Standard library header <iterator>

#include <compare>
#include <concepts>
namespace std {
  template<class T> using /* 带引用 */ = T&;  // 仅作展示用途
  template<class T> concept /* 可引用 */       // 仅作展示用途
    = requires { typename /* 带引用 */<T>; };
  template<class T> concept /* 可解引用 */     // 仅作展示用途
    = requires(T& t) {
      { *t } -> /* 可引用 */;  // 不要求保持相等性
    };
  // associated types
  // incrementable traits
  template<class> struct incrementable_traits;
  template<class T>
    using iter_difference_t = /* 查看描述 */;
  // 间接可读特性
  template<class> struct indirectly_readable_traits;
  template<class T>
    using iter_value_t = /* 查看描述 */;
  // iterator traits
  template<class I> struct iterator_traits;
  template<class T> requires is_object_v<T> struct iterator_traits<T*>;
  template</* 可解引用 */ T>
    using iter_reference_t = decltype(*declval<T&>());
  namespace ranges {
    // customization point objects
    inline namespace /* 未指定 */ {
      // ranges::iter_move
      inline constexpr /* 未指定 */ iter_move = /* 未指定 */;
      // ranges::iter_swap
      inline constexpr /* 未指定 */ iter_swap = /* 未指定 */;
    }
  }
  template</* 可解引用 */ T>
    requires requires(T& t) {
      { ranges::iter_move(t) } -> /* 可引用 */;
    }
  using iter_rvalue_reference_t
    = decltype(ranges::iter_move(declval<T&>()));
  // 迭代器概念
  // concept indirectly_readable
  template<class In>
    concept indirectly_readable = /* 查看描述 */;
  template<indirectly_readable T>
    using iter_common_reference_t =
      common_reference_t<iter_reference_t<T>, iter_value_t<T>&>;
  // concept indirectly_writable
  template<class Out, class T>
    concept indirectly_writable = /* 查看描述 */;
  // concept weakly_incrementable
  template<class I>
    concept weakly_incrementable = /* 查看描述 */;
  // concept incrementable
  template<class I>
    concept incrementable = /* 查看描述 */;
  // concept input_or_output_iterator
  template<class I>
    concept input_or_output_iterator = /* 查看描述 */;
  // concept sentinel_for
  template<class S, class I>
    concept sentinel_for = /* 查看描述 */;
  // concept sized_sentinel_for
  template<class S, class I>
    inline constexpr bool disable_sized_sentinel_for = false;
  template<class S, class I>
    concept sized_sentinel_for = /* 查看描述 */;
  // concept input_iterator
  template<class I>
    concept input_iterator = /* 查看描述 */;
  // concept output_iterator
  template<class I, class T>
    concept output_iterator = /* 查看描述 */;
  // concept forward_iterator
  template<class I>
    concept forward_iterator = /* 查看描述 */;
  // concept bidirectional_iterator
  template<class I>
    concept bidirectional_iterator = /* 查看描述 */;
  // concept random_access_iterator
  template<class I>
    concept random_access_iterator = /* 查看描述 */;
  // concept contiguous_iterator
  template<class I>
    concept contiguous_iterator = /* 查看描述 */;
  // 间接可调用要求
  // 间接可调用对象
  template<class F, class I>
    concept indirectly_unary_invocable = /* 查看描述 */;
  template<class F, class I>
    concept indirectly_regular_unary_invocable = /* 查看描述 */;
  template<class F, class I>
    concept indirect_unary_predicate = /* 查看描述 */;
  template<class F, class I1, class I2>
    concept indirect_binary_predicate = /* 查看描述 */;
  template<class F, class I1, class I2 = I1>
    concept indirect_equivalence_relation = /* 查看描述 */;
  template<class F, class I1, class I2 = I1>
    concept indirect_strict_weak_order = /* 查看描述 */;
  template<class F, class... Is>
    requires (indirectly_readable<Is> && ...) && invocable<F, iter_reference_t<Is>...>
      using indirect_result_t = invoke_result_t<F, iter_reference_t<Is>...>;
  // projected
  template<indirectly_readable I, indirectly_regular_unary_invocable<I> Proj>
    using projected = /* 查看描述 */;
  template<indirectly_­readable I, indirectly_­regular_­unary_­invocable<I> Proj>
    using projected_value_t = remove_cvref_t<invoke_result_t<Proj&, iter_value_t<I>&>>;
  // 通用算法要求
  // concept indirectly_movable
  template<class In, class Out>
    concept indirectly_movable = /* 查看描述 */;
  template<class In, class Out>
    concept indirectly_movable_storable = /* 查看描述 */;
  // concept indirectly_copyable
  template<class In, class Out>
    concept indirectly_copyable = /* 查看描述 */;
  template<class In, class Out>
    concept indirectly_copyable_storable = /* 查看描述 */;
  // concept indirectly_swappable
  template<class I1, class I2 = I1>
    concept indirectly_swappable = /* 查看描述 */;
  // concept indirectly_comparable
  template<class I1, class I2, class R, class P1 = identity, class P2 = identity>
    concept indirectly_comparable = /* 查看描述 */;
  // 概念 permutable
  template<class I>
    concept permutable = /* 查看描述 */;
  // concept mergeable
  template<class I1, class I2, class Out,
      class R = ranges::less, class P1 = identity, class P2 = identity>
    concept mergeable = /* 查看描述 */;
  // concept sortable
  template<class I, class R = ranges::less, class P = identity>
    concept sortable = /* 查看描述 */;
  // primitives
  // 迭代器标签
  struct input_iterator_tag { };
  struct output_iterator_tag { };
  struct forward_iterator_tag: public input_iterator_tag { };
  struct bidirectional_iterator_tag: public forward_iterator_tag { };
  struct random_access_iterator_tag: public bidirectional_iterator_tag { };
  struct contiguous_iterator_tag: public random_access_iterator_tag { };
  // 迭代器操作
  template<class InputIt, class Distance>
    constexpr void advance(InputIt& i, Distance n);
  template<class InputIt>
    constexpr typename iterator_traits<InputIt>::difference_type
      distance(InputIt first, InputIt last);
  template<class InputIt>
    constexpr InputIt
      next(InputIt x, typename iterator_traits<InputIt>::difference_type n = 1);
  template<class BidirIt>
    constexpr BidirIt
      prev(BidirIt x, typename iterator_traits<BidirIt>::difference_type n = 1);
  // range iterator operations
  namespace ranges {
    // ranges::advance
    template<input_or_output_iterator I>
      constexpr void advance(I& i, iter_difference_t<I> n);
    template<input_or_output_iterator I, sentinel_for<I> S>
      constexpr void advance(I& i, S bound);
    template<input_or_output_iterator I, sentinel_for<I> S>
      constexpr iter_difference_t<I> advance(I& i, iter_difference_t<I> n, S bound);
    // ranges::distance
    template<class I, sentinel_for<I> S>
      requires (!sized_sentinel_for<S, I>)
      constexpr iter_difference_t<I> distance(I first, S last);
    template<class I, sized_sentinel_for<decay_t<I>> S>
      constexpr iter_difference_t<decay_t<I>> distance(I&& first, S last);
    template<range R>
      constexpr range_difference_t<R> distance(R&& r);
    // ranges::next
    template<input_or_output_iterator I>
      constexpr I next(I x);
    template<input_or_output_iterator I>
      constexpr I next(I x, iter_difference_t<I> n);
    template<input_or_output_iterator I, sentinel_for<I> S>
      constexpr I next(I x, S bound);
    template<input_or_output_iterator I, sentinel_for<I> S>
      constexpr I next(I x, iter_difference_t<I> n, S bound);
    // ranges::prev
    template<bidirectional_iterator I>
      constexpr I prev(I x);
    template<bidirectional_iterator I>
      constexpr I prev(I x, iter_difference_t<I> n);
