ranges_algo.h

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// Core algorithmic facilities -*- C++ -*-
 
// Copyright (C) 2020-2023 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
 
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
 
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.
 
/** @file bits/ranges_algo.h
 *  This is an internal header file, included by other library headers.
 *  Do not attempt to use it directly. @headername{algorithm}
 */
 
#ifndef _RANGES_ALGO_H
#define _RANGES_ALGO_H 1
 
#if __cplusplus > 201703L
 
#if __cplusplus > 202002L
#include <optional>
#endif
#include <bits/ranges_algobase.h>
#include <bits/ranges_util.h>
#include <bits/uniform_int_dist.h> // concept uniform_random_bit_generator
 
#if __cpp_lib_concepts
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
namespace ranges
{
  namespace __detail
  {
    template<typename _Comp, typename _Proj>
      constexpr auto
      __make_comp_proj(_Comp& __comp, _Proj& __proj)
      {
        return [&] (auto&& __lhs, auto&& __rhs) -> bool {
          using _TL = decltype(__lhs);
          using _TR = decltype(__rhs);
          return std::__invoke(__comp,
                               std::__invoke(__proj, std::forward<_TL>(__lhs)),
                               std::__invoke(__proj, std::forward<_TR>(__rhs)));
        };
      }
 
    template<typename _Pred, typename _Proj>
      constexpr auto
      __make_pred_proj(_Pred& __pred, _Proj& __proj)
      {
        return [&] <typename _Tp> (_Tp&& __arg) -> bool {
          return std::__invoke(__pred,
                               std::__invoke(__proj, std::forward<_Tp>(__arg)));
        };
      }
  } // namespace __detail
 
  struct __all_of_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (!(bool)std::__invoke(__pred, std::__invoke(__proj, *__first)))
            return false;
        return true;
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr bool
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __all_of_fn all_of{};
 
  struct __any_of_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            return true;
        return false;
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr bool
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __any_of_fn any_of{};
 
  struct __none_of_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            return false;
        return true;
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr bool
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __none_of_fn none_of{};
 
  template<typename _Iter, typename _Fp>
    struct in_fun_result
    {
      [[no_unique_address]] _Iter in;
      [[no_unique_address]] _Fp fun;
 
      template<typename _Iter2, typename _F2p>
        requires convertible_to<const _Iter&, _Iter2>
          && convertible_to<const _Fp&, _F2p>
        constexpr
        operator in_fun_result<_Iter2, _F2p>() const &
        { return {in, fun}; }
 
      template<typename _Iter2, typename _F2p>
        requires convertible_to<_Iter, _Iter2> && convertible_to<_Fp, _F2p>
        constexpr
        operator in_fun_result<_Iter2, _F2p>() &&
        { return {std::move(in), std::move(fun)}; }
    };
 
  template<typename _Iter, typename _Fp>
    using for_each_result = in_fun_result<_Iter, _Fp>;
 
  struct __for_each_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirectly_unary_invocable<projected<_Iter, _Proj>> _Fun>
      constexpr for_each_result<_Iter, _Fun>
      operator()(_Iter __first, _Sent __last, _Fun __f, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          std::__invoke(__f, std::__invoke(__proj, *__first));
        return { std::move(__first), std::move(__f) };
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirectly_unary_invocable<projected<iterator_t<_Range>, _Proj>>
               _Fun>
      constexpr for_each_result<borrowed_iterator_t<_Range>, _Fun>
      operator()(_Range&& __r, _Fun __f, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__f), std::move(__proj));
      }
  };
 
  inline constexpr __for_each_fn for_each{};
 
  template<typename _Iter, typename _Fp>
    using for_each_n_result = in_fun_result<_Iter, _Fp>;
 
  struct __for_each_n_fn
  {
    template<input_iterator _Iter, typename _Proj = identity,
             indirectly_unary_invocable<projected<_Iter, _Proj>> _Fun>
      constexpr for_each_n_result<_Iter, _Fun>
      operator()(_Iter __first, iter_difference_t<_Iter> __n,
                 _Fun __f, _Proj __proj = {}) const
      {
        if constexpr (random_access_iterator<_Iter>)
          {
            if (__n <= 0)
              return {std::move(__first), std::move(__f)};
            auto __last = __first + __n;
            return ranges::for_each(std::move(__first), std::move(__last),
                                    std::move(__f), std::move(__proj));
          }
        else
          {
            while (__n-- > 0)
              {
                std::__invoke(__f, std::__invoke(__proj, *__first));
                ++__first;
              }
            return {std::move(__first), std::move(__f)};
          }
      }
  };
 
  inline constexpr __for_each_n_fn for_each_n{};
 
