines if an element exists in a certain range
(niebloid) [edit]
returns range of elements matching a specific key
(niebloid) [edit]
Other operations on sorted ranges
merges two sorted ranges
(niebloid) [edit]
merges two ordered ranges in-place
(niebloid) [edit]
Set operations (on sorted ranges)
returns true if one set is a subset of another
(niebloid) [edit]
computes the difference between two sets
(niebloid) [edit]
computes the intersection of two sets
(niebloid) [edit]
computes the symmetric difference between two sets
(niebloid) [edit]
computes the union of two sets
(niebloid) [edit]
Heap operations
checks if the given range is a max heap
(niebloid) [edit]
finds the largest subrange that is a max heap
(niebloid) [edit]
creates a max heap out of a range of elements
(niebloid) [edit]
adds an element to a max heap
(niebloid) [edit]
removes the largest element from a max heap
(niebloid) [edit]
turns a max heap into a range of elements sorted in ascending order
(niebloid) [edit]
Minimum/maximum operations
returns the greater of the given values
(niebloid) [edit]
returns the largest element in a range
(niebloid) [edit]
returns the smaller of the given values
(niebloid) [edit]
returns the smallest element in a range
(niebloid) [edit]
returns the smaller and larger of two elements
(niebloid) [edit]
returns the smallest and the largest elements in a range
(niebloid) [edit]
Comparison operations
determines if two sets of elements are the same
(niebloid) [edit]
returns true if one range is lexicographically less than another
(niebloid) [edit]
Permutation operations
determines if a sequence is a permutation of another sequence
(niebloid) [edit]
generates the next greater lexicographic permutation of a range of elements
(niebloid) [edit]
generates the next smaller lexicographic permutation of a range of elements
(niebloid) [edit]

[edit] Synopsis

#include <initializer_list>
 
namespace std {
  // non-modifying sequence operations
  // all of
  template<class InputIter, class Pred>
    constexpr bool all_of(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    bool all_of(ExecutionPolicy&& exec,
                ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool all_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool all_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // any of
  template<class InputIter, class Pred>
    constexpr bool any_of(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    bool any_of(ExecutionPolicy&& exec,
                ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool any_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool any_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // none of
  template<class InputIter, class Pred>
    constexpr bool none_of(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    bool none_of(ExecutionPolicy&& exec,
                 ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool none_of(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool none_of(R&& r, Pred pred, Proj proj = {});
  }
 
  // for each
  template<class InputIter, class Function>
    constexpr Function for_each(InputIter first, InputIter last, Function f);
  template<class ExecutionPolicy, class ForwardIter, class Function>
    void for_each(ExecutionPolicy&& exec,
                  ForwardIter first, ForwardIter last, Function f);
 
  namespace ranges {
    template<class I, class F>
    struct for_each_result {
      [[no_unique_address]] I in;
      [[no_unique_address]] F fun;
 
      template<class I2, class F2>
        requires convertible_to<const I&, I2> && convertible_to<const F&, F2>
        operator for_each_result<I2, F2>() const & {
          return {in, fun};
        }
 
      template<class I2, class F2>
        requires convertible_to<I, I2> && convertible_to<F, F2>
        operator for_each_result<I2, F2>() && {
          return {std::move(in), std::move(fun)};
        }
    };
 
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirectly_unary_invocable<projected<I, Proj>> Fun>
      constexpr for_each_result<I, Fun>
        for_each(I first, S last, Fun f, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirectly_unary_invocable<projected<iterator_t<R>, Proj>> Fun>
      constexpr for_each_result<safe_iterator_t<R>, Fun>
        for_each(R&& r, Fun f, Proj proj = {});
  }
 
  template<class InputIter, class Size, class Function>
    constexpr InputIter for_each_n(InputIter first, Size n, Function f);
  template<class ExecutionPolicy, class ForwardIter, class Size, class Function>
    ForwardIter for_each_n(ExecutionPolicy&& exec,
                           ForwardIter first, Size n, Function f);
 
  // find
  template<class InputIter, class T>
    constexpr InputIter find(InputIter first, InputIter last, const T& value);
  template<class ExecutionPolicy, class ForwardIter, class T>
    ForwardIter find(ExecutionPolicy&& exec,
                     ForwardIter first, ForwardIter last,const T& value);
  template<class InputIter, class Pred>
    constexpr InputIter find_if(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    ForwardIter find_if(ExecutionPolicy&& exec,
                        ForwardIter first, ForwardIter last, Pred pred);
  template<class InputIter, class Pred>
    constexpr InputIter find_if_not(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    ForwardIter find_if_not(ExecutionPolicy&& exec,
                            ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_relation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr I find(I first, S last, const T& value, Proj proj = {});
    template<input_range R, class T, class Proj = identity>
      requires indirect_relation<ranges::equal_to,
                                 projected<iterator_t<R>, Proj>, const T*>
      constexpr safe_iterator_t<R>
        find(R&& r, const T& value, Proj proj = {});
    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 = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        find_if(R&& r, Pred pred, Proj proj = {});
    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 = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        find_if_not(R&& r, Pred pred, Proj proj = {});
  }
 
  // find end
  template<class ForwardIter1, class ForwardIter2>
    constexpr ForwardIter1
      find_end(ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2);
  template<class ForwardIter1, class ForwardIter2, class BinaryPred>
    constexpr ForwardIter1
      find_end(ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter1
      find_end(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1,
           class ForwardIter2, class BinaryPred>
    ForwardIter1
      find_end(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
 
  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1,
             forward_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 subrange<I1>
        find_end(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_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 safe_subrange_t<R1>
        find_end(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // find first
  template<class InputIter, class ForwardIter>
    constexpr InputIter
      find_first_of(InputIter first1, InputIter last1,
                    ForwardIter first2, ForwardIter last2);
  template<class InputIter, class ForwardIter, class BinaryPred>
    constexpr InputIter
      find_first_of(InputIter first1, InputIter last1,
                    ForwardIter first2, ForwardIter last2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter1
      find_first_of(ExecutionPolicy&& exec,
                    ForwardIter1 first1, ForwardIter1 last1,
                    ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1,
           class ForwardIter2, class BinaryPred>
    ForwardIter1
      find_first_of(ExecutionPolicy&& exec,
                    ForwardIter1 first1, ForwardIter1 last1,
                    ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
 
  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1,
             forward_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_relation<projected<I1, Proj1>,
                               projected<I2, Proj2>> Pred = ranges::equal_to>
      constexpr I1 find_first_of(I1 first1, S1 last1, I2 first2, S2 last2,
                                 Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, forward_range R2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_relation<projected<iterator_t<R1>, Proj1>,
                               projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to>
      constexpr safe_iterator_t<R1>
        find_first_of(R1&& r1, R2&& r2, Pred pred = {},
                      Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // adjacent find
  template<class ForwardIter>
    constexpr ForwardIter
      adjacent_find(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class BinaryPred>
    constexpr ForwardIter
      adjacent_find(ForwardIter first, ForwardIter last, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter
      adjacent_find(ExecutionPolicy&& exec,
                    ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class BinaryPred>
    ForwardIter
      adjacent_find(ExecutionPolicy&& exec,
                    ForwardIter first, ForwardIter last, BinaryPred pred);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_relation<projected<I, Proj>> Pred = ranges::equal_to>
      constexpr I adjacent_find(I first, S last, Pred pred = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_relation<projected<iterator_t<R>, Proj>> Pred = ranges::equal_to>
      constexpr safe_iterator_t<R>
        adjacent_find(R&& r, Pred pred = {}, Proj proj = {});
  }
 
  // count
  template<class InputIter, class T>
    constexpr typename iterator_traits<InputIter>::difference_type
      count(InputIter first, InputIter last, const T& value);
  template<class ExecutionPolicy, class ForwardIter, class T>
    typename iterator_traits<ForwardIter>::difference_type
      count(ExecutionPolicy&& exec,
            ForwardIter first, ForwardIter last, const T& value);
  template<class InputIter, class Pred>
    constexpr typename iterator_traits<InputIter>::difference_type
      count_if(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    typename iterator_traits<ForwardIter>::difference_type
      count_if(ExecutionPolicy&& exec,
               ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_relation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr iter_difference_t<I>
        count(I first, S last, const T& value, Proj proj = {});
    template<input_range R, class T, class Proj = identity>
      requires indirect_relation<ranges::equal_to, projected<iterator_t<R>, Proj>,
                                 const T*>
      constexpr range_difference_t<R>
        count(R&& r, const T& value, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr iter_difference_t<I>
        count_if(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr range_difference_t<R>
        count_if(R&& r, Pred pred, Proj proj = {});
  }
 