    template<bidirectional_iterator I>
      constexpr I prev(I x, iter_difference_t<I> n, I bound);
  }
  // 预定义的迭代器和哨兵
  // 反向迭代器
  template<class It> class reverse_iterator;
  template<class It1, class It2>
    constexpr bool operator==(const reverse_iterator<It1>& x,
                              const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator!=(const reverse_iterator<It1>& x,
                              const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator<(const reverse_iterator<It1>& x,
                             const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator>(const reverse_iterator<It1>& x,
                             const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator<=(const reverse_iterator<It1>& x,
                              const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator>=(const reverse_iterator<It1>& x,
                              const reverse_iterator<It2>& y);
  template<class It1, three_way_comparable_with<It1> It2>
    constexpr compare_three_way_result_t<It1, It2>
      operator<=>(const reverse_iterator<It1>& x, const reverse_iterator<It2>& y);
  template<class It1, class It2>
    constexpr auto operator-(const reverse_iterator<It1>& x,
                             const reverse_iterator<It2>& y)
      -> decltype(y.base() - x.base());
  template<class It>
    constexpr reverse_iterator<It> operator+(iter_difference_t<It> n,
                                             const reverse_iterator<It>& x);
  template<class It>
    constexpr reverse_iterator<It> make_reverse_iterator(It i);
  template<class It1, class It2>
      requires (!sized_sentinel_for<It1, It2>)
    inline constexpr bool disable_sized_sentinel_for<reverse_iterator<It1>,
                                                     reverse_iterator<It2>> = true;
  // 插入迭代器
  template<class Container> class back_insert_iterator;
  template<class Container>
    constexpr back_insert_iterator<Container> back_inserter(Container& x);
  template<class Container> class front_insert_iterator;
  template<class Container>
    constexpr front_insert_iterator<Container> front_inserter(Container& x);
  template<class Container> class insert_iterator;
  template<class Container>
    constexpr insert_iterator<Container>
      inserter(Container& x, ranges::iterator_t<Container> i);
  // move iterators and sentinels
  template<class It> class move_iterator;
  template<class It1, class It2>
    constexpr bool operator==(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator<(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator>(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator<=(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, class It2>
    constexpr bool operator>=(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, three_way_comparable_with<It1> It2>
    constexpr compare_three_way_result_t<It1, It2>
      operator<=>(const move_iterator<It1>& x, const move_iterator<It2>& y);
  template<class It1, class It2>
    constexpr auto operator-(const move_iterator<It1>& x, const move_iterator<It2>& y)
      -> decltype(x.base() - y.base());
  template<class It>
    constexpr move_iterator<It>
      operator+(iter_difference_t<It> n, const move_iterator<It>& x);
  template<class It>
    constexpr move_iterator<It> make_move_iterator(It i);
  template<semiregular S> class move_sentinel;
  // 常用迭代器
  template<input_or_output_iterator I, sentinel_for<I> S>
    requires (!same_as<I, S> && copyable<I>)
      class common_iterator;
  template<class I, class S>
    struct incrementable_traits<common_iterator<I, S>>;
  template<input_iterator I, class S>
    struct iterator_traits<common_iterator<I, S>>;
  // 默认哨兵
  struct default_sentinel_t;
  inline constexpr default_sentinel_t default_sentinel{};
  // 计数迭代器
  template<input_or_output_iterator I> class counted_iterator;
  template<input_iterator I>
    requires /* 查看描述 */
    struct iterator_traits<counted_iterator<I>>;
  // 不可达哨兵
  struct unreachable_sentinel_t;
  inline constexpr unreachable_sentinel_t unreachable_sentinel{};
  // 流迭代器
  template<class T, class CharT = char, class Traits = char_traits<CharT>,
           class Distance = ptrdiff_t>
  class istream_iterator;
  template<class T, class CharT, class Traits, class Distance>
    bool operator==(const istream_iterator<T, CharT, Traits, Distance>& x,
                    const istream_iterator<T, CharT, Traits, Distance>& y);
  template<class T, class CharT = char, class traits = char_traits<CharT>>
      class ostream_iterator;
  template<class CharT, class Traits = char_traits<CharT>>
    class istreambuf_iterator;
  template<class CharT, class Traits>
    bool operator==(const istreambuf_iterator<CharT, Traits>& a,
                    const istreambuf_iterator<CharT, Traits>& b);
  template<class CharT, class Traits = char_traits<CharT>>
    class ostreambuf_iterator;
  // 范围访问
  template<class C> constexpr auto begin(C& c) -> decltype(c.begin());
  template<class C> constexpr auto begin(const C& c) -> decltype(c.begin());
  template<class C> constexpr auto end(C& c) -> decltype(c.end());
  template<class C> constexpr auto end(const C& c) -> decltype(c.end());
  template<class T, size_t N> constexpr T* begin(T (&a)[N]) noexcept;
  template<class T, size_t N> constexpr T* end(T (&a)[N]) noexcept;
  template<class C> constexpr auto cbegin(const C& c) noexcept(noexcept(std::begin(c)))
    -> decltype(std::begin(c));
  template<class C> constexpr auto cend(const C& c) noexcept(noexcept(std::end(c)))
    -> decltype(std::end(c));
  template<class C> constexpr auto rbegin(C& c) -> decltype(c.rbegin());
  template<class C> constexpr auto rbegin(const C& c) -> decltype(c.rbegin());
  template<class C> constexpr auto rend(C& c) -> decltype(c.rend());
  template<class C> constexpr auto rend(const C& c) -> decltype(c.rend());
  template<class T, size_t N> constexpr reverse_iterator<T*> rbegin(T (&a)[N]);
  template<class T, size_t N> constexpr reverse_iterator<T*> rend(T (&a)[N]);
  template<class E> constexpr reverse_iterator<const E*> rbegin(initializer_list<E> il);
  template<class E> constexpr reverse_iterator<const E*> rend(initializer_list<E> il);
  template<class C> constexpr auto crbegin(const C& c) -> decltype(std::rbegin(c));
  template<class C> constexpr auto crend(const C& c) -> decltype(std::rend(c));
  template<class C> constexpr auto size(const C& c) -> decltype(c.size());
  template<class T, size_t N> constexpr size_t size(const T (&a)[N]) noexcept;
  template<class C> constexpr auto ssize(const C& c)
    -> common_type_t<ptrdiff_t, make_signed_t<decltype(c.size())>>;
  template<class T, ptrdiff_t N> constexpr ptrdiff_t ssize(const T (&a)[N]) noexcept;
  template<class C> constexpr auto empty(const C& c) -> decltype(c.empty());
  template<class T, size_t N> constexpr bool empty(const T (&a)[N]) noexcept;
  template<class E> constexpr bool empty(initializer_list<E> il) noexcept;
  template<class C> constexpr auto data(C& c) -> decltype(c.data());
  template<class C> constexpr auto data(const C& c) -> decltype(c.data());
  template<class T, size_t N> constexpr T* data(T (&a)[N]) noexcept;
  template<class E> constexpr const E* data(initializer_list<E> il) noexcept;
}