  // find, find_if and find_if_not are defined in <bits/ranges_util.h>.
 
  struct __find_first_of_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             forward_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<_Iter1, _Iter2, _Pred, _Proj1, _Proj2>
      constexpr _Iter1
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        for (; __first1 != __last1; ++__first1)
          for (auto __iter = __first2; __iter != __last2; ++__iter)
            if (std::__invoke(__pred,
                              std::__invoke(__proj1, *__first1),
                              std::__invoke(__proj2, *__iter)))
              return __first1;
        return __first1;
      }
 
    template<input_range _Range1, forward_range _Range2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<iterator_t<_Range1>, iterator_t<_Range2>,
                                     _Pred, _Proj1, _Proj2>
      constexpr borrowed_iterator_t<_Range1>
      operator()(_Range1&& __r1, _Range2&& __r2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__pred),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __find_first_of_fn find_first_of{};
 
  struct __count_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<_Iter, _Proj>,
                                         const _Tp*>
      constexpr iter_difference_t<_Iter>
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Proj __proj = {}) const
      {
        iter_difference_t<_Iter> __n = 0;
        for (; __first != __last; ++__first)
          if (std::__invoke(__proj, *__first) == __value)
            ++__n;
        return __n;
      }
 
    template<input_range _Range, typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<_Range>, _Proj>,
                                         const _Tp*>
      constexpr range_difference_t<_Range>
      operator()(_Range&& __r, const _Tp& __value, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__proj));
      }
  };
 
  inline constexpr __count_fn count{};
 
  struct __count_if_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr iter_difference_t<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        iter_difference_t<_Iter> __n = 0;
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            ++__n;
        return __n;
      }
 
    template<input_range _Range,
             typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr range_difference_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __count_if_fn count_if{};
 
  // in_in_result, mismatch and search are defined in <bits/ranges_util.h>.
 
  struct __search_n_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Tp,
             typename _Pred = ranges::equal_to, typename _Proj = identity>
      requires indirectly_comparable<_Iter, const _Tp*, _Pred, _Proj>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last, iter_difference_t<_Iter> __count,
                 const _Tp& __value, _Pred __pred = {}, _Proj __proj = {}) const
      {
        if (__count <= 0)
          return {__first, __first};
 
        auto __value_comp = [&] <typename _Rp> (_Rp&& __arg) -> bool {
            return std::__invoke(__pred, std::forward<_Rp>(__arg), __value);
        };
        if (__count == 1)
          {
            __first = ranges::find_if(std::move(__first), __last,
                                      std::move(__value_comp),
                                      std::move(__proj));
            if (__first == __last)
              return {__first, __first};
            else
              {
                auto __end = __first;
                return {__first, ++__end};
              }
          }
 
        if constexpr (sized_sentinel_for<_Sent, _Iter>
                      && random_access_iterator<_Iter>)
          {
            auto __tail_size = __last - __first;
            auto __remainder = __count;
 
            while (__remainder <= __tail_size)
              {
                __first += __remainder;
                __tail_size -= __remainder;
                auto __backtrack = __first;
                while (__value_comp(std::__invoke(__proj, *--__backtrack)))
                  {
                    if (--__remainder == 0)
                      return {__first - __count, __first};
                  }
                __remainder = __count + 1 - (__first - __backtrack);
              }
            auto __i = __first + __tail_size;
            return {__i, __i};
          }
        else
          {
            __first = ranges::find_if(__first, __last, __value_comp, __proj);
            while (__first != __last)
              {
                auto __n = __count;
                auto __i = __first;
                ++__i;
                while (__i != __last && __n != 1
                       && __value_comp(std::__invoke(__proj, *__i)))
                  {
                    ++__i;
                    --__n;
                  }
                if (__n == 1)
                  return {__first, __i};
                if (__i == __last)
                  return {__i, __i};
                __first = ranges::find_if(++__i, __last, __value_comp, __proj);
              }
            return {__first, __first};
          }
      }
 