  // mismatch
  template<class InputIter1, class InputIter2>
    constexpr pair<InputIter1, InputIter2>
      mismatch(InputIter1 first1, InputIter1 last1, InputIter2 first2);
  template<class InputIter1, class InputIter2, class BinaryPred>
    constexpr pair<InputIter1, InputIter2>
      mismatch(InputIter1 first1, InputIter1 last1, InputIter2 first2, BinaryPred pred);
  template<class InputIter1, class InputIter2>
    constexpr pair<InputIter1, InputIter2>
      mismatch(InputIter1 first1, InputIter1 last1, InputIter2 first2, InputIter2 last2);
  template<class InputIter1, class InputIter2, class BinaryPred>
    constexpr pair<InputIter1, InputIter2>
      mismatch(InputIter1 first1, InputIter1 last1, InputIter2 first2, InputIter2 last2,
               BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    pair<ForwardIter1, ForwardIter2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1, ForwardIter2 first2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    pair<ForwardIter1, ForwardIter2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    pair<ForwardIter1, ForwardIter2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    pair<ForwardIter1, ForwardIter2>
      mismatch(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
 
  namespace ranges {
    template<class I1, class I2>
    struct mismatch_result {
      [[no_unique_address]] I1 in1;
      [[no_unique_address]] I2 in2;
 
      template<class II1, class II2>
        requires convertible_to<const I1&, II1> && convertible_to<const I2&, II2>
        operator mismatch_result<II1, II2>() const & {
          return {in1, in2};
        }
 
      template<class II1, class II2>
        requires convertible_to<I1, II1> && convertible_to<I2, II2>
        operator mismatch_result<II1, II2>() && {
          return {std::move(in1), std::move(in2)};
        }
    };
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_relation<projected<I1, Proj1>,
                               projected<I2, Proj2>> Pred = ranges::equal_to>
      constexpr mismatch_result<I1, I2>
        mismatch(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_relation<projected<iterator_t<R1>, Proj1>,
                               projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to>
      constexpr mismatch_result<safe_iterator_t<R1>, safe_iterator_t<R2>>
        mismatch(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // equal
  template<class InputIter1, class InputIter2>
    constexpr bool equal(InputIter1 first1, InputIter1 last1, InputIter2 first2);
  template<class InputIter1, class InputIter2, class BinaryPred>
    constexpr bool equal(InputIter1 first1, InputIter1 last1,
                         InputIter2 first2, BinaryPred pred);
  template<class InputIter1, class InputIter2>
    constexpr bool equal(InputIter1 first1, InputIter1 last1,
                         InputIter2 first2, InputIter2 last2);
  template<class InputIter1, class InputIter2, class BinaryPred>
    constexpr bool equal(InputIter1 first1, InputIter1 last1,
                         InputIter2 first2, InputIter2 last2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    bool equal(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1, ForwardIter2 first2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    bool equal(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    bool equal(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    bool equal(ExecutionPolicy&& exec,
               ForwardIter1 first1, ForwardIter1 last1,
               ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
 
  namespace ranges {
    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 bool equal(I1 first1, S1 last1, I2 first2, S2 last2,
                           Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    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 bool equal(R1&& r1, R2&& r2, Pred pred = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // is permutation
  template<class ForwardIter1, class ForwardIter2>
    constexpr bool is_permutation(ForwardIter1 first1, ForwardIter1 last1,
                                  ForwardIter2 first2);
  template<class ForwardIter1, class ForwardIter2, class BinaryPred>
    constexpr bool is_permutation(ForwardIter1 first1, ForwardIter1 last1,
                                  ForwardIter2 first2, BinaryPred pred);
  template<class ForwardIter1, class ForwardIter2>
    constexpr bool is_permutation(ForwardIter1 first1, ForwardIter1 last1,
                                  ForwardIter2 first2, ForwardIter2 last2);
  template<class ForwardIter1, class ForwardIter2, class BinaryPred>
    constexpr bool is_permutation(ForwardIter1 first1, ForwardIter1 last1,
                                  ForwardIter2 first2, ForwardIter2 last2,
                                  BinaryPred pred);
 
  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1, forward_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 bool is_permutation(I1 first1, S1 last1, I2 first2, S2 last2,
                                    Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_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 bool is_permutation(R1&& r1, R2&& r2, Pred pred = {},
                                    Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // search
  template<class ForwardIter1, class ForwardIter2>
    constexpr ForwardIter1
      search(ForwardIter1 first1, ForwardIter1 last1,
             ForwardIter2 first2, ForwardIter2 last2);
  template<class ForwardIter1, class ForwardIter2, class BinaryPred>
    constexpr ForwardIter1
      search(ForwardIter1 first1, ForwardIter1 last1,
             ForwardIter2 first2, ForwardIter2 last2,
             BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter1
      search(ExecutionPolicy&& exec,
             ForwardIter1 first1, ForwardIter1 last1,
             ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    ForwardIter1
      search(ExecutionPolicy&& exec,
             ForwardIter1 first1, ForwardIter1 last1,
             ForwardIter2 first2, ForwardIter2 last2, BinaryPred pred);
 
  namespace ranges {
    template<forward_iterator I1, sentinel_for<I1> S1, forward_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 subrange<I1>
        search(I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {},
               Proj1 proj1 = {}, Proj2 proj2 = {});
    template<forward_range R1, forward_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 safe_subrange_t<R1>
        search(R1&& r1, R2&& r2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class ForwardIter, class Size, class T>
    constexpr ForwardIter
      search_n(ForwardIter first, ForwardIter last, Size count, const T& value);
  template<class ForwardIter, class Size, class T, class BinaryPred>
    constexpr ForwardIter
      search_n(ForwardIter first, ForwardIter last, Size count, const T& value,
               BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter, class Size, class T>
    ForwardIter
      search_n(ExecutionPolicy&& exec,
               ForwardIter first, ForwardIter last, Size count, const T& value);
  template<class ExecutionPolicy, class ForwardIter, class Size, class T,
           class BinaryPred>
    ForwardIter
      search_n(ExecutionPolicy&& exec,
               ForwardIter first, ForwardIter last, Size count, const T& value,
               BinaryPred pred);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T,
             class Pred = ranges::equal_to, class Proj = identity>
      requires indirectly_comparable<I, const T*, Pred, Proj>
      constexpr subrange<I>
        search_n(I first, S last, iter_difference_t<I> count,
                 const T& value, Pred pred = {}, Proj proj = {});
    template<forward_range R, class T, class Pred = ranges::equal_to,
             class Proj = identity>
      requires indirectly_comparable<iterator_t<R>, const T*, Pred, Proj>
      constexpr safe_subrange_t<R>
        search_n(R&& r, range_difference_t<R> count,
                 const T& value, Pred pred = {}, Proj proj = {});
  }
 
  template<class ForwardIter, class Searcher>
    constexpr ForwardIter
      search(ForwardIter first, ForwardIter last, const Searcher& searcher);
 
  // mutating sequence operations
  // copy
  template<class InputIter, class OutputIter>
    constexpr OutputIter copy(InputIter first, InputIter last, OutputIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter2 copy(ExecutionPolicy&& exec,
                      ForwardIter1 first, ForwardIter1 last, ForwardIter2 result);
 
  namespace ranges {
    template<class I, class O>
    struct copy_result {
      [[no_unique_address]] I in;
      [[no_unique_address]] O out;
 
      template<class I2, class O2>
        requires convertible_to<const I&, I2> && convertible_to<const O&, O2>
        operator copy_result<I2, O2>() const & {
          return {in, out};
        }
 
      template<class I2, class O2>
        requires convertible_to<I, I2> && convertible_to<O, O2>
        operator copy_result<I2, O2>() && {
          return {std::move(in), std::move(out)};
        }
    };
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr copy_result<I, O>
        copy(I first, S last, O result);
    template<input_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr copy_result<safe_iterator_t<R>, O>
        copy(R&& r, O result);
  }
 
  template<class InputIter, class Size, class OutputIter>
    constexpr OutputIter copy_n(InputIter first, Size n, OutputIter result);
  template<class ExecutionPolicy, class ForwardIter1, class Size,
           class ForwardIter2>
    ForwardIter2 copy_n(ExecutionPolicy&& exec,
                        ForwardIter1 first, Size n, ForwardIter2 result);
 
  namespace ranges {
    template<class I, class O>
    using copy_n_result = copy_result<I, O>;
 
    template<input_iterator I, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr copy_n_result<I, O>
        copy_n(I first, iter_difference_t<I> n, O result);
  }
 
  template<class InputIter, class OutputIter, class Pred>
    constexpr OutputIter copy_if(InputIter first, InputIter last,
                                 OutputIter result, Pred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class Pred>
    ForwardIter2 copy_if(ExecutionPolicy&& exec,
                         ForwardIter1 first, ForwardIter1 last,
                         ForwardIter2 result, Pred pred);
 
  namespace ranges {
    template<class I, class O>
    using copy_if_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S,
             weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr copy_if_result<I, O>
        copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr copy_if_result<safe_iterator_t<R>, O>
        copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }
 
  template<class BidirectionalIter1, class BidirectionalIter2>
    constexpr BidirectionalIter2
      copy_backward(BidirectionalIter1 first, BidirectionalIter1 last,
                    BidirectionalIter2 result);
 
  namespace ranges {
    template<class I1, class I2>
    using copy_backward_result = copy_result<I1, I2>;
 
    template<bidirectional_iterator I1, sentinel_for<I1> S1, bidirectional_iterator I2>
      requires indirectly_copyable<I1, I2>
      constexpr copy_backward_result<I1, I2>
        copy_backward(I1 first, S1 last, I2 result);
    template<bidirectional_range R, bidirectional_iterator I>
      requires indirectly_copyable<iterator_t<R>, I>
      constexpr copy_backward_result<safe_iterator_t<R>, I>
        copy_backward(R&& r, I result);
  }
 
