標準ライブラリヘッダ <algorithm>

 

C++

言語

標準ライブラリヘッダ

フリースタンディング処理系とホスト処理系

名前付き要件

言語サポートライブラリ

コンセプトライブラリ (C++20)

診断ライブラリ

ユーティリティライブラリ

文字列ライブラリ

コンテナライブラリ

イテレータライブラリ

範囲ライブラリ (C++20)

アルゴリズムライブラリ

数値演算ライブラリ

ローカライゼーションライブラリ

入出力ライブラリ

ファイルシステムライブラリ (C++17)

正規表現ライブラリ (C++11)

アトミック操作ライブラリ (C++11)

スレッドサポートライブラリ (C++11)

技術仕様書

 

標準ライブラリヘッダ

言語サポート
<cstddef> <cstdlib> <version> <limits> <climits>	<cfloat> <cstdint> <new> <typeinfo>	<source_location> <exception> <initializer_list> <compare>	<coroutine> <csignal> <csetjmp> <cstdarg>
コンセプト
<concepts>
診断
<stdexcept>	<cassert>	<cerrno>	<system_error>
汎用ユーティリティ
<utility> <memory> <memory_resource> <scoped_allocator>	<bitset> <tuple> <optional> <any>	<variant> <type_traits> <ratio> <chrono>	<typeindex> <functional> <ctime>
文字列
<string> <string_view> <cstring>	<charconv> <format>	<cctype> <cwctype>	<cwchar> <cuchar>
ローカライゼーション
<locale>	<codecvt>	<clocale>
コンテナ
<span> <array> <vector>	<deque> <forward_list> <list>	<map> <set> <queue>	<unordered_map> <unordered_set> <stack>
イテレータ
<iterator>
範囲
<ranges>
アルゴリズム
<algorithm>	<execution>
数値演算
<complex> <random>	<valarray> <numeric>	<bit> <numbers>	<cfenv> <cmath>
入出力
<iosfwd> <ios> <iomanip> <streambuf>	<istream> <ostream> <iostream>	<sstream> <spanstream> <fstream> <syncstream>	<cstdio> <cinttypes> <strstream>
正規表現
<regex>
ファイルシステムサポート
<filesystem>
スレッドサポート
<thread> <atomic> <mutex>	<shared_mutex> <condition_variable> <future>	<stop_token> <semaphore>	<latch> <barrier>
C互換
<ciso646> <cstdalign>	<cstdbool> <ccomplex>	<ctgmath> <stdatomic.h>

 