    template<forward_range _Range, typename _Tp,
             typename _Pred = ranges::equal_to, typename _Proj = identity>
      requires indirectly_comparable<iterator_t<_Range>, const _Tp*,
                                     _Pred, _Proj>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, range_difference_t<_Range> __count,
               const _Tp& __value, _Pred __pred = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__count), __value,
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __search_n_fn search_n{};
 
  struct __find_end_fn
  {
    template<forward_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             forward_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<_Iter1, _Iter2, _Pred, _Proj1, _Proj2>
      constexpr subrange<_Iter1>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        if constexpr (bidirectional_iterator<_Iter1>
                      && bidirectional_iterator<_Iter2>)
          {
            auto __i1 = ranges::next(__first1, __last1);
            auto __i2 = ranges::next(__first2, __last2);
            auto __rresult
              = ranges::search(reverse_iterator<_Iter1>{__i1},
                               reverse_iterator<_Iter1>{__first1},
                               reverse_iterator<_Iter2>{__i2},
                               reverse_iterator<_Iter2>{__first2},
                               std::move(__pred),
                               std::move(__proj1), std::move(__proj2));
            auto __result_first = ranges::end(__rresult).base();
            auto __result_last = ranges::begin(__rresult).base();
            if (__result_last == __first1)
              return {__i1, __i1};
            else
              return {__result_first, __result_last};
          }
        else
          {
            auto __i = ranges::next(__first1, __last1);
            if (__first2 == __last2)
              return {__i, __i};
 
            auto __result_begin = __i;
            auto __result_end = __i;
            for (;;)
              {
                auto __new_range = ranges::search(__first1, __last1,
                                                  __first2, __last2,
                                                  __pred, __proj1, __proj2);
                auto __new_result_begin = ranges::begin(__new_range);
                auto __new_result_end = ranges::end(__new_range);
                if (__new_result_begin == __last1)
                  return {__result_begin, __result_end};
                else
                  {
                    __result_begin = __new_result_begin;
                    __result_end = __new_result_end;
                    __first1 = __result_begin;
                    ++__first1;
                  }
              }
          }
      }
 
    template<forward_range _Range1, forward_range _Range2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<iterator_t<_Range1>, iterator_t<_Range2>,
                                     _Pred, _Proj1, _Proj2>
      constexpr borrowed_subrange_t<_Range1>
      operator()(_Range1&& __r1, _Range2&& __r2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__pred),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __find_end_fn find_end{};
 
  // adjacent_find is defined in <bits/ranges_util.h>.
 
  struct __is_permutation_fn
  {
    template<forward_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             forward_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_equivalence_relation<projected<_Iter1, _Proj1>,
                                           projected<_Iter2, _Proj2>> _Pred
               = ranges::equal_to>
      constexpr bool
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        constexpr bool __sized_iters
          = (sized_sentinel_for<_Sent1, _Iter1>
             && sized_sentinel_for<_Sent2, _Iter2>);
        if constexpr (__sized_iters)
          {
            auto __d1 = ranges::distance(__first1, __last1);
            auto __d2 = ranges::distance(__first2, __last2);
            if (__d1 != __d2)
              return false;
          }
 