namespace std {
  template<class In>
    concept /*indirectlyReadableImpl*/ = // 仅用于说明
      requires(const In in) {
        typename iter_value_t<In>;
        typename iter_reference_t<In>;
        typename iter_rvalue_reference_t<In>;
        { *in } -> same_as<iter_reference_t<In>>
        { iter_move(in) } -> same_as<iter_rvalue_reference_t<In>>
      } &&
      common_reference_with<iter_reference_t<In>&&, iter_value_t<In>&> &&
      common_reference_with<iter_reference_t<In>&&, iter_rvalue_reference_t<In>&&> &&
      common_reference_with<iter_rvalue_reference_t<In>&&, const iter_value_t<In>&>;
  template<class In>
    concept indirectly_readable =
      /*indirectlyReadableImpl*/<remove_cvref_t<In>>
}

namespace std {
  template<class Out, class T>
    concept indirectly_writable =
      requires(Out&& o, T&& t) {
        *o = std::forward<T>(t); // 不要求保持相等性
        *std::forward<Out>(o) = std::forward<T>(t);
        // 不要求保持相等性
        const_cast<const iter_reference_t<Out>&&>(*o) =
        std::forward<T>(t); // 不要求保持相等性
        const_cast<const iter_reference_t<Out>&&>(*std::forward<Out>(o)) =
        std::forward<T>(t); // 不要求保持相等性
      };
}