  // move
  template<class InputIter, class OutputIter>
    constexpr OutputIter move(InputIter first, InputIter last, OutputIter result);
  template<class ExecutionPolicy, class ForwardIter1,
           class ForwardIter2>
    ForwardIter2 move(ExecutionPolicy&& exec,
                      ForwardIter1 first, ForwardIter1 last, ForwardIter2 result);
 
  namespace ranges {
    template<class I, class O>
    using move_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_movable<I, O>
      constexpr move_result<I, O>
        move(I first, S last, O result);
    template<input_range R, weakly_incrementable O>
      requires indirectly_movable<iterator_t<R>, O>
      constexpr move_result<safe_iterator_t<R>, O>
        move(R&& r, O result);
  }
 
  template<class BidirectionalIter1, class BidirectionalIter2>
    constexpr BidirectionalIter2
      move_backward(BidirectionalIter1 first, BidirectionalIter1 last,
                    BidirectionalIter2 result);
 
  namespace ranges {
    template<class I1, class I2>
    using move_backward_result = copy_result<I1, I2>;
 
    template<bidirectional_iterator I1, sentinel_for<I1> S1, bidirectional_iterator I2>
      requires indirectly_movable<I1, I2>
      constexpr move_backward_result<I1, I2>
        move_backward(I1 first, S1 last, I2 result);
    template<bidirectional_range R, bidirectional_iterator I>
      requires indirectly_movable<iterator_t<R>, I>
      constexpr move_backward_result<safe_iterator_t<R>, I>
        move_backward(R&& r, I result);
  }
 
  // swap
  template<class ForwardIter1, class ForwardIter2>
    constexpr ForwardIter2 swap_ranges(ForwardIter1 first1, ForwardIter1 last1,
                                       ForwardIter2 first2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter2 swap_ranges(ExecutionPolicy&& exec,
                             ForwardIter1 first1, ForwardIter1 last1,
                             ForwardIter2 first2);
 
  namespace ranges {
    template<class I1, class I2>
    using swap_ranges_result = mismatch_result<I1, I2>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2>
      requires indirectly_swappable<I1, I2>
      constexpr swap_ranges_result<I1, I2>
        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 swap_ranges_result<safe_iterator_t<R1>, safe_iterator_t<R2>>
        swap_ranges(R1&& r1, R2&& r2);
  }
 
  template<class ForwardIter1, class ForwardIter2>
    constexpr void iter_swap(ForwardIter1 a, ForwardIter2 b);
 
  // transform
  template<class InputIter, class OutputIter, class UnaryOp>
    constexpr OutputIter
      transform(InputIter first1, InputIter last1, OutputIter result, UnaryOp op);
  template<class InputIter1, class InputIter2, class OutputIter, class BinaryOp>
    constexpr OutputIter
      transform(InputIter1 first1, InputIter1 last1, InputIter2 first2, OutputIter result,
                BinaryOp binary_op);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class UnaryOp>
    ForwardIter2
      transform(ExecutionPolicy&& exec,
                ForwardIter1 first1, ForwardIter1 last1, ForwardIter2 result, UnaryOp op);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class BinaryOp>
    ForwardIter
      transform(ExecutionPolicy&& exec,
                ForwardIter1 first1, ForwardIter1 last1,
                ForwardIter2 first2, ForwardIter result, BinaryOp binary_op);
 
  namespace ranges {
    template<class I, class O>
    using unary_transform_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
             copy_constructible F, class Proj = identity>
      requires writable<O, indirect_result_t<F&, projected<I, Proj>>>
      constexpr unary_transform_result<I, O>
        transform(I first1, S last1, O result, F op, Proj proj = {});
    template<input_range R, weakly_incrementable O, copy_constructible F,
             class Proj = identity>
      requires writable<O, indirect_result_t<F&, projected<iterator_t<R>, Proj>>>
      constexpr unary_transform_result<safe_iterator_t<R>, O>
        transform(R&& r, O result, F op, Proj proj = {});
 
    template<class I1, class I2, class O>
    struct binary_transform_result {
      [[no_unique_address]] I1 in1;
      [[no_unique_address]] I2 in2;
      [[no_unique_address]] O  out;
 
      template<class II1, class II2, class OO>
        requires convertible_to<const I1&, II1> &&
          convertible_to<const I2&, II2> && convertible_to<const O&, OO>
        operator binary_transform_result<II1, II2, OO>() const & {
          return {in1, in2, out};
        }
 
      template<class II1, class II2, class OO>
        requires convertible_to<I1, II1> &&
          convertible_to<I2, II2> && convertible_to<O, OO>
        operator binary_transform_result<II1, II2, OO>() && {
          return {std::move(in1), std::move(in2), std::move(out)};
        }
    };
 
    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 writable<O, indirect_result_t<F&, projected<I1, Proj1>,
                                             projected<I2, Proj2>>>
      constexpr binary_transform_result<I1, I2, O>
        transform(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             copy_constructible F, class Proj1 = identity, class Proj2 = identity>
      requires writable<O, indirect_result_t<F&, projected<iterator_t<R1>, Proj1>,
                                             projected<iterator_t<R2>, Proj2>>>
      constexpr binary_transform_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        transform(R1&& r1, R2&& r2, O result,
                  F binary_op, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // replace
  template<class ForwardIter, class T>
    constexpr void replace(ForwardIter first, ForwardIter last,
                           const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIter, class T>
    void replace(ExecutionPolicy&& exec,
                 ForwardIter first, ForwardIter last,
                 const T& old_value, const T& new_value);
  template<class ForwardIter, class Pred, class T>
    constexpr void replace_if(ForwardIter first, ForwardIter last,
                              Pred pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIter, class Pred, class T>
    void replace_if(ExecutionPolicy&& exec,
                    ForwardIter first, ForwardIter last, Pred pred, const T& new_value);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S,
             class T1, class T2, class Proj = identity>
      requires writable<I, const T2&> &&
               indirect_relation<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr I
        replace(I first, S last, const T1& old_value, const T2& new_value,
                Proj proj = {});
    template<input_range R, class T1, class T2, class Proj = identity>
      requires writable<iterator_t<R>, const T2&> &&
               indirect_relation<ranges::equal_to, projected<iterator_t<R>, Proj>,
                                 const T1*>
      constexpr safe_iterator_t<R>
        replace(R&& r, const T1& old_value, const T2& new_value, Proj proj = {});
    template<input_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires writable<I, const T&>
      constexpr I replace_if(I first, S last, Pred pred, const T& new_value,
                             Proj proj = {});
    template<input_range R, class T, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires writable<iterator_t<R>, const T&>
      constexpr safe_iterator_t<R>
        replace_if(R&& r, Pred pred, const T& new_value, Proj proj = {});
  }
 
  template<class InputIter, class OutputIter, class T>
    constexpr OutputIter replace_copy(InputIter first, InputIter last, OutputIter result,
                                      const T& old_value, const T& new_value);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class T>
    ForwardIter2 replace_copy(ExecutionPolicy&& exec,
                              ForwardIter1 first, ForwardIter1 last, ForwardIter2 result,
                              const T& old_value, const T& new_value);
  template<class InputIter, class OutputIter, class Pred, class T>
    constexpr OutputIter replace_copy_if(InputIter first, InputIter last,
                                         OutputIter result,
                                         Pred pred, const T& new_value);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class Pred, class T>
    ForwardIter2 replace_copy_if(ExecutionPolicy&& exec,
                                 ForwardIter1 first, ForwardIter1 last,
                                 ForwardIter2 result, Pred pred, const T& new_value);
 
  namespace ranges {
    template<class I, class O>
    using replace_copy_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, class T1, class T2,
             output_iterator<const T2&> O, class Proj = identity>
      requires indirectly_copyable<I, O> &&
               indirect_relation<ranges::equal_to, projected<I, Proj>, const T1*>
      constexpr replace_copy_result<I, O>
        replace_copy(I first, S last, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});
    template<input_range R, class T1, class T2, output_iterator<const T2&> O,
             class Proj = identity>
      requires indirectly_copyable<iterator_t<R>, O> &&
               indirect_relation<ranges::equal_to,
                                 projected<iterator_t<R>, Proj>, const T1*>
      constexpr replace_copy_result<safe_iterator_t<R>, O>
        replace_copy(R&& r, O result, const T1& old_value, const T2& new_value,
                     Proj proj = {});
 
    template<class I, class O>
    using replace_copy_if_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, class T, output_iterator<const T&> O,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr replace_copy_if_result<I, O>
        replace_copy_if(I first, S last, O result, Pred pred, const T& new_value,
                        Proj proj = {});
    template<input_range R, class T, output_iterator<const T&> O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr replace_copy_if_result<safe_iterator_t<R>, O>
        replace_copy_if(R&& r, O result, Pred pred, const T& new_value, Proj proj = {});
  }
 