        // Efficiently compare identical prefixes:  O(N) if sequences
        // have the same elements in the same order.
        for (; __first1 != __last1 && __first2 != __last2;
             ++__first1, (void)++__first2)
          if (!(bool)std::__invoke(__pred,
                                   std::__invoke(__proj1, *__first1),
                                   std::__invoke(__proj2, *__first2)))
              break;
 
        if constexpr (__sized_iters)
          {
            if (__first1 == __last1)
              return true;
          }
        else
          {
            auto __d1 = ranges::distance(__first1, __last1);
            auto __d2 = ranges::distance(__first2, __last2);
            if (__d1 == 0 && __d2 == 0)
              return true;
            if (__d1 != __d2)
              return false;
          }
 
        for (auto __scan = __first1; __scan != __last1; ++__scan)
          {
            auto&& __proj_scan = std::__invoke(__proj1, *__scan);
            auto __comp_scan = [&] <typename _Tp> (_Tp&& __arg) -> bool {
              return std::__invoke(__pred, __proj_scan,
                                   std::forward<_Tp>(__arg));
            };
            if (__scan != ranges::find_if(__first1, __scan,
                                          __comp_scan, __proj1))
              continue; // We've seen this one before.
 
            auto __matches = ranges::count_if(__first2, __last2,
                                              __comp_scan, __proj2);
            if (__matches == 0
                || ranges::count_if(__scan, __last1,
                                    __comp_scan, __proj1) != __matches)
              return false;
          }
        return true;
      }
 
    template<forward_range _Range1, forward_range _Range2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_equivalence_relation<
               projected<iterator_t<_Range1>, _Proj1>,
               projected<iterator_t<_Range2>, _Proj2>> _Pred = ranges::equal_to>
      constexpr bool
      operator()(_Range1&& __r1, _Range2&& __r2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__pred),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __is_permutation_fn is_permutation{};
 
  template<typename _Iter, typename _Out>
    using copy_if_result = in_out_result<_Iter, _Out>;
 
  struct __copy_if_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out, typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires indirectly_copyable<_Iter, _Out>
      constexpr copy_if_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            {
              *__result = *__first;
              ++__result;
            }
        return {std::move(__first), std::move(__result)};
      }
 
    template<input_range _Range, weakly_incrementable _Out,
             typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
      constexpr copy_if_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __copy_if_fn copy_if{};
 
  template<typename _Iter1, typename _Iter2>
    using swap_ranges_result = in_in_result<_Iter1, _Iter2>;
 
  struct __swap_ranges_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2>
      requires indirectly_swappable<_Iter1, _Iter2>
      constexpr swap_ranges_result<_Iter1, _Iter2>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2) const
      {
        for (; __first1 != __last1 && __first2 != __last2;
             ++__first1, (void)++__first2)
          ranges::iter_swap(__first1, __first2);
        return {std::move(__first1), std::move(__first2)};
      }
 
    template<input_range _Range1, input_range _Range2>
      requires indirectly_swappable<iterator_t<_Range1>, iterator_t<_Range2>>
      constexpr swap_ranges_result<borrowed_iterator_t<_Range1>,
                                   borrowed_iterator_t<_Range2>>
      operator()(_Range1&& __r1, _Range2&& __r2) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2));
      }
  };
 
  inline constexpr __swap_ranges_fn swap_ranges{};
 
  template<typename _Iter, typename _Out>
    using unary_transform_result = in_out_result<_Iter, _Out>;
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    struct in_in_out_result
    {
      [[no_unique_address]] _Iter1 in1;
      [[no_unique_address]] _Iter2 in2;
      [[no_unique_address]] _Out  out;
 
      template<typename _IIter1, typename _IIter2, typename _OOut>
        requires convertible_to<const _Iter1&, _IIter1>
          && convertible_to<const _Iter2&, _IIter2>
          && convertible_to<const _Out&, _OOut>
        constexpr
        operator in_in_out_result<_IIter1, _IIter2, _OOut>() const &
        { return {in1, in2, out}; }
 
      template<typename _IIter1, typename _IIter2, typename _OOut>
        requires convertible_to<_Iter1, _IIter1>
          && convertible_to<_Iter2, _IIter2>
          && convertible_to<_Out, _OOut>
        constexpr
        operator in_in_out_result<_IIter1, _IIter2, _OOut>() &&
        { return {std::move(in1), std::move(in2), std::move(out)}; }
    };
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    using binary_transform_result = in_in_out_result<_Iter1, _Iter2, _Out>;
 