namespace std {
  template<class T>
    inline constexpr bool /*is_integer_like*/ = /* 见描述 */; // 仅用于说明
  template<class T>
    inline constexpr bool /*is_signed_integer_like*/ =  // 仅用于说明
      /* 见描述 */;
  template<class I>
    concept weakly_incrementable =
      default_initializable<I> && movable<I> &&
      requires(I i) {
        typename iter_difference_t<I>;
        requires /*is_signed_integer_like*/<iter_difference_t<I>>;
        { ++i } -> same_as<I&>;   // 不要求保持相等性
        i++;                      // 不要求保持相等性
      };
}

namespace std {
  template<class I>
    concept incrementable =
      regular<I> &&
      weakly_incrementable<I> &&
      requires(I i) {
        { i++ } -> same_as<I>;
      };
}

namespace std {
  template<class I>
    concept input_or_output_iterator =
      requires(I i) {
        { *i } -> can-reference;
      } &&
      weakly_incrementable<I>;
}

namespace std {
  template<class S, class I>
    concept sentinel_for =
      semiregular<S> &&
      input_or_output_iterator<I> &&
      /*WeaklyEqualityComparableWith*/<S, I>;
}

namespace std {
  template<class S, class I>
    concept sized_sentinel_for =
      sentinel_for<S, I> &&
      !disable_sized_sentinel<remove_cv_t<S>, remove_cv_t<I>> &&
      requires(const I& i, const S& s) {
        { s - i } -> same_as<iter_difference_t<I>>;
        { i - s } -> same_as<iter_difference_t<I>>;
      };
}

namespace std {
  template<class I>
    concept input_iterator =
      input_or_output_iterator<I> &&
      indirectly_readable<I> &&
      requires { typename /* ITER_CONCEPT */(I); } &&
      derived_from</* ITER_CONCEPT */(I), input_iterator_tag>;
}

namespace std {
  template<class I, class T>
    concept output_iterator =
      input_or_output_iterator<I> &&
      indirectly_writable<I, T> &&
      requires(I i, T&& t) {
        *i++ = std::forward<T>(t); // 不要求保持相等性
      };
}

namespace std {
  template<class I>
    concept forward_iterator =
      input_iterator<I> &&
      derived_from</* ITER_CONCEPT */(I), forward_iterator_tag> &&
      incrementable<I> &&
      sentinel_for<I, I>;
}

namespace std {
  template<class I>
    concept bidirectional_iterator =
      forward_iterator<I> &&
      derived_from</* ITER_CONCEPT */(I), bidirectional_iterator_tag> &&
      requires(I i) {
        { --i } -> same_as<I&>;
        { i-- } -> same_as<I>;
      };
}

namespace std {
  template<class I>
    concept random_access_iterator =
      bidirectional_iterator<I> &&
      derived_from</* 迭代器概念 */(I), random_access_iterator_tag> &&
      totally_ordered<I> &&
      sized_sentinel_for<I, I> &&
      requires(I i, const I j, const iter_difference_t<I> n) {
        { i += n } -> same_as<I&>;
        { j +  n } -> same_as<I>;
        { n +  j } -> same_as<I>;
        { i -= n } -> same_as<I&>;
        { j -  n } -> same_as<I>;
        {  j[n]  } -> same_as<iter_reference_t<I>>;
      };
}

namespace std {
  template<class I>
    concept contiguous_iterator =
      random_access_iterator<I> &&
      derived_from</* ITER_CONCEPT */(I), contiguous_iterator_tag> &&
      is_lvalue_reference_v<iter_reference_t<I>> &&
      same_as<iter_value_t<I>, remove_cvref_t<iter_reference_t<I>>> &&
      requires(const I& i) {
        { to_address(i) } -> same_as<add_pointer_t<iter_reference_t<I>>>;
      };
}

namespace std {
  template<class F, class I>
    concept indirectly_unary_invocable =
      indirectly_readable<I> &&
      copy_constructible<F> &&
      invocable<F&, iter_value_t<I>&> &&
      invocable<F&, iter_reference_t<I>> &&
      common_reference_with<
        invoke_result_t<F&, iter_value_t<I>&>,
        invoke_result_t<F&, iter_reference_t<I>>>;
}

namespace std {
  template<class F, class I>
    concept indirectly_regular_unary_invocable =
      indirectly_readable<I> &&
      copy_constructible<F> &&
      regular_invocable<F&, iter_value_t<I>&> &&
      regular_invocable<F&, iter_reference_t<I>> &&
      common_reference_with<
        invoke_result_t<F&, iter_value_t<I>&>,
        invoke_result_t<F&, iter_reference_t<I>>>;
}

namespace std {
  template<class F, class I>
    concept indirect_unary_predicate =
      indirectly_readable<I> &&
      copy_constructible<F> &&
      predicate<F&, iter_value_t<I>&> &&
      predicate<F&, iter_reference_t<I>>;
}

namespace std {
  template<class F, class I1, class I2 = I1>
    concept indirect_binary_predicate =
      indirectly_readable<I1> && indirectly_readable<I2> &&
      copy_constructible<F> &&
      predicate<F&, iter_value_t<I1>&, iter_value_t<I2>&> &&
      predicate<F&, iter_value_t<I1>&, iter_reference_t<I2>> &&
      predicate<F&, iter_reference_t<I1>, iter_value_t<I2>&> &&
      predicate<F&, iter_reference_t<I1>, iter_reference_t<I2>>;
}