  // fill
  template<class ForwardIter, class T>
    constexpr void fill(ForwardIter first, ForwardIter last, const T& value);
  template<class ExecutionPolicy, class ForwardIter, class T>
    void fill(ExecutionPolicy&& exec,
              ForwardIter first, ForwardIter last, const T& value);
  template<class OutputIter, class Size, class T>
    constexpr OutputIter fill_n(OutputIter first, Size n, const T& value);
  template<class ExecutionPolicy, class ForwardIter,
           class Size, class T>
    ForwardIter fill_n(ExecutionPolicy&& exec, ForwardIter first, Size n, const T& value);
 
  namespace ranges {
    template<class T, output_iterator<const T&> O, sentinel_for<O> S>
      constexpr O fill(O first, S last, const T& value);
    template<class T, output_range<const T&> R>
      constexpr safe_iterator_t<R> fill(R&& r, const T& value);
    template<class T, output_iterator<const T&> O>
      constexpr O fill_n(O first, iter_difference_t<O> n, const T& value);
  }
 
  // generate
  template<class ForwardIter, class Generator>
    constexpr void generate(ForwardIter first, ForwardIter last, Generator gen);
  template<class ExecutionPolicy, class ForwardIter, class Generator>
    void generate(ExecutionPolicy&& exec,
                  ForwardIter first, ForwardIter last, Generator gen);
  template<class OutputIter, class Size, class Generator>
    constexpr OutputIter generate_n(OutputIter first, Size n, Generator gen);
  template<class ExecutionPolicy, class ForwardIter, class Size, class Generator>
    ForwardIter generate_n(ExecutionPolicy&& exec,
                           ForwardIter first, Size n, Generator gen);
 
  namespace ranges {
    template<input_or_output_iterator O, sentinel_for<O> S, copy_constructible F>
      requires invocable<F&> && writable<O, invoke_result_t<F&>>
      constexpr O generate(O first, S last, F gen);
    template<class R, copy_constructible F>
      requires invocable<F&> && output_range<R, invoke_result_t<F&>>
      constexpr safe_iterator_t<R> generate(R&& r, F gen);
    template<input_or_output_iterator O, copy_constructible F>
      requires invocable<F&> && writable<O, invoke_result_t<F&>>
      constexpr O generate_n(O first, iter_difference_t<O> n, F gen);
  }
 
  // remove
  template<class ForwardIter, class T>
    constexpr ForwardIter remove(ForwardIter first, ForwardIter last, const T& value);
  template<class ExecutionPolicy, class ForwardIter, class T>
    ForwardIter remove(ExecutionPolicy&& exec,
                       ForwardIter first, ForwardIter last, const T& value);
  template<class ForwardIter, class Pred>
    constexpr ForwardIter remove_if(ForwardIter first, ForwardIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    ForwardIter remove_if(ExecutionPolicy&& exec,
                          ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<permutable I, sentinel_for<I> S, class T, class Proj = identity>
      requires indirect_relation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr subrange<I> remove(I first, S last, const T& value, Proj proj = {});
    template<forward_range R, class T, class Proj = identity>
      requires permutable<iterator_t<R>> &&
               indirect_relation<ranges::equal_to,
                                 projected<iterator_t<R>, Proj>, const T*>
      constexpr safe_subrange_t<R>
        remove(R&& r, const T& value, Proj proj = {});
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr subrange<I> remove_if(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      constexpr safe_subrange_t<R>
        remove_if(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class InputIter, class OutputIter, class T>
    constexpr OutputIter
      remove_copy(InputIter first, InputIter last, OutputIter result, const T& value);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class T>
    ForwardIter2
      remove_copy(ExecutionPolicy&& exec,
                  ForwardIter1 first, ForwardIter1 last,
                  ForwardIter2 result, const T& value);
  template<class InputIter, class OutputIter, class Pred>
    constexpr OutputIter
      remove_copy_if(InputIter first, InputIter last, OutputIter result, Pred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class Pred>
    ForwardIter2
      remove_copy_if(ExecutionPolicy&& exec,
                     ForwardIter1 first, ForwardIter1 last,
                     ForwardIter2 result, Pred pred);
 
  namespace ranges {
    template<class I, class O>
    using remove_copy_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O, class T,
             class Proj = identity>
      requires indirectly_copyable<I, O> &&
               indirect_relation<ranges::equal_to, projected<I, Proj>, const T*>
      constexpr remove_copy_result<I, O>
        remove_copy(I first, S last, O result, const T& value, Proj proj = {});
    template<input_range R, weakly_incrementable O, class T, class Proj = identity>
      requires indirectly_copyable<iterator_t<R>, O> &&
               indirect_relation<ranges::equal_to,
                                 projected<iterator_t<R>, Proj>, const T*>
      constexpr remove_copy_result<safe_iterator_t<R>, O>
        remove_copy(R&& r, O result, const T& value, Proj proj = {});
 
    template<class I, class O>
    using remove_copy_if_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O>
      constexpr remove_copy_if_result<I, O>
        remove_copy_if(I first, S last, O result, Pred pred, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr remove_copy_if_result<safe_iterator_t<R>, O>
        remove_copy_if(R&& r, O result, Pred pred, Proj proj = {});
  }
 
  // unique
  template<class ForwardIter>
    constexpr ForwardIter unique(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class BinaryPred>
    constexpr ForwardIter unique(ForwardIter first, ForwardIter last, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter unique(ExecutionPolicy&& exec,
                       ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class BinaryPred>
    ForwardIter unique(ExecutionPolicy&& exec,
                       ForwardIter first, ForwardIter last, BinaryPred pred);
 
  namespace ranges {
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_relation<projected<I, Proj>> C = ranges::equal_to>
      constexpr subrange<I> unique(I first, S last, C comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires permutable<iterator_t<R>>
      constexpr safe_subrange_t<R>
        unique(R&& r, C comp = {}, Proj proj = {});
  }
 
  template<class InputIter, class OutputIter>
    constexpr OutputIter
      unique_copy(InputIter first, InputIter last, OutputIter result);
  template<class InputIter, class OutputIter, class BinaryPred>
    constexpr OutputIter
      unique_copy(InputIter first, InputIter last, OutputIter result, BinaryPred pred);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter2
      unique_copy(ExecutionPolicy&& exec,
                  ForwardIter1 first, ForwardIter1 last, ForwardIter2 result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class BinaryPred>
    ForwardIter2
      unique_copy(ExecutionPolicy&& exec,
                  ForwardIter1 first, ForwardIter1 last,
                  ForwardIter2 result, BinaryPred pred);
 
  namespace ranges {
    template<class I, class O>
    using unique_copy_result = copy_result<I, O>;
 
    template<input_iterator I, sentinel_for<I> S, weakly_incrementable O,
             class Proj = identity,
             indirect_relation<projected<I, Proj>> C = ranges::equal_to>
      requires indirectly_copyable<I, O> &&
               (forward_iterator<I> ||
                (input_iterator<O> && same_as<iter_value_t<I>, iter_value_t<O>>) ||
                indirectly_copyable_storable<I, O>)
      constexpr unique_copy_result<I, O>
        unique_copy(I first, S last, O result, C comp = {}, Proj proj = {});
    template<input_range R, weakly_incrementable O, class Proj = identity,
             indirect_relation<projected<iterator_t<R>, Proj>> C = ranges::equal_to>
      requires indirectly_copyable<iterator_t<R>, O> &&
               (forward_iterator<iterator_t<R>> ||
                (input_iterator<O> && same_as<range_value_t<R>, iter_value_t<O>>) ||
                indirectly_copyable_storable<iterator_t<R>, O>)
      constexpr unique_copy_result<safe_iterator_t<R>, O>
        unique_copy(R&& r, O result, C comp = {}, Proj proj = {});
  }
 