  struct __transform_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out,
             copy_constructible _Fp, typename _Proj = identity>
      requires indirectly_writable<_Out,
                                   indirect_result_t<_Fp&,
                                     projected<_Iter, _Proj>>>
      constexpr unary_transform_result<_Iter, _Out>
      operator()(_Iter __first1, _Sent __last1, _Out __result,
                 _Fp __op, _Proj __proj = {}) const
      {
        for (; __first1 != __last1; ++__first1, (void)++__result)
          *__result = std::__invoke(__op, std::__invoke(__proj, *__first1));
        return {std::move(__first1), std::move(__result)};
      }
 
    template<input_range _Range, weakly_incrementable _Out,
             copy_constructible _Fp, typename _Proj = identity>
      requires indirectly_writable<_Out,
                                   indirect_result_t<_Fp&,
                                     projected<iterator_t<_Range>, _Proj>>>
      constexpr unary_transform_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result, _Fp __op, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result),
                       std::move(__op), std::move(__proj));
      }
 
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, copy_constructible _Fp,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_writable<_Out,
                                   indirect_result_t<_Fp&,
                                     projected<_Iter1, _Proj1>,
                                     projected<_Iter2, _Proj2>>>
      constexpr binary_transform_result<_Iter1, _Iter2, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2,
                 _Out __result, _Fp __binary_op,
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        for (; __first1 != __last1 && __first2 != __last2;
             ++__first1, (void)++__first2, ++__result)
          *__result = std::__invoke(__binary_op,
                                    std::__invoke(__proj1, *__first1),
                                    std::__invoke(__proj2, *__first2));
        return {std::move(__first1), std::move(__first2), std::move(__result)};
      }
 
    template<input_range _Range1, input_range _Range2,
             weakly_incrementable _Out, copy_constructible _Fp,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_writable<_Out,
                                   indirect_result_t<_Fp&,
                                     projected<iterator_t<_Range1>, _Proj1>,
                                     projected<iterator_t<_Range2>, _Proj2>>>
      constexpr binary_transform_result<borrowed_iterator_t<_Range1>,
                                        borrowed_iterator_t<_Range2>, _Out>
      operator()(_Range1&& __r1, _Range2&& __r2, _Out __result, _Fp __binary_op,
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__binary_op),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __transform_fn transform{};
 
  struct __replace_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp1, typename _Tp2, typename _Proj = identity>
      requires indirectly_writable<_Iter, const _Tp2&>
        && indirect_binary_predicate<ranges::equal_to, projected<_Iter, _Proj>,
                                     const _Tp1*>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 const _Tp1& __old_value, const _Tp2& __new_value,
                 _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__proj, *__first) == __old_value)
            *__first = __new_value;
        return __first;
      }
 
    template<input_range _Range,
             typename _Tp1, typename _Tp2, typename _Proj = identity>
      requires indirectly_writable<iterator_t<_Range>, const _Tp2&>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<iterator_t<_Range>, _Proj>,
                                     const _Tp1*>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r,
                 const _Tp1& __old_value, const _Tp2& __new_value,
                 _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __old_value, __new_value, std::move(__proj));
      }
  };
 
  inline constexpr __replace_fn replace{};
 
  struct __replace_if_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires indirectly_writable<_Iter, const _Tp&>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, const _Tp& __new_value, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            *__first = __new_value;
        return std::move(__first);
      }
 
    template<input_range _Range, typename _Tp, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires indirectly_writable<iterator_t<_Range>, const _Tp&>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r,
                 _Pred __pred, const _Tp& __new_value, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), __new_value, std::move(__proj));
      }
  };
 
  inline constexpr __replace_if_fn replace_if{};
 
  template<typename _Iter, typename _Out>
    using replace_copy_result = in_out_result<_Iter, _Out>;
 