namespace std {
  template<class F, class I1, class I2 = I1>
    concept indirect_equivalence_relation =
      indirectly_readable<I1> && indirectly_readable<I2> &&
      copy_constructible<F> &&
      equivalence_relation<F&, iter_value_t<I1>&, iter_value_t<I2>&> &&
      equivalence_relation<F&, iter_value_t<I1>&, iter_reference_t<I2>> &&
      equivalence_relation<F&, iter_reference_t<I1>, iter_value_t<I2>&> &&
      equivalence_relation<F&, iter_reference_t<I1>, iter_reference_t<I2>>;
}

namespace std {
  template<class F, class I1, class I2 = I1>
    concept indirect_strict_weak_order =
      indirectly_readable<I1> && indirectly_readable<I2> &&
      copy_constructible<F> &&
      strict_weak_order<F&, iter_value_t<I1>&, iter_value_t<I2>&> &&
      strict_weak_order<F&, iter_value_t<I1>&, iter_reference_t<I2>> &&
      strict_weak_order<F&, iter_reference_t<I1>, iter_value_t<I2>&> &&
      strict_weak_order<F&, iter_reference_t<I1>, iter_reference_t<I2>>;
}

namespace std {
  template<class In, class Out>
    concept indirectly_movable =
      indirectly_readable<In> &&
      indirectly_writable<Out, iter_rvalue_reference_t<In>>;
}

namespace std {
  template<class In, class Out>
    concept indirectly_movable_storable =
      indirectly_movable<In, Out> &&
      indirectly_writable<Out, iter_value_t<In>> &&
      movable<iter_value_t<In>> &&
      constructible_from<iter_value_t<In>, iter_rvalue_reference_t<In>> &&
      assignable_from<iter_value_t<In>&, iter_rvalue_reference_t<In>>;
}

namespace std {
  template<class In, class Out>
    concept indirectly_copyable =
      indirectly_readable<In> &&
      indirectly_writable<Out, iter_reference_t<In>>;
}

namespace std {
  template<class In, class Out>
    concept indirectly_copyable_storable =
      indirectly_copyable<In, Out> &&
      indirectly_writable<Out, iter_value_t<In>&> &&
      indirectly_writable<Out, const iter_value_t<In>&> &&
      indirectly_writable<Out, iter_value_t<In>&&> &&
      indirectly_writable<Out, const iter_value_t<In>&&> &&
      copyable<iter_value_t<In>> &&
      constructible_from<iter_value_t<In>, iter_reference_t<In>> &&
      assignable_from<iter_value_t<In>&, iter_reference_t<In>>;
}

namespace std {
  template<class I1, class I2 = I1>
    concept indirectly_swappable =
      indirectly_readable<I1> && indirectly_readable<I2> &&
      requires(const I1 i1, const I2 i2) {
        ranges::iter_swap(i1, i1);
        ranges::iter_swap(i2, i2);
        ranges::iter_swap(i1, i2);
        ranges::iter_swap(i2, i1);
      };
}

namespace std {
  template<class I1, class I2, class R, class P1 = identity, class P2 = identity>
    concept indirectly_comparable =
      indirect_predicate<R, projected<I1, P1>, projected<I2, P2>>;
}

namespace std {
  template<class I>
    concept permutable =
      forward_iterator<I> &&
      indirectly_movable_storable<I, I> &&
      indirectly_swappable<I, I>;
}

namespace std {
  template<class I1, class I2, class Out, class R = ranges::less,
           class P1 = identity, class P2 = identity>
    concept mergeable =
      input_iterator<I1> &&
      input_iterator<I2> &&
      weakly_incrementable<Out> &&
      indirectly_copyable<I1, Out> &&
      indirectly_copyable<I2, Out> &&
      indirect_strict_weak_order<R, projected<I1, P1>, projected<I2, P2>>;
}

namespace std {
  template<class I, class R = ranges::less, class P = identity>
    concept sortable =
      permutable<I> &&
      indirect_strict_weak_order<R, projected<I, P>>;
}

namespace std {
  template<class> struct incrementable_traits { };
  template<class T>
    requires is_object_v<T>
  struct incrementable_traits<T*> {
    using difference_type = ptrdiff_t;
  };
  template<class I>
  struct incrementable_traits<const I>
    : incrementable_traits<I> { };
  template<class T>
    requires requires { typename T::difference_type; }
  struct incrementable_traits<T> {
    using difference_type = typename T::difference_type;
  };
  template<class T>
    requires (!requires { typename T::difference_type; } &&
              requires(const T& a, const T& b) { { a - b } -> integral; })
  struct incrementable_traits<T> {
    using difference_type = make_signed_t<decltype(declval<T>() - declval<T>())>;
  };
  template<class T>
    using iter_difference_t = /* 详见描述 */;
}