  // reverse
  template<class BidirectionalIter>
    constexpr void reverse(BidirectionalIter first, BidirectionalIter last);
  template<class ExecutionPolicy, class BidirectionalIter>
    void reverse(ExecutionPolicy&& exec,
                 BidirectionalIter first, BidirectionalIter last);
 
  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S>
      requires permutable<I>
      constexpr I reverse(I first, S last);
    template<bidirectional_range R>
      requires permutable<iterator_t<R>>
      constexpr safe_iterator_t<R> reverse(R&& r);
  }
 
  template<class BidirectionalIter, class OutputIter>
    constexpr OutputIter
      reverse_copy(BidirectionalIter first, BidirectionalIter last, OutputIter result);
  template<class ExecutionPolicy, class BidirectionalIter, class ForwardIter>
    ForwardIter
      reverse_copy(ExecutionPolicy&& exec,
                   BidirectionalIter first, BidirectionalIter last, ForwardIter result);
 
  namespace ranges {
    template<class I, class O>
    using reverse_copy_result = copy_result<I, O>;
 
    template<bidirectional_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr reverse_copy_result<I, O>
        reverse_copy(I first, S last, O result);
    template<bidirectional_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr reverse_copy_result<safe_iterator_t<R>, O>
        reverse_copy(R&& r, O result);
  }
 
  // rotate
  template<class ForwardIter>
    constexpr ForwardIter rotate(ForwardIter first, ForwardIter middle, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter rotate(ExecutionPolicy&& exec,
                       ForwardIter first, ForwardIter middle, ForwardIter last);
 
  namespace ranges {
    template<permutable I, sentinel_for<I> S>
      constexpr subrange<I> rotate(I first, I middle, S last);
    template<forward_range R>
      requires permutable<iterator_t<R>>
      constexpr safe_subrange_t<R> rotate(R&& r, iterator_t<R> middle);
  }
 
  template<class ForwardIter, class OutputIter>
    constexpr OutputIter
      rotate_copy(ForwardIter first, ForwardIter middle,
                  ForwardIter last, OutputIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    ForwardIter2
      rotate_copy(ExecutionPolicy&& exec,
                  ForwardIter1 first, ForwardIter1 middle,
                  ForwardIter1 last, ForwardIter2 result);
 
  namespace ranges {
    template<class I, class O>
    using rotate_copy_result = copy_result<I, O>;
 
    template<forward_iterator I, sentinel_for<I> S, weakly_incrementable O>
      requires indirectly_copyable<I, O>
      constexpr rotate_copy_result<I, O>
        rotate_copy(I first, I middle, S last, O result);
    template<forward_range R, weakly_incrementable O>
      requires indirectly_copyable<iterator_t<R>, O>
      constexpr rotate_copy_result<safe_iterator_t<R>, O>
        rotate_copy(R&& r, iterator_t<R> middle, O result);
  }
 
  // sample
  template<class PopulationIter, class SampleIter,
           class Distance, class UniformRandomBitGenerator>
    SampleIter sample(PopulationIter first, PopulationIter last,
                      SampleIter out, Distance n, UniformRandomBitGenerator&& g);
 
  // shuffle
  template<class RandomAccessIter, class UniformRandomBitGenerator>
    void shuffle(RandomAccessIter first, RandomAccessIter last,
                 UniformRandomBitGenerator&& g);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Gen>
      requires permutable<I> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      I shuffle(I first, S last, Gen&& g);
    template<random_access_range R, class Gen>
      requires permutable<iterator_t<R>> &&
               uniform_random_bit_generator<remove_reference_t<Gen>>
      safe_iterator_t<R> shuffle(R&& r, Gen&& g);
  }
 
  // shift
  template<class ForwardIter>
    constexpr ForwardIter
      shift_left(ForwardIter first, ForwardIter last,
                 typename iterator_traits<ForwardIter>::difference_type n);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter
      shift_left(ExecutionPolicy&& exec,
                 ForwardIter first, ForwardIter last,
                 typename iterator_traits<ForwardIter>::difference_type n);
  template<class ForwardIter>
    constexpr ForwardIter
      shift_right(ForwardIter first, ForwardIter last,
                  typename iterator_traits<ForwardIter>::difference_type n);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter
      shift_right(ExecutionPolicy&& exec,
                  ForwardIter first, ForwardIter last,
                  typename iterator_traits<ForwardIter>::difference_type n);
 
  // sorting and related operations
  // sorting
  template<class RandomAccessIter>
    constexpr void sort(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void sort(RandomAccessIter first, RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    void sort(ExecutionPolicy&& exec,
              RandomAccessIter first, RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    void sort(ExecutionPolicy&& exec,
              RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        sort(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        sort(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    void stable_sort(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    void stable_sort(RandomAccessIter first, RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    void stable_sort(ExecutionPolicy&& exec,
                     RandomAccessIter first, RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    void stable_sort(ExecutionPolicy&& exec,
                     RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      I stable_sort(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      safe_iterator_t<R>
        stable_sort(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr void partial_sort(RandomAccessIter first,
                                RandomAccessIter middle,
                                RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void partial_sort(RandomAccessIter first,
                                RandomAccessIter middle,
                                RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    void partial_sort(ExecutionPolicy&& exec,
                      RandomAccessIter first,
                      RandomAccessIter middle,
                      RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    void partial_sort(ExecutionPolicy&& exec,
                      RandomAccessIter first,
                      RandomAccessIter middle,
                      RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        partial_sort(I first, I middle, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        partial_sort(R&& r, iterator_t<R> middle, Cmp comp = {},
                     Proj proj = {});
  }
 
  template<class InputIter, class RandomAccessIter>
    constexpr RandomAccessIter
      partial_sort_copy(InputIter first, InputIter last,
                        RandomAccessIter result_first, RandomAccessIter result_last);
  template<class InputIter, class RandomAccessIter, class Cmp>
    constexpr RandomAccessIter
      partial_sort_copy(InputIter first, InputIter last,
                        RandomAccessIter result_first, RandomAccessIter result_last,
                        Cmp comp);
  template<class ExecutionPolicy, class ForwardIter, class RandomAccessIter>
    RandomAccessIter
      partial_sort_copy(ExecutionPolicy&& exec, 
                        ForwardIter first, ForwardIter last,
                        RandomAccessIter result_first, RandomAccessIter result_last);
  template<class ExecutionPolicy, class ForwardIter, class RandomAccessIter,
           class Cmp>
    RandomAccessIter
      partial_sort_copy(ExecutionPolicy&& exec, 
                        ForwardIter first, ForwardIter last,
                        RandomAccessIter result_first, RandomAccessIter result_last,
                        Cmp comp);
 
  namespace ranges {
    template<class I, class O> using partial_sort_copy_result = copy_result<I, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             random_access_iterator I2, sentinel_for<I2> S2,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires indirectly_copyable<I1, I2> && sortable<I2, Cmp, Proj2> &&
               indirect_strict_weak_order<Cmp, projected<I1, Proj1>, projected<I2, Proj2>>
      constexpr partial_sort_copy_result<I1, I2>
        partial_sort_copy(I1 first, S1 last, I2 result_first, S2 result_last,
                          Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, random_access_range R2, class Cmp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires indirectly_copyable<iterator_t<R1>, iterator_t<R2>> &&
               sortable<iterator_t<R2>, Cmp, Proj2> &&
               indirect_strict_weak_order<Cmp, projected<iterator_t<R1>, Proj1>,
                                          projected<iterator_t<R2>, Proj2>>
      constexpr partial_sort_copy_result<safe_iterator_t<R1>, safe_iterator_t<R2>>
        partial_sort_copy(R1&& r, R2&& result_r, Cmp comp = {},
                          Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class ForwardIter>
    constexpr bool is_sorted(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class Cmp>
    constexpr bool is_sorted(ForwardIter first, ForwardIter last, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter>
    bool is_sorted(ExecutionPolicy&& exec,
                   ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class Cmp>
    bool is_sorted(ExecutionPolicy&& exec,
                   ForwardIter first, ForwardIter last, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr bool is_sorted(I first, S last, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order< projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr bool is_sorted(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter>
    constexpr ForwardIter
      is_sorted_until(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class Cmp>
    constexpr ForwardIter
      is_sorted_until(ForwardIter first, ForwardIter last, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter
      is_sorted_until(ExecutionPolicy&& exec,
                      ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class Cmp>
    ForwardIter
      is_sorted_until(ExecutionPolicy&& exec,
                      ForwardIter first, ForwardIter last, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr I is_sorted_until(I first, S last, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<
               projected<iterator_t<R>, Proj>> Cmp = ranges::less>
      constexpr safe_iterator_t<R>
        is_sorted_until(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  // Nth element
  template<class RandomAccessIter>
    constexpr void nth_element(RandomAccessIter first, RandomAccessIter nth,
                               RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void nth_element(RandomAccessIter first, RandomAccessIter nth,
                               RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    void nth_element(ExecutionPolicy&& exec,
                     RandomAccessIter first, RandomAccessIter nth,
                     RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    void nth_element(ExecutionPolicy&& exec,
                     RandomAccessIter first, RandomAccessIter nth,
                     RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        nth_element(I first, I nth, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        nth_element(R&& r, iterator_t<R> nth, Cmp comp = {}, Proj proj = {});
  }
 