See More

このヘッダはアルゴリズムライブラリの一部です。

関数

非変更シーケンス操作
all_ofany_ofnone_of (C++11)(C++11)(C++11)	述語が指定範囲の要素のすべてに対して true を返すかどうか、いずれかに対して true を返すかどうか、またはいずれに対しても true を返さないかどうか、調べます (関数テンプレート)
for_each	指定範囲の要素に関数を適用します (関数テンプレート)
for_each_n (C++17)	指定個数の要素に関数を適用します (関数テンプレート)
countcount_if	一定の基準を満たす要素の数を返します (関数テンプレート)
mismatch	2つの範囲が異なる最初の位置を探します (関数テンプレート)
findfind_iffind_if_not (C++11)	一定の基準を満たす最初の要素を探します (関数テンプレート)
find_end	指定された要素の並びが現れる最後の位置を探します (関数テンプレート)
find_first_of	指定された要素のいずれかが現れる位置を探します (関数テンプレート)
adjacent_find	同じ要素 (または指定された述語を満たす要素) 2つが隣接している最初の位置を探します (関数テンプレート)
search	指定範囲の要素に対して検索を行います (関数テンプレート)
search_n	指定個数の連続する指定要素を指定範囲から検索します (関数テンプレート)
変更シーケンス操作
copycopy_if (C++11)	指定範囲の要素を新しい位置にコピーします (関数テンプレート)
copy_n (C++11)	指定個数の要素を新しい位置にコピーします (関数テンプレート)
copy_backward	指定範囲の要素を後ろからコピーします (関数テンプレート)
move (C++11)	指定範囲の要素を新しい位置にムーブします (関数テンプレート)
move_backward (C++11)	指定範囲の要素を後ろからムーブします (関数テンプレート)
fill	指定された要素を範囲内の全要素にコピー代入します (関数テンプレート)
fill_n	指定された要素を指定個数の要素にコピー代入します (関数テンプレート)
transform	指定範囲の要素に関数を適用し、結果を別の範囲に格納します (関数テンプレート)
generate	関数を連続的に呼び出した結果を指定範囲の全要素に代入します (関数テンプレート)
generate_n	関数を連続的に呼び出した結果を指定個数の要素に代入します (関数テンプレート)
removeremove_if	一定の基準を満たす要素を削除します (関数テンプレート)
remove_copyremove_copy_if	指定範囲の要素から一定の基準を満たすものを除いてコピーします (関数テンプレート)
replacereplace_if	一定の基準を満たすすべての値を別の値に置き換えます (関数テンプレート)
replace_copyreplace_copy_if	一定の基準を満たす要素を別の値に置き換えながら指定範囲をコピーします (関数テンプレート)
swap	2つのオブジェクトの値を入れ替えます (関数テンプレート)
swap_ranges	2つの範囲の要素を入れ替えます (関数テンプレート)
iter_swap	2つのイテレータが指す要素を入れ替えます (関数テンプレート)
reverse	指定範囲の要素の順序を反転させます (関数テンプレート)
reverse_copy	指定範囲の要素の順序を反転させたコピーを作成します (関数テンプレート)
rotate	指定範囲の要素の順序を回転させます (関数テンプレート)
rotate_copy	指定範囲の要素の順序を回転させたコピーを作成します (関数テンプレート)
shift_leftshift_right (C++20)	範囲内の要素をシフトします (関数テンプレート)
random_shuffleshuffle (C++17未満)(C++11)	指定範囲の要素をランダムに並べ替えます (関数テンプレート)
sample (C++17)	指定個数の要素をランダムに選択します (関数テンプレート)
unique	指定範囲の連続している重複要素を削除します (関数テンプレート)
unique_copy	指定範囲の要素の連続している重複要素が含まれないコピーを作成します (関数テンプレート)
分割操作
is_partitioned (C++11)	指定範囲が指定した述語で分割されているかどうか調べます (関数テンプレート)
partition	指定範囲の要素を2つのグループに分割します (関数テンプレート)
partition_copy (C++11)	指定範囲の要素を2つのグループに分割しながらコピーします (関数テンプレート)
stable_partition	相対的な順序を維持しながら要素を2つのグループに分割します (関数テンプレート)
partition_point (C++11)	分割された範囲の分割点を探します (関数テンプレート)
ソート操作
is_sorted (C++11)	指定範囲が昇順にソートされているか調べます (関数テンプレート)
is_sorted_until (C++11)	最も大きなソート済みの部分範囲を探します (関数テンプレート)
sort	指定範囲を昇順にソートします (関数テンプレート)
partial_sort	指定範囲の最初の N 個の要素をソートします (関数テンプレート)
partial_sort_copy	指定範囲の最初の N 個の要素がソートされたコピーを作成します (関数テンプレート)
stable_sort	等しい要素間の順序を維持しながら指定範囲の要素をソートします (関数テンプレート)
nth_element	指定された要素で分割されるように指定範囲を部分ソートします (関数テンプレート)
二分探索操作 (ソート済み範囲用)
lower_bound	指定された値より小さくない最初の要素を指すイテレータを返します (関数テンプレート)
upper_bound	指定された値より大きい最初の要素へのイテレータを返します (関数テンプレート)
binary_search	指定範囲に要素が存在するかどうか調べます (関数テンプレート)
equal_range	特定のキーに一致する要素の範囲を返します (関数テンプレート)
ソート済み範囲用のその他の操作
merge	2つのソート済み範囲をマージします (関数テンプレート)
inplace_merge	2つのソート済み範囲をその場でマージします (関数テンプレート)
集合演算 (ソート済み範囲用)
includes	ある集合が別の集合の部分集合であるかどうか調べます (関数テンプレート)
set_difference	2つの集合の差を計算します (関数テンプレート)
set_intersection	2つの集合の交叉を計算します (関数テンプレート)
set_symmetric_difference	2つの集合の対称差を計算します (関数テンプレート)
set_union	2つの集合の和を計算します (関数テンプレート)
ヒープ操作
is_heap (C++11)	指定範囲が最大ヒープであるかどうか調べます (関数テンプレート)
is_heap_until (C++11)	最大ヒープである最も大きな部分範囲を探します (関数テンプレート)
make_heap	指定範囲の要素から最大ヒープを作成します (関数テンプレート)
push_heap	最大ヒープに要素を追加します (関数テンプレート)
pop_heap	最大ヒープから最も大きな要素を削除します (関数テンプレート)
sort_heap	最大ヒープを昇順にソートされた要素の範囲に変換します (関数テンプレート)
最小/最大演算
max	指定された値の大きい方を返します (関数テンプレート)
max_element	指定範囲の最も大きな要素を返します (関数テンプレート)
min	指定された値の小さい方を返します (関数テンプレート)
min_element	指定範囲の最も小さな要素を返します (関数テンプレート)
minmax (C++11)	2つの要素の小さい方と大きい方を返します (関数テンプレート)
minmax_element (C++11)	指定範囲の最も小さな要素と最も大きな要素を返します (関数テンプレート)
clamp (C++17)	値を境界値の間にクランプします (関数テンプレート)
比較演算
equal	2つの要素集合が同じかどうか調べます (関数テンプレート)
lexicographical_compare	ある範囲が別の範囲より辞書的に小さいかどうか調べます (関数テンプレート)
lexicographical_compare_three_way (C++20)	三方比較を用いて2つの範囲を比較します (関数テンプレート)
順列操作
is_permutation (C++11)	あるシーケンスが別のシーケンスの順列並び替えになっているかどうか調べます (関数テンプレート)
next_permutation	指定範囲の要素より辞書的に大きな次の順列を生成します (関数テンプレート)
prev_permutation	指定範囲の要素より辞書的に小さな次の順列を生成します (関数テンプレート)