namespace std {
  template<class> struct /*cond_value_type*/ { };   // 仅用于说明
  template<class T>
    requires is_object_v<T>
  struct /*cond_value_type*/ {
    using value_type = remove_cv_t<T>;
  };
  template<class> struct indirectly_readable_traits { };
  template<class T>
  struct indirectly_readable_traits<T*>
    : /*cond_value_type*/<T> { };
  template<class I>
    requires is_array_v<I>
  struct indirectly_readable_traits<I> {
    using value_type = remove_cv_t<remove_extent_t<I>>;
  };
  template<class I>
  struct indirectly_readable_traits<const I>
    : indirectly_readable_traits<I> { };
  template<class T>
    requires requires { typename T::value_type; }
  struct indirectly_readable_traits<T>
    : /*cond_value_type*/<typename T::value_type> { };
  template<class T>
    requires requires { typename T::element_type; }
  struct indirectly_readable_traits<T>
    : /*cond_value_type*/<typename T::element_type> { };
}

namespace std {
  template<class I, class Proj>
  struct /*projected-impl*/ {                        // 仅用于说明
    struct /*type*/ {                                // 仅用于说明
      using value_type = remove_cvref_t<indirect_result_t<Proj&, I>>;
      using difference_type = iter_difference_t<I>;  // 仅当 I 满足 weakly_incrementable 概念时存在
                                                                     // 
      indirect_result_t<Proj&, I> operator*() const; // 未定义
    };
  };
  template<indirectly_readable I, indirectly_regular_unary_invocable<I> Proj>
  using projected = /*projected-impl*/<I, Proj>::/*type*/;
}

namespace std {
  template<class I>
  struct iterator_traits {
    using iterator_category = /* 参见描述 */;
    using value_type        = /* 参见描述 */;
    using difference_type   = /* 参见描述 */;
    using pointer           = /* 参见描述 */;
    using reference         = /* 参见描述 */;
  };
  template<class T>
    requires is_object_v<T>
  struct iterator_traits<T*> {
    using iterator_concept  = contiguous_iterator_tag;
    using iterator_category = random_access_iterator_tag;
    using value_type        = remove_cv_t<T>;
    using difference_type   = ptrdiff_t;
    using pointer           = T*;
    using reference         = T&;
  };
}

namespace std {
  struct input_iterator_tag { };
  struct output_iterator_tag { };
  struct forward_iterator_tag: public input_iterator_tag { };
  struct bidirectional_iterator_tag: public forward_iterator_tag { };
  struct random_access_iterator_tag: public bidirectional_iterator_tag { };
  struct contiguous_iterator_tag: public random_access_iterator_tag { };
}

namespace std {
  template<class Iter>
  class reverse_iterator {
  public:
    using iterator_type     = Iter;
    using iterator_concept  = /* 见描述 */;
    using iterator_category = /* 见描述 */;
    using value_type        = iter_value_t<Iter>;
    using difference_type   = iter_difference_t<Iter>;
    using pointer           = typename iterator_traits<Iter>::pointer;
    using reference         = iter_reference_t<Iter>;
    constexpr reverse_iterator();
    constexpr explicit reverse_iterator(Iter x);
    template<class U> constexpr reverse_iterator(const reverse_iterator<U>& u);
    template<class U> constexpr reverse_iterator& operator=(const reverse_iterator<U>& u);
    constexpr Iter base() const;
    constexpr reference operator*() const;
    constexpr pointer   operator->() const requires /* 见描述 */;
    constexpr reverse_iterator& operator++();
    constexpr reverse_iterator  operator++(int);
    constexpr reverse_iterator& operator--();
    constexpr reverse_iterator  operator--(int);
    constexpr reverse_iterator  operator+ (difference_type n) const;
    constexpr reverse_iterator& operator+=(difference_type n);
    constexpr reverse_iterator  operator- (difference_type n) const;
    constexpr reverse_iterator& operator-=(difference_type n);
    constexpr /* 未指定 */ operator[](difference_type n) const;
    friend constexpr iter_rvalue_reference_t<Iter>
      iter_move(const reverse_iterator& i) noexcept(/* 见描述 */);
    template<indirectly_swappable<Iter> Iter2>
      friend constexpr void
        iter_swap(const reverse_iterator& x,
                  const reverse_iterator<Iter2>& y) noexcept(/* 见描述 */);
  protected:
    Iter current;
  };
}

namespace std {
  template<class Container>
  class back_insert_iterator {
  protected:
    Container* container = nullptr;
  public:
    using iterator_category = output_iterator_tag;
    using value_type        = void;
    using difference_type   = ptrdiff_t;
    using pointer           = void;
    using reference         = void;
    using container_type    = Container;
    constexpr back_insert_iterator() noexcept = default;
    constexpr explicit back_insert_iterator(Container& x);
    constexpr back_insert_iterator& operator=(const typename Container::value_type& value);
    constexpr back_insert_iterator& operator=(typename Container::value_type&& value);
    constexpr back_insert_iterator& operator*();
    constexpr back_insert_iterator& operator++();
    constexpr back_insert_iterator  operator++(int);
  };
}

namespace std {
  template<class Container>
  class front_insert_iterator {
  protected:
    Container* container = nullptr;
  public:
    using iterator_category = output_iterator_tag;
    using value_type        = void;
    using difference_type   = ptrdiff_t;
    using pointer           = void;
    using reference         = void;
    using container_type    = Container;
    constexpr front_insert_iterator(Container& x) noexcept = default;
    constexpr explicit front_insert_iterator(Container& x);
    constexpr front_insert_iterator&
      operator=(const typename Container::value_type& value);
    constexpr front_insert_iterator& operator=(typename Container::value_type&& value);
    constexpr front_insert_iterator& operator*();
    constexpr front_insert_iterator& operator++();
    constexpr front_insert_iterator  operator++(int);
  };
}