  struct __replace_copy_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp1, typename _Tp2, output_iterator<const _Tp2&> _Out,
             typename _Proj = identity>
      requires indirectly_copyable<_Iter, _Out>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<_Iter, _Proj>, const _Tp1*>
      constexpr replace_copy_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 const _Tp1& __old_value, const _Tp2& __new_value,
                 _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first, (void)++__result)
          if (std::__invoke(__proj, *__first) == __old_value)
            *__result = __new_value;
          else
            *__result = *__first;
        return {std::move(__first), std::move(__result)};
      }
 
    template<input_range _Range, typename _Tp1, typename _Tp2,
             output_iterator<const _Tp2&> _Out, typename _Proj = identity>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<iterator_t<_Range>, _Proj>,
                                     const _Tp1*>
      constexpr replace_copy_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 const _Tp1& __old_value, const _Tp2& __new_value,
                 _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result), __old_value,
                       __new_value, std::move(__proj));
      }
  };
 
  inline constexpr __replace_copy_fn replace_copy{};
 
  template<typename _Iter, typename _Out>
    using replace_copy_if_result = in_out_result<_Iter, _Out>;
 
  struct __replace_copy_if_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, output_iterator<const _Tp&> _Out,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires indirectly_copyable<_Iter, _Out>
      constexpr replace_copy_if_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 _Pred __pred, const _Tp& __new_value, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first, (void)++__result)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            *__result = __new_value;
          else
            *__result = *__first;
        return {std::move(__first), std::move(__result)};
      }
 
    template<input_range _Range,
             typename _Tp, output_iterator<const _Tp&> _Out,
             typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
      constexpr replace_copy_if_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 _Pred __pred, const _Tp& __new_value, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result), std::move(__pred),
                       __new_value, std::move(__proj));
      }
  };
 
  inline constexpr __replace_copy_if_fn replace_copy_if{};
 
  struct __generate_n_fn
  {
    template<input_or_output_iterator _Out, copy_constructible _Fp>
      requires invocable<_Fp&>
        && indirectly_writable<_Out, invoke_result_t<_Fp&>>
      constexpr _Out
      operator()(_Out __first, iter_difference_t<_Out> __n, _Fp __gen) const
      {
        for (; __n > 0; --__n, (void)++__first)
          *__first = std::__invoke(__gen);
        return __first;
      }
  };
 
  inline constexpr __generate_n_fn generate_n{};
 
  struct __generate_fn
  {
    template<input_or_output_iterator _Out, sentinel_for<_Out> _Sent,
             copy_constructible _Fp>
      requires invocable<_Fp&>
        && indirectly_writable<_Out, invoke_result_t<_Fp&>>
      constexpr _Out
      operator()(_Out __first, _Sent __last, _Fp __gen) const
      {
        for (; __first != __last; ++__first)
          *__first = std::__invoke(__gen);
        return __first;
      }
 
    template<typename _Range, copy_constructible _Fp>
      requires invocable<_Fp&> && output_range<_Range, invoke_result_t<_Fp&>>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Fp __gen) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__gen));
      }
  };
 
  inline constexpr __generate_fn generate{};
 
  struct __remove_if_fn
  {
    template<permutable _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        __first = ranges::find_if(__first, __last, __pred, __proj);
        if (__first == __last)
          return {__first, __first};
 
        auto __result = __first;
        ++__first;
        for (; __first != __last; ++__first)
          if (!std::__invoke(__pred, std::__invoke(__proj, *__first)))
            {
              *__result = std::move(*__first);
              ++__result;
            }
 
        return {__result, __first};
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires permutable<iterator_t<_Range>>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __remove_if_fn remove_if{};
 
  struct __remove_fn
  {
    template<permutable _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<_Iter, _Proj>,
                                         const _Tp*>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Proj __proj = {}) const
      {
        auto __pred = [&] (auto&& __arg) -> bool {
          return std::forward<decltype(__arg)>(__arg) == __value;
        };
        return ranges::remove_if(__first, __last,
                                 std::move(__pred), std::move(__proj));
      }
 
    template<forward_range _Range, typename _Tp, typename _Proj = identity>
      requires permutable<iterator_t<_Range>>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<iterator_t<_Range>, _Proj>,
                                     const _Tp*>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, const _Tp& __value, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__proj));
      }
  };
 