  // binary search
  template<class ForwardIter, class T>
    constexpr ForwardIter
      lower_bound(ForwardIter first, ForwardIter last, const T& value);
  template<class ForwardIter, class T, class Cmp>
    constexpr ForwardIter
      lower_bound(ForwardIter first, ForwardIter last, const T& value, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Cmp = ranges::less>
      constexpr I lower_bound(I first, S last, const T& value, Cmp comp = {},
                              Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_iterator_t<R>
        lower_bound(R&& r, const T& value, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter, class T>
    constexpr ForwardIter
      upper_bound(ForwardIter first, ForwardIter last, const T& value);
  template<class ForwardIter, class T, class Cmp>
    constexpr ForwardIter
      upper_bound(ForwardIter first, ForwardIter last, const T& value, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Cmp = ranges::less>
      constexpr I upper_bound(I first, S last, const T& value, Cmp comp = {},
                              Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_iterator_t<R>
        upper_bound(R&& r, const T& value, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter, class T>
    constexpr pair<ForwardIter, ForwardIter>
      equal_range(ForwardIter first, ForwardIter last, const T& value);
  template<class ForwardIter, class T, class Cmp>
    constexpr pair<ForwardIter, ForwardIter>
      equal_range(ForwardIter first, ForwardIter last, const T& value, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Cmp = ranges::less>
      constexpr subrange<I>
        equal_range(I first, S last, const T& value, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_subrange_t<R>
        equal_range(R&& r, const T& value, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter, class T>
    constexpr bool
      binary_search(ForwardIter first, ForwardIter last, const T& value);
  template<class ForwardIter, class T, class Cmp>
    constexpr bool
      binary_search(ForwardIter first, ForwardIter last, const T& value, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<I, Proj>> Cmp = ranges::less>
      constexpr bool binary_search(I first, S last, const T& value, Cmp comp = {},
                                   Proj proj = {});
    template<forward_range R, class T, class Proj = identity,
             indirect_strict_weak_order<const T*, projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr bool binary_search(R&& r, const T& value, Cmp comp = {},
                                   Proj proj = {});
  }
 
  // partitions
  template<class InputIter, class Pred>
    constexpr bool is_partitioned(InputIter first, InputIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    bool is_partitioned(ExecutionPolicy&& exec,
                        ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<input_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr bool is_partitioned(I first, S last, Pred pred, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr bool is_partitioned(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class ForwardIter, class Pred>
    constexpr ForwardIter partition(ForwardIter first, ForwardIter last, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class Pred>
    ForwardIter partition(ExecutionPolicy&& exec,
                          ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<permutable I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr subrange<I>
        partition(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      constexpr safe_subrange_t<R>
        partition(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class BidirectionalIter, class Pred>
    BidirectionalIter stable_partition(BidirectionalIter first, BidirectionalIter last,
                                       Pred pred);
  template<class ExecutionPolicy, class BidirectionalIter, class Pred>
    BidirectionalIter stable_partition(ExecutionPolicy&& exec,
                                       BidirectionalIter first, BidirectionalIter last,
                                       Pred pred);
 
  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      requires permutable<I>
      subrange<I> stable_partition(I first, S last, Pred pred, Proj proj = {});
    template<bidirectional_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires permutable<iterator_t<R>>
      safe_subrange_t<R> stable_partition(R&& r, Pred pred, Proj proj = {});
  }
 
  template<class InputIter, class OutputIter1, class OutputIter2, class Pred>
    constexpr pair<OutputIter1, OutputIter2>
      partition_copy(InputIter first, InputIter last,
                     OutputIter1 out_true, OutputIter2 out_false, Pred pred);
  template<class ExecutionPolicy, class ForwardIter, class ForwardIter1,
           class ForwardIter2, class Pred>
    pair<ForwardIter1, ForwardIter2>
      partition_copy(ExecutionPolicy&& exec,
                     ForwardIter first, ForwardIter last,
                     ForwardIter1 out_true, ForwardIter2 out_false, Pred pred);
 
  namespace ranges {
    template<class I, class O1, class O2>
    struct partition_copy_result {
      [[no_unique_address]] I  in;
      [[no_unique_address]] O1 out1;
      [[no_unique_address]] O2 out2;
 
      template<class II, class OO1, class OO2>
        requires convertible_to<const I&, II> &&
          convertible_to<const O1&, OO1> && convertible_to<const O2&, OO2>
        operator partition_copy_result<II, OO1, OO2>() const & {
          return {in, out1, out2};
        }
 
      template<class II, class OO1, class OO2>
        requires convertible_to<I, II> &&
          convertible_to<O1, OO1> && convertible_to<O2, OO2>
        operator partition_copy_result<II, OO1, OO2>() && {
          return {std::move(in), std::move(out1), std::move(out2)};
        }
    };
 
    template<input_iterator I, sentinel_for<I> S,
             weakly_incrementable O1, weakly_incrementable O2,
             class Proj = identity, indirect_unary_predicate<projected<I, Proj>> Pred>
      requires indirectly_copyable<I, O1> && indirectly_copyable<I, O2>
      constexpr partition_copy_result<I, O1, O2>
        partition_copy(I first, S last, O1 out_true, O2 out_false, Pred pred,
                       Proj proj = {});
    template<input_range R, weakly_incrementable O1, weakly_incrementable O2,
             class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      requires indirectly_copyable<iterator_t<R>, O1> &&
               indirectly_copyable<iterator_t<R>, O2>
      constexpr partition_copy_result<safe_iterator_t<R>, O1, O2>
        partition_copy(R&& r, O1 out_true, O2 out_false, Pred pred, Proj proj = {});
  }
 
  template<class ForwardIter, class Pred>
    constexpr ForwardIter
      partition_point(ForwardIter first, ForwardIter last, Pred pred);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_unary_predicate<projected<I, Proj>> Pred>
      constexpr I partition_point(I first, S last, Pred pred, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
      constexpr safe_iterator_t<R>
        partition_point(R&& r, Pred pred, Proj proj = {});
  }
 
  // merge
  template<class InputIter1, class InputIter2, class OutputIter>
    constexpr OutputIter
      merge(InputIter1 first1, InputIter1 last1,
            InputIter2 first2, InputIter2 last2, OutputIter result);
  template<class InputIter1, class InputIter2, class OutputIter,
           class Cmp>
    constexpr OutputIter
      merge(InputIter1 first1, InputIter1 last1,
            InputIter2 first2, InputIter2 last2, OutputIter result, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter>
    ForwardIter
      merge(ExecutionPolicy&& exec,
            ForwardIter1 first1, ForwardIter1 last1,
            ForwardIter2 first2, ForwardIter2 last2, ForwardIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class Cmp>
    ForwardIter
      merge(ExecutionPolicy&& exec,
            ForwardIter1 first1, ForwardIter1 last1,
            ForwardIter2 first2, ForwardIter2 last2, ForwardIter result, Cmp comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using merge_result = binary_transform_result<I1, I2, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Cmp = ranges::less, class Proj1 = identity,
             class Proj2 = identity>
      requires mergeable<I1, I2, O, Cmp, Proj1, Proj2>
      constexpr merge_result<I1, I2, O>
        merge(I1 first1, S1 last1, I2 first2, S2 last2, O result,
              Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Cmp, Proj1, Proj2>
      constexpr merge_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        merge(R1&& r1, R2&& r2, O result,
              Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class BidirectionalIter>
    void inplace_merge(BidirectionalIter first,
                       BidirectionalIter middle,
                       BidirectionalIter last);
  template<class BidirectionalIter, class Cmp>
    void inplace_merge(BidirectionalIter first,
                       BidirectionalIter middle,
                       BidirectionalIter last, Cmp comp);
  template<class ExecutionPolicy, class BidirectionalIter>
    void inplace_merge(ExecutionPolicy&& exec,
                       BidirectionalIter first,
                       BidirectionalIter middle,
                       BidirectionalIter last);
  template<class ExecutionPolicy, class BidirectionalIter, class Cmp>
    void inplace_merge(ExecutionPolicy&& exec,
                       BidirectionalIter first,
                       BidirectionalIter middle,
                       BidirectionalIter last, Cmp comp);
 
  namespace ranges {
    template<bidirectional_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      I inplace_merge(I first, I middle, S last, Cmp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      safe_iterator_t<R>
        inplace_merge(R&& r, iterator_t<R> middle, Cmp comp = {},
                      Proj proj = {});
  }
 