namespace std {
  template<class Container>
  class insert_iterator {
  protected:
    Container* container = nullptr;
    ranges::iterator_t<Container> iter = ranges::iterator_t<Container>();
  public:
    using iterator_category = output_iterator_tag;
    using value_type        = void;
    using difference_type   = ptrdiff_t;
    using pointer           = void;
    using reference         = void;
    using container_type    = Container;
    insert_iterator() = default;
    constexpr insert_iterator(Container& x, ranges::iterator_t<Container> i);
    constexpr insert_iterator& operator=(const typename Container::value_type& value);
    constexpr insert_iterator& operator=(typename Container::value_type&& value);
    constexpr insert_iterator& operator*();
    constexpr insert_iterator& operator++();
    constexpr insert_iterator& operator++(int);
  };
}

namespace std {
  template<class Iter>
  class move_iterator {
  public:
    using iterator_type     = Iter;
    using iterator_concept  = /* 参见描述 */;
    using iterator_category = /* 参见描述 */;
    using value_type        = iter_value_t<Iter>;
    using difference_type   = iter_difference_t<Iter>;
    using pointer           = Iter;
    using reference         = iter_rvalue_reference_t<Iter>;
    constexpr move_iterator();
    constexpr explicit move_iterator(Iter i);
    template<class U> constexpr move_iterator(const move_iterator<U>& u);
    template<class U> constexpr move_iterator& operator=(const move_iterator<U>& u);
    constexpr iterator_type base() const &;
    constexpr iterator_type base() &&;
    constexpr reference operator*() const;
    constexpr pointer operator->() const;
    constexpr move_iterator& operator++();
    constexpr auto operator++(int);
    constexpr move_iterator& operator--();
    constexpr move_iterator operator--(int);
    constexpr move_iterator operator+(difference_type n) const;
    constexpr move_iterator& operator+=(difference_type n);
    constexpr move_iterator operator-(difference_type n) const;
    constexpr move_iterator& operator-=(difference_type n);
    constexpr reference operator[](difference_type n) const;
    template<sentinel_for<Iter> S>
      friend constexpr bool
        operator==(const move_iterator& x, const move_sentinel<S>& y);
    template<sized_sentinel_for<Iter> S>
      friend constexpr iter_difference_t<Iter>
        operator-(const move_sentinel<S>& x, const move_iterator& y);
    template<sized_sentinel_for<Iter> S>
      friend constexpr iter_difference_t<Iter>
        operator-(const move_iterator& x, const move_sentinel<S>& y);
    friend constexpr iter_rvalue_reference_t<Iter>
      iter_move(const move_iterator& i)
        noexcept(noexcept(ranges::iter_move(i.current)));
    template<indirectly_swappable<Iter> Iter2>
      friend constexpr void
        iter_swap(const move_iterator& x, const move_iterator<Iter2>& y)
          noexcept(noexcept(ranges::iter_swap(x.current, y.current)));
  private:
    Iter current;     // 仅用于说明
  };
}

namespace std {
  template<semiregular S>
  class move_sentinel {
  public:
    constexpr move_sentinel();
    constexpr explicit move_sentinel(S s);
    template<class S2>
      requires convertible_to<const S2&, S>
        constexpr move_sentinel(const move_sentinel<S2>& s);
    template<class S2>
      requires assignable_from<S&, const S2&>
        constexpr move_sentinel& operator=(const move_sentinel<S2>& s);
    constexpr S base() const;
  private:
    S last;     // 仅用于说明
  };
}

namespace std {
  template<input_or_output_iterator I, sentinel_for<I> S>
    requires (!same_as<I, S> && copyable<I>)
  class common_iterator {
  public:
    constexpr common_iterator() = default;
    constexpr common_iterator(I i);
    constexpr common_iterator(S s);
    template<class I2, class S2>
      requires convertible_to<const I2&, I> && convertible_to<const S2&, S>
        constexpr common_iterator(const common_iterator<I2, S2>& x);
    template<class I2, class S2>
      requires convertible_to<const I2&, I> && convertible_to<const S2&, S> &&
               assignable_from<I&, const I2&> && assignable_from<S&, const S2&>
        common_iterator& operator=(const common_iterator<I2, S2>& x);
    decltype(auto) operator*();
    decltype(auto) operator*() const
      requires dereferenceable<const I>;
    decltype(auto) operator->() const
      requires /* 查看描述 */;
    common_iterator& operator++();
    decltype(auto) operator++(int);
    template<class I2, sentinel_for<I> S2>
      requires sentinel_for<S, I2>
    friend bool operator==(
      const common_iterator& x, const common_iterator<I2, S2>& y);
    template<class I2, sentinel_for<I> S2>
      requires sentinel_for<S, I2> && equality_comparable_with<I, I2>
    friend bool operator==(
      const common_iterator& x, const common_iterator<I2, S2>& y);
    template<sized_sentinel_for<I> I2, sized_sentinel_for<I> S2>
      requires sized_sentinel_for<S, I2>
    friend iter_difference_t<I2> operator-(
      const common_iterator& x, const common_iterator<I2, S2>& y);
    friend constexpr decltype(auto) iter_move(const common_iterator& i)
      noexcept(noexcept(ranges::iter_move(declval<const I&>())))
        requires input_iterator<I>;
    template<indirectly_swappable<I> I2, class S2>
      friend void iter_swap(const common_iterator& x, const common_iterator<I2, S2>& y)
        noexcept(noexcept(ranges::iter_swap(declval<const I&>(), declval<const I2&>())));
  private:
    variant<I, S> v_;   // 仅作展示用途
  };
  template<class I, class S>
  struct incrementable_traits<common_iterator<I, S>> {
    using difference_type = iter_difference_t<I>;
  };
  template<input_iterator I, class S>
  struct iterator_traits<common_iterator<I, S>> {
    using iterator_concept = /* 查看描述 */;
    using iterator_category = /* 查看描述 */;
    using value_type = iter_value_t<I>;
    using difference_type = iter_difference_t<I>;
    using pointer = /* 查看描述 */;
    using reference = iter_reference_t<I>;
  };
}