ニーブロイド

名前空間 std::ranges で定義
非変更シーケンス操作
all_ofany_ofnone_of	指定範囲内の要素のすべて、1個以上、または0個に対して述語が true を返すかどうか調べます (ニーブロイド)
for_each	指定範囲の要素に関数を適用します (ニーブロイド)
countcount_if	特定の基準を満たす要素の数を返します (ニーブロイド)
mismatch	2つの範囲が異なる最初の位置を探します (ニーブロイド)
findfind_iffind_if_not	特定の基準を満たす最初の要素を探します (ニーブロイド)
find_end	特定の範囲内の要素の最後のシーケンスを探します (ニーブロイド)
find_first_of	要素の集合のいずれかを検索します (ニーブロイド)
adjacent_find	最初の等しい (または指定の述語を満たす) 隣接する2つの項目を探します (ニーブロイド)
search	指定範囲の要素に対して検索を行います (ニーブロイド)
search_n	指定個数の連続する指定要素を指定範囲から検索します (ニーブロイド)
変更シーケンス操作
copycopy_if	指定範囲の要素を新しい位置にコピーします (ニーブロイド)
copy_n	指定個数の要素を新しい位置にコピーします (ニーブロイド)
copy_backward	指定範囲の要素を逆順にコピーします (ニーブロイド)
move	指定範囲の要素を新しい位置にムーブします (ニーブロイド)
move_backward	指定範囲の要素を新しい位置に逆順でムーブします (ニーブロイド)
fill	特定の値を指定範囲の要素に代入します (ニーブロイド)
fill_n	値を指定個数の要素に代入します (ニーブロイド)
transform	指定範囲の要素に関数を適用します (ニーブロイド)
generate	関数の結果を指定範囲に保存します (ニーブロイド)
generate_n	関数の N 回の適用の結果を保存します (ニーブロイド)
removeremove_if	特定の基準を満たす要素を削除します (ニーブロイド)
remove_copyremove_copy_if	特定の基準を満たす要素を省きながら指定範囲の要素をコピーします (ニーブロイド)
replacereplace_if	特定の基準を満たすすべての値を別の値に置き換えます (ニーブロイド)
replace_copyreplace_copy_if	特定の基準を満たす要素を別の値で置換しながら範囲をコピーします (ニーブロイド)
swap_ranges	2つの範囲の要素を入れ替えます (ニーブロイド)
reverse	指定範囲の要素の順序を反転させます (ニーブロイド)
reverse_copy	指定範囲の逆順のコピーを作成します (ニーブロイド)
rotate	指定範囲の要素の順序を回転させます (ニーブロイド)
rotate_copy	指定範囲の要素をコピーして回転させます (ニーブロイド)
shuffle	措定範囲の要素をランダムに並べ替えます (ニーブロイド)
unique	指定範囲の連続する重複要素を削除します (ニーブロイド)
unique_copy	連続する重複を含まない要素の範囲のコピーを作成します (ニーブロイド)
分割操作
is_partitioned	指定範囲が指定の述語で分割されているかどうか判定します (ニーブロイド)
partition	指定範囲の要素を2つのグループに分割します (ニーブロイド)
partition_copy	要素を2つのグループに分割しながら指定範囲をコピーします (ニーブロイド)
stable_partition	相対順序を維持しながら要素を2つのグループに分割します (ニーブロイド)
partition_point	分割済み範囲の分割点を探します (ニーブロイド)
ソート操作
is_sorted	指定範囲が昇順にソートされているかどうか調べます (ニーブロイド)
is_sorted_until	最も大きなソート済み部分範囲を探します (ニーブロイド)
sort	指定範囲を昇順にソートします (ニーブロイド)
partial_sort	指定範囲の最初の N 個の要素をソートします (ニーブロイド)
partial_sort_copy	指定範囲の要素をコピーして部分的にソートします (ニーブロイド)
stable_sort	等しい要素間の順序を維持しながら指定範囲の要素をソートします (ニーブロイド)
nth_element	指定要素で分割されることを保証しながら指定範囲を部分的にソートします (ニーブロイド)
二分探索操作 (ソート済み範囲用)
lower_bound	指定された値より小さくない最初の要素を指すイテレータを返します (ニーブロイド)
upper_bound	特定の値より大きい最初の要素を指すイテレータを返します (ニーブロイド)
binary_search	特定の範囲に要素が存在するかどうか判定します (ニーブロイド)
equal_range	特定のキーにマッチする要素の範囲を返します (ニーブロイド)
ソート済み範囲用のその他の操作
merge	2つのソート済み範囲をマージします (ニーブロイド)
inplace_merge	2つの順序付き範囲をその場でマージします (ニーブロイド)
集合演算 (ソート済み範囲用)
includes	ある集合が別の集合の部分集合であれば true を返します (ニーブロイド)
set_difference	2つの集合の差を計算します (ニーブロイド)
set_intersection	2つの集合の交差を計算します (ニーブロイド)
set_symmetric_difference	2つの集合の対称差を計算します (ニーブロイド)
set_union	2つの集合の和を計算します (ニーブロイド)
ヒープ操作
is_heap	指定された範囲が最大ヒープかどうか調べます (ニーブロイド)
is_heap_until	最大ヒープである最も大きな部分範囲を探します (ニーブロイド)
make_heap	指定範囲の要素から最大ヒープを作成します (ニーブロイド)
push_heap	最大ヒープに要素を追加します (ニーブロイド)
pop_heap	最大ヒープから最も大きな要素を削除します (ニーブロイド)
sort_heap	最大ヒープを昇順にソートされた要素の範囲に変換します (ニーブロイド)
最小/最大演算
max	指定された値の大きい方を返します (ニーブロイド)
max_element	指定範囲の最も大きな要素を返します (ニーブロイド)
min	指定された値の小さい方を返します (ニーブロイド)
min_element	指定範囲の最も小さな要素を返します (ニーブロイド)
minmax	2つの要素の小さい方と大きい方を返します (ニーブロイド)
minmax_element	指定範囲の最も小さな要素と最も大きな要素を返します (ニーブロイド)
比較演算
equal	2つの集合の要素が同じかどうか判定します (ニーブロイド)
lexicographical_compare	ある範囲が別の範囲より辞書順で小さい場合に true を返します (ニーブロイド)
順列操作
is_permutation	シーケンスが別のシーケンスの順列かどうか判定します (ニーブロイド)
next_permutation	指定範囲の要素より辞書的に大きな次の順列を生成します (ニーブロイド)
prev_permutation	指定範囲の要素より辞書的に小さな次の順列を生成します (ニーブロイド)

概要

#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<borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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<borrowed_iterator_t<R1>, borrowed_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 borrowed_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 borrowed_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<borrowed_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<borrowed_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<borrowed_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<borrowed_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<borrowed_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<borrowed_iterator_t<R1>, borrowed_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<borrowed_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<borrowed_iterator_t<R1>, borrowed_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 borrowed_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 borrowed_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<borrowed_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<borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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<borrowed_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<borrowed_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 borrowed_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<borrowed_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 borrowed_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<borrowed_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 borrowed_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<borrowed_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>>
      borrowed_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 borrowed_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>
      borrowed_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 borrowed_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<borrowed_iterator_t<R1>, borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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>>
      borrowed_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<borrowed_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 borrowed_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<borrowed_iterator_t<R1>, borrowed_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>
      borrowed_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<borrowed_iterator_t<R1>, borrowed_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<borrowed_iterator_t<R1>, borrowed_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<borrowed_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<borrowed_iterator_t<R1>, borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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 borrowed_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<borrowed_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<borrowed_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<borrowed_iterator_t<R>>
        prev_permutation(R&& r, Cmp comp = {}, Proj proj = {});
  }
}