  // set operations
  template<class InputIter1, class InputIter2>
    constexpr bool includes(InputIter1 first1, InputIter1 last1,
                            InputIter2 first2, InputIter2 last2);
  template<class InputIter1, class InputIter2, class Cmp>
    constexpr bool includes(InputIter1 first1, InputIter1 last1,
                            InputIter2 first2, InputIter2 last2, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    bool includes(ExecutionPolicy&& exec,
                  ForwardIter1 first1, ForwardIter1 last1,
                  ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class Cmp>
    bool includes(ExecutionPolicy&& exec,
                  ForwardIter1 first1, ForwardIter1 last1,
                  ForwardIter2 first2, ForwardIter2 last2, Cmp comp);
 
  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Cmp =
               ranges::less>
      constexpr bool includes(I1 first1, S1 last1, I2 first2, S2 last2, Cmp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, class Proj1 = identity,
             class Proj2 = identity,
             indirect_strict_weak_order<
               projected<iterator_t<R1>, Proj1>,
               projected<iterator_t<R2>, Proj2>> Cmp = ranges::less>
      constexpr bool includes(R1&& r1, R2&& r2, Cmp comp = {},
                              Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIter1, class InputIter2, class OutputIter>
    constexpr OutputIter
      set_union(InputIter1 first1, InputIter1 last1,
                InputIter2 first2, InputIter2 last2, OutputIter result);
  template<class InputIter1, class InputIter2, class OutputIter, class Cmp>
    constexpr OutputIter
      set_union(InputIter1 first1, InputIter1 last1, InputIter2 first2, InputIter2 last2,
                OutputIter result, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter>
    ForwardIter
      set_union(ExecutionPolicy&& exec,
                ForwardIter1 first1, ForwardIter1 last1,
                ForwardIter2 first2, ForwardIter2 last2, ForwardIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class Cmp>
    ForwardIter
      set_union(ExecutionPolicy&& exec,
                ForwardIter1 first1, ForwardIter1 last1,
                ForwardIter2 first2, ForwardIter2 last2,
                ForwardIter result, Cmp comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_union_result = binary_transform_result<I1, I2, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Cmp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Cmp, Proj1, Proj2>
      constexpr set_union_result<I1, I2, O>
        set_union(I1 first1, S1 last1, I2 first2, S2 last2, O result, Cmp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Cmp, Proj1, Proj2>
      constexpr set_union_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_union(R1&& r1, R2&& r2, O result, Cmp comp = {},
                  Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIter1, class InputIter2, class OutputIter>
    constexpr OutputIter
      set_intersection(InputIter1 first1, InputIter1 last1,
                       InputIter2 first2, InputIter2 last2, OutputIter result);
  template<class InputIter1, class InputIter2, class OutputIter, class Cmp>
    constexpr OutputIter
      set_intersection(InputIter1 first1, InputIter1 last1,
                       InputIter2 first2, InputIter2 last2,
                       OutputIter result, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter>
    ForwardIter
      set_intersection(ExecutionPolicy&& exec,
                       ForwardIter1 first1, ForwardIter1 last1,
                       ForwardIter2 first2, ForwardIter2 last2, ForwardIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class Cmp>
    ForwardIter
      set_intersection(ExecutionPolicy&& exec,
                       ForwardIter1 first1, ForwardIter1 last1,
                       ForwardIter2 first2, ForwardIter2 last2,
                       ForwardIter result, Cmp comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_intersection_result = binary_transform_result<I1, I2, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Cmp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Cmp, Proj1, Proj2>
      constexpr set_intersection_result<I1, I2, O>
        set_intersection(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                         Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Cmp, Proj1, Proj2>
      constexpr set_intersection_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_intersection(R1&& r1, R2&& r2, O result,
                         Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIter1, class InputIter2, class OutputIter>
    constexpr OutputIter
      set_difference(InputIter1 first1, InputIter1 last1,
                     InputIter2 first2, InputIter2 last2, OutputIter result);
  template<class InputIter1, class InputIter2, class OutputIter, class Cmp>
    constexpr OutputIter
      set_difference(InputIter1 first1, InputIter1 last1,
                     InputIter2 first2, InputIter2 last2,
                     OutputIter result, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter>
    ForwardIter
      set_difference(ExecutionPolicy&& exec,
                     ForwardIter1 first1, ForwardIter1 last1,
                     ForwardIter2 first2, ForwardIter2 last2, ForwardIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class Cmp>
    ForwardIter
      set_difference(ExecutionPolicy&& exec,
                     ForwardIter1 first1, ForwardIter1 last1,
                     ForwardIter2 first2, ForwardIter2 last2,
                     ForwardIter result, Cmp comp);
 
  namespace ranges {
    template<class I, class O>
    using set_difference_result = copy_result<I, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Cmp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Cmp, Proj1, Proj2>
      constexpr set_difference_result<I1, O>
        set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                       Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Cmp, Proj1, Proj2>
      constexpr set_difference_result<safe_iterator_t<R1>, O>
        set_difference(R1&& r1, R2&& r2, O result,
                       Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  template<class InputIter1, class InputIter2, class OutputIter>
    constexpr OutputIter
      set_symmetric_difference(InputIter1 first1, InputIter1 last1,
                               InputIter2 first2, InputIter2 last2, OutputIter result);
  template<class InputIter1, class InputIter2, class OutputIter, class Cmp>
    constexpr OutputIter
      set_symmetric_difference(InputIter1 first1, InputIter1 last1,
                               InputIter2 first2, InputIter2 last2,
                               OutputIter result, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter>
    ForwardIter
      set_symmetric_difference(ExecutionPolicy&& exec,
                               ForwardIter1 first1, ForwardIter1 last1,
                               ForwardIter2 first2, ForwardIter2 last2,
                               ForwardIter result);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2,
           class ForwardIter, class Cmp>
    ForwardIter
      set_symmetric_difference(ExecutionPolicy&& exec,
                               ForwardIter1 first1, ForwardIter1 last1,
                               ForwardIter2 first2, ForwardIter2 last2,
                               ForwardIter result, Cmp comp);
 
  namespace ranges {
    template<class I1, class I2, class O>
    using set_symmetric_difference_result = binary_transform_result<I1, I2, O>;
 
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             weakly_incrementable O, class Cmp = ranges::less,
             class Proj1 = identity, class Proj2 = identity>
      requires mergeable<I1, I2, O, Cmp, Proj1, Proj2>
      constexpr set_symmetric_difference_result<I1, I2, O>
        set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                 Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, weakly_incrementable O,
             class Cmp = ranges::less, class Proj1 = identity, class Proj2 = identity>
      requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Cmp, Proj1, Proj2>
      constexpr
        set_symmetric_difference_result<safe_iterator_t<R1>, safe_iterator_t<R2>, O>
        set_symmetric_difference(R1&& r1, R2&& r2, O result, Cmp comp = {},
                                 Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // heap operations
  template<class RandomAccessIter>
    constexpr void push_heap(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void push_heap(RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        push_heap(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        push_heap(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr void pop_heap(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void pop_heap(RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        pop_heap(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        pop_heap(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr void make_heap(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void make_heap(RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        make_heap(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        make_heap(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr void sort_heap(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr void sort_heap(RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr I
        sort_heap(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Cmp = ranges::less, class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr safe_iterator_t<R>
        sort_heap(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr bool is_heap(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr bool is_heap(RandomAccessIter first, RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    bool is_heap(ExecutionPolicy&& exec,
                 RandomAccessIter first, RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    bool is_heap(ExecutionPolicy&& exec,
                 RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr bool is_heap(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr bool is_heap(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class RandomAccessIter>
    constexpr RandomAccessIter
      is_heap_until(RandomAccessIter first, RandomAccessIter last);
  template<class RandomAccessIter, class Cmp>
    constexpr RandomAccessIter
      is_heap_until(RandomAccessIter first, RandomAccessIter last, Cmp comp);
  template<class ExecutionPolicy, class RandomAccessIter>
    RandomAccessIter
      is_heap_until(ExecutionPolicy&& exec,
                    RandomAccessIter first, RandomAccessIter last);
  template<class ExecutionPolicy, class RandomAccessIter, class Cmp>
    RandomAccessIter
      is_heap_until(ExecutionPolicy&& exec,
                    RandomAccessIter first, RandomAccessIter last, Cmp comp);
 