  inline constexpr __remove_fn remove{};
 
  template<typename _Iter, typename _Out>
    using remove_copy_if_result = in_out_result<_Iter, _Out>;
 
  struct __remove_copy_if_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out, typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires indirectly_copyable<_Iter, _Out>
      constexpr remove_copy_if_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (!std::__invoke(__pred, std::__invoke(__proj, *__first)))
            {
              *__result = *__first;
              ++__result;
            }
        return {std::move(__first), std::move(__result)};
      }
 
    template<input_range _Range, weakly_incrementable _Out,
             typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
      constexpr remove_copy_if_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __remove_copy_if_fn remove_copy_if{};
 
  template<typename _Iter, typename _Out>
    using remove_copy_result = in_out_result<_Iter, _Out>;
 
  struct __remove_copy_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out, typename _Tp, typename _Proj = identity>
      requires indirectly_copyable<_Iter, _Out>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<_Iter, _Proj>,
                                     const _Tp*>
      constexpr remove_copy_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 const _Tp& __value, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (!(std::__invoke(__proj, *__first) == __value))
            {
              *__result = *__first;
              ++__result;
            }
        return {std::move(__first), std::move(__result)};
      }
 
    template<input_range _Range, weakly_incrementable _Out,
             typename _Tp, typename _Proj = identity>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
        && indirect_binary_predicate<ranges::equal_to,
                                     projected<iterator_t<_Range>, _Proj>,
                                     const _Tp*>
      constexpr remove_copy_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 const _Tp& __value, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result), __value, std::move(__proj));
      }
  };
 
  inline constexpr __remove_copy_fn remove_copy{};
 
  struct __unique_fn
  {
    template<permutable _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_equivalence_relation<
               projected<_Iter, _Proj>> _Comp = ranges::equal_to>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        __first = ranges::adjacent_find(__first, __last, __comp, __proj);
        if (__first == __last)
          return {__first, __first};
 
        auto __dest = __first;
        ++__first;
        while (++__first != __last)
          if (!std::__invoke(__comp,
                             std::__invoke(__proj, *__dest),
                             std::__invoke(__proj, *__first)))
            *++__dest = std::move(*__first);
        return {++__dest, __first};
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_equivalence_relation<
               projected<iterator_t<_Range>, _Proj>> _Comp = ranges::equal_to>
      requires permutable<iterator_t<_Range>>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __unique_fn unique{};
 
  namespace __detail
  {
    template<typename _Out, typename _Tp>
      concept __can_reread_output = input_iterator<_Out>
        && same_as<_Tp, iter_value_t<_Out>>;
  }
 
  template<typename _Iter, typename _Out>
    using unique_copy_result = in_out_result<_Iter, _Out>;
 
  struct __unique_copy_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out, typename _Proj = identity,
             indirect_equivalence_relation<
               projected<_Iter, _Proj>> _Comp = ranges::equal_to>
      requires indirectly_copyable<_Iter, _Out>
        && (forward_iterator<_Iter>
            || __detail::__can_reread_output<_Out, iter_value_t<_Iter>>
            || indirectly_copyable_storable<_Iter, _Out>)
      constexpr unique_copy_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return {std::move(__first), std::move(__result)};
 
        // TODO: perform a closer comparison with reference implementations
        if constexpr (forward_iterator<_Iter>)
          {
            auto __next = __first;
            *__result = *__next;
            while (++__next != __last)
              if (!std::__invoke(__comp,
                                 std::__invoke(__proj, *__first),
                                 std::__invoke(__proj, *__next)))
                {
                  __first = __next;
                  *++__result = *__first;
                }
            return {__next, std::move(++__result)};
          }
        else if constexpr (__detail::__can_reread_output<_Out, iter_value_t<_Iter>>)
          {
            *__result = *__first;
            while (++__first != __last)
              if (!std::__invoke(__comp,
                                 std::__invoke(__proj, *__result),
                                 std::__invoke(__proj, *__first)))
                  *++__result = *__first;
            return {std::move(__first), std::move(++__result)};
          }
        else // indirectly_copyable_storable<_Iter, _Out>
          {
            auto __value = *__first;
            *__result = __value;
            while (++__first != __last)
              {
                if (!(bool)std::__invoke(__comp,
                                         std::__invoke(__proj, *__first),
                                         std::__invoke(__proj, __value)))
                  {
                    __value = *__first;
                    *++__result = __value;
                  }
              }
            return {std::move(__first), std::move(++__result)};
          }
      }
 