namespace std {
  struct default_sentinel_t { };
}

namespace std {
  template<input_or_output_iterator I>
  class counted_iterator {
  public:
    using iterator_type = I;
    constexpr counted_iterator() = default;
    constexpr counted_iterator(I x, iter_difference_t<I> n);
    template<class I2>
      requires convertible_to<const I2&, I>
        constexpr counted_iterator(const counted_iterator<I2>& x);
    template<class I2>
      requires assignable_from<I&, const I2&>
        constexpr counted_iterator& operator=(const counted_iterator<I2>& x);
    constexpr I base() const & requires copy_constructible<I>;
    constexpr I base() &&;
    constexpr iter_difference_t<I> count() const noexcept;
    constexpr decltype(auto) operator*();
    constexpr decltype(auto) operator*() const
      requires dereferenceable<const I>;
    constexpr auto operator->() const noexcept
      requires contiguous_iterator<I>;
    constexpr counted_iterator& operator++();
    decltype(auto) operator++(int);
    constexpr counted_iterator operator++(int)
      requires forward_iterator<I>;
    constexpr counted_iterator& operator--()
      requires bidirectional_iterator<I>;
    constexpr counted_iterator operator--(int)
      requires bidirectional_iterator<I>;
    constexpr counted_iterator operator+(iter_difference_t<I> n) const
      requires random_access_iterator<I>;
    friend constexpr counted_iterator operator+(
      iter_difference_t<I> n, const counted_iterator& x)
        requires random_access_iterator<I>;
    constexpr counted_iterator& operator+=(iter_difference_t<I> n)
      requires random_access_iterator<I>;
    constexpr counted_iterator operator-(iter_difference_t<I> n) const
      requires random_access_iterator<I>;
    template<common_with<I> I2>
      friend constexpr iter_difference_t<I2> operator-(
        const counted_iterator& x, const counted_iterator<I2>& y);
    friend constexpr iter_difference_t<I> operator-(
      const counted_iterator& x, default_sentinel_t);
    friend constexpr iter_difference_t<I> operator-(
      default_sentinel_t, const counted_iterator& y);
    constexpr counted_iterator& operator-=(iter_difference_t<I> n)
      requires random_access_iterator<I>;
    constexpr decltype(auto) operator[](iter_difference_t<I> n) const
      requires random_access_iterator<I>;
    template<common_with<I> I2>
      friend constexpr bool operator==(
        const counted_iterator& x, const counted_iterator<I2>& y);
    friend constexpr bool operator==(
      const counted_iterator& x, default_sentinel_t);
    template<common_with<I> I2>
      friend constexpr strong_ordering operator<=>(
        const counted_iterator& x, const counted_iterator<I2>& y);
    friend constexpr decltype(auto) iter_move(const counted_iterator& i)
      noexcept(noexcept(ranges::iter_move(i.current)))
        requires input_iterator<I>;
    template<indirectly_swappable<I> I2>
      friend constexpr void iter_swap(const counted_iterator& x,
                                      const counted_iterator<I2>& y)
        noexcept(noexcept(ranges::iter_swap(x.current, y.current)));
  private:
    I current = I();                    // 仅作展示用途
    iter_difference_t<I> length = 0;    // 仅作展示用途
  };
  template<input_iterator I>
  struct iterator_traits<counted_iterator<I>> : iterator_traits<I> {
    using pointer = void;
  };
}

namespace std {
  struct unreachable_sentinel_t {
    template<weakly_incrementable I>
      friend constexpr bool operator==(unreachable_sentinel_t, const I&) noexcept
      { return false; }
  };
}

namespace std {
  template<class T, class CharT = char, class Traits = char_traits<CharT>,
           class Distance = ptrdiff_t>
  class istream_iterator {
  public:
    using iterator_category = input_iterator_tag;
    using value_type        = T;
    using difference_type   = Distance;
    using pointer           = const T*;
    using reference         = const T&;
    using char_type         = CharT;
    using traits_type       = Traits;
    using istream_type      = basic_istream<CharT, Traits>;
    constexpr istream_iterator();
    constexpr istream_iterator(default_sentinel_t);
    istream_iterator(istream_type& s);
    istream_iterator(const istream_iterator& x) = default;
    ~istream_iterator() = default;
    istream_iterator& operator=(const istream_iterator&) = default;
    const T& operator*() const;
    const T* operator->() const;
    istream_iterator& operator++();
    istream_iterator  operator++(int);
    friend bool operator==(const istream_iterator& i, default_sentinel_t);
  private:
    basic_istream<CharT, Traits>* in_stream; // 仅用于说明
    T value;                                 // 仅用于说明
  };
}