  namespace ranges {
    template<random_access_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr I is_heap_until(I first, S last, Cmp comp = {}, Proj proj = {});
    template<random_access_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_iterator_t<R>
        is_heap_until(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  // minimum and maximum
  template<class T> constexpr const T& min(const T& a, const T& b);
  template<class T, class Cmp>
    constexpr const T& min(const T& a, const T& b, Cmp comp);
  template<class T>
    constexpr T min(initializer_list<T> t);
  template<class T, class Cmp>
    constexpr T min(initializer_list<T> t, Cmp comp);
 
  namespace ranges {
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr const T& min(const T& a, const T& b, Cmp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr T min(initializer_list<T> r, Cmp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr range_value_t<R>
        min(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class T> constexpr const T& max(const T& a, const T& b);
  template<class T, class Cmp>
    constexpr const T& max(const T& a, const T& b, Cmp comp);
  template<class T>
    constexpr T max(initializer_list<T> t);
  template<class T, class Cmp>
    constexpr T max(initializer_list<T> t, Cmp comp);
 
  namespace ranges {
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr const T& max(const T& a, const T& b, Cmp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr T max(initializer_list<T> r, Cmp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr range_value_t<R>
        max(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class T> constexpr pair<const T&, const T&> minmax(const T& a, const T& b);
  template<class T, class Cmp>
    constexpr pair<const T&, const T&> minmax(const T& a, const T& b, Cmp comp);
  template<class T>
    constexpr pair<T, T> minmax(initializer_list<T> t);
  template<class T, class Cmp>
    constexpr pair<T, T> minmax(initializer_list<T> t, Cmp comp);
 
  namespace ranges {
    template<class T>
    struct minmax_result {
      [[no_unique_address]] T min;
      [[no_unique_address]] T max;
 
      template<class T2>
        requires convertible_to<const T&, T2>
        operator minmax_result<T2>() const & {
          return {min, max};
        }
 
      template<class T2>
        requires convertible_to<T, T2>
        operator minmax_result<T2>() && {
          return {std::move(min), std::move(max)};
        }
    };
 
    template<class T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr minmax_result<const T&>
        minmax(const T& a, const T& b, Cmp comp = {}, Proj proj = {});
    template<copyable T, class Proj = identity,
             indirect_strict_weak_order<projected<const T*, Proj>> Cmp = ranges::less>
      constexpr minmax_result<T>
        minmax(initializer_list<T> r, Cmp comp = {}, Proj proj = {});
    template<input_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      requires indirectly_copyable_storable<iterator_t<R>, range_value_t<R>*>
      constexpr minmax_result<range_value_t<R>>
        minmax(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter>
    constexpr ForwardIter min_element(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class Cmp>
    constexpr ForwardIter min_element(ForwardIter first, ForwardIter last, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter min_element(ExecutionPolicy&& exec,
                            ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class Cmp>
    ForwardIter min_element(ExecutionPolicy&& exec,
                            ForwardIter first, ForwardIter last, Cmp comp);
 
  namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr I min_element(I first, S last, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_iterator_t<R>
        min_element(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter>
    constexpr ForwardIter max_element(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class Cmp>
    constexpr ForwardIter max_element(ForwardIter first, ForwardIter last, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter>
    ForwardIter max_element(ExecutionPolicy&& exec,
                            ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class Cmp>
    ForwardIter max_element(ExecutionPolicy&& exec,
                            ForwardIter first, ForwardIter last, Cmp comp);
 
 namespace ranges {
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr I max_element(I first, S last, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr safe_iterator_t<R>
        max_element(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class ForwardIter>
    constexpr pair<ForwardIter, ForwardIter>
      minmax_element(ForwardIter first, ForwardIter last);
  template<class ForwardIter, class Cmp>
    constexpr pair<ForwardIter, ForwardIter>
      minmax_element(ForwardIter first, ForwardIter last, Cmp comp);
  template<class ExecutionPolicy, class ForwardIter>
    pair<ForwardIter, ForwardIter>
      minmax_element(ExecutionPolicy&& exec,
                     ForwardIter first, ForwardIter last);
  template<class ExecutionPolicy, class ForwardIter, class Cmp>
    pair<ForwardIter, ForwardIter>
      minmax_element(ExecutionPolicy&& exec,
                     ForwardIter first, ForwardIter last, Cmp comp);
 
  namespace ranges {
    template<class I>
    using minmax_element_result = minmax_result<I>;
 
    template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
             indirect_strict_weak_order<projected<I, Proj>> Cmp = ranges::less>
      constexpr minmax_element_result<I>
        minmax_element(I first, S last, Cmp comp = {}, Proj proj = {});
    template<forward_range R, class Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Cmp =
               ranges::less>
      constexpr minmax_element_result<safe_iterator_t<R>>
        minmax_element(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  // bounded value
  template<class T>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi);
  template<class T, class Cmp>
    constexpr const T& clamp(const T& v, const T& lo, const T& hi, Cmp comp);
 
  // lexicographical comparison
  template<class InputIter1, class InputIter2>
    constexpr bool
      lexicographical_compare(InputIter1 first1, InputIter1 last1,
                              InputIter2 first2, InputIter2 last2);
  template<class InputIter1, class InputIter2, class Cmp>
    constexpr bool
      lexicographical_compare(InputIter1 first1, InputIter1 last1,
                              InputIter2 first2, InputIter2 last2,
                              Cmp comp);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2>
    bool
      lexicographical_compare(ExecutionPolicy&& exec,
                              ForwardIter1 first1, ForwardIter1 last1,
                              ForwardIter2 first2, ForwardIter2 last2);
  template<class ExecutionPolicy, class ForwardIter1, class ForwardIter2, class Cmp>
    bool
      lexicographical_compare(ExecutionPolicy&& exec,
                              ForwardIter1 first1, ForwardIter1 last1,
                              ForwardIter2 first2, ForwardIter2 last2,
                              Cmp comp);
 
  namespace ranges {
    template<input_iterator I1, sentinel_for<I1> S1,
             input_iterator I2, sentinel_for<I2> S2,
             class Proj1 = identity, class Proj2 = identity,
             indirect_strict_weak_order<projected<I1, Proj1>, projected<I2, Proj2>> Cmp =
               ranges::less>
      constexpr bool
        lexicographical_compare(I1 first1, S1 last1, I2 first2, S2 last2,
                                Cmp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
    template<input_range R1, input_range R2, class Proj1 = identity,
             class Proj2 = identity,
             indirect_strict_weak_order<
               projected<iterator_t<R1>, Proj1>,
               projected<iterator_t<R2>, Proj2>> Cmp = ranges::less>
      constexpr bool
        lexicographical_compare(R1&& r1, R2&& r2, Cmp comp = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});
  }
 
  // three-way comparison algorithms
  template<class InputIter1, class InputIter2, class Cmp>
    constexpr auto
      lexicographical_compare_three_way(InputIter1 b1, InputIter1 e1,
                                        InputIter2 b2, InputIter2 e2, Cmp comp)
        -> common_comparison_category_t<decltype(comp(*b1, *b2)), strong_ordering>;
  template<class InputIter1, class InputIter2>
    constexpr auto
      lexicographical_compare_three_way(InputIter1 b1, InputIter1 e1,
                                        InputIter2 b2, InputIter2 e2);
 
  // permutations
  template<class BidirectionalIter>
    constexpr bool next_permutation(BidirectionalIter first, BidirectionalIter last);
  template<class BidirectionalIter, class Cmp>
    constexpr bool next_permutation(BidirectionalIter first, BidirectionalIter last,
                                    Cmp comp);
 
  namespace ranges {
    template<class I>
    struct next_permutation_result {
      bool found;
      I in;
    };
 
    template<bidirectional_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr next_permutation_result<I>
        next_permutation(I first, S last, Cmp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr next_permutation_result<safe_iterator_t<R>>
        next_permutation(R&& r, Cmp comp = {}, Proj proj = {});
  }
 
  template<class BidirectionalIter>
    constexpr bool prev_permutation(BidirectionalIter first,
                                    BidirectionalIter last);
  template<class BidirectionalIter, class Cmp>
    constexpr bool prev_permutation(BidirectionalIter first,
                                    BidirectionalIter last, Cmp comp);
 
  namespace ranges {
    template<class I>
    using prev_permutation_result = next_permutation_result<I>;
 
    template<bidirectional_iterator I, sentinel_for<I> S, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<I, Cmp, Proj>
      constexpr prev_permutation_result<I>
        prev_permutation(I first, S last, Cmp comp = {}, Proj proj = {});
    template<bidirectional_range R, class Cmp = ranges::less,
             class Proj = identity>
      requires sortable<iterator_t<R>, Cmp, Proj>
      constexpr prev_permutation_result<safe_iterator_t<R>>
        prev_permutation(R&& r, Cmp comp = {}, Proj proj = {});
  }
}