    template<input_range _Range,
             weakly_incrementable _Out, typename _Proj = identity,
             indirect_equivalence_relation<
               projected<iterator_t<_Range>, _Proj>> _Comp = ranges::equal_to>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
        && (forward_iterator<iterator_t<_Range>>
            || __detail::__can_reread_output<_Out, range_value_t<_Range>>
            || indirectly_copyable_storable<iterator_t<_Range>, _Out>)
      constexpr unique_copy_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __unique_copy_fn unique_copy{};
 
  struct __reverse_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent>
      requires permutable<_Iter>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last) const
      {
        auto __i = ranges::next(__first, __last);
        auto __tail = __i;
 
        if constexpr (random_access_iterator<_Iter>)
          {
            if (__first != __last)
              {
                --__tail;
                while (__first < __tail)
                  {
                    ranges::iter_swap(__first, __tail);
                    ++__first;
                    --__tail;
                  }
              }
            return __i;
          }
        else
          {
            for (;;)
              if (__first == __tail || __first == --__tail)
                break;
              else
                {
                  ranges::iter_swap(__first, __tail);
                  ++__first;
                }
            return __i;
          }
      }
 
    template<bidirectional_range _Range>
      requires permutable<iterator_t<_Range>>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r));
      }
  };
 
  inline constexpr __reverse_fn reverse{};
 
  template<typename _Iter, typename _Out>
    using reverse_copy_result = in_out_result<_Iter, _Out>;
 
  struct __reverse_copy_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out>
      requires indirectly_copyable<_Iter, _Out>
      constexpr reverse_copy_result<_Iter, _Out>
      operator()(_Iter __first, _Sent __last, _Out __result) const
      {
        auto __i = ranges::next(__first, __last);
        auto __tail = __i;
        while (__first != __tail)
          {
            --__tail;
            *__result = *__tail;
            ++__result;
          }
        return {__i, std::move(__result)};
      }
 
    template<bidirectional_range _Range, weakly_incrementable _Out>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
      constexpr reverse_copy_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, _Out __result) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__result));
      }
  };
 
  inline constexpr __reverse_copy_fn reverse_copy{};
 
  struct __rotate_fn
  {
    template<permutable _Iter, sentinel_for<_Iter> _Sent>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Iter __middle, _Sent __last) const
      {
        auto __lasti = ranges::next(__first, __last);
        if (__first == __middle)
          return {__lasti, __lasti};
        if (__last == __middle)
          return {std::move(__first), std::move(__lasti)};
 
        if constexpr (random_access_iterator<_Iter>)
          {
            auto __n = __lasti - __first;
            auto __k = __middle - __first;
 
            if (__k == __n - __k)
              {
                ranges::swap_ranges(__first, __middle, __middle, __middle + __k);
                return {std::move(__middle), std::move(__lasti)};
              }
 
            auto __p = __first;
            auto __ret = __first + (__lasti - __middle);
 
            for (;;)
              {
                if (__k < __n - __k)
                  {
                    // TODO: is_pod is deprecated, but this condition is
                    // consistent with the STL implementation.
                    if constexpr (__is_pod(iter_value_t<_Iter>))
                      if (__k == 1)
                        {
                          auto __t = std::move(*__p);
                          ranges::move(__p + 1, __p + __n, __p);
                          *(__p + __n - 1) = std::move(__t);
                          return {std::move(__ret), std::move(__lasti)};
                        }
                    auto __q = __p + __k;
                    for (decltype(__n) __i = 0; __i < __n - __k; ++ __i)
                      {
                        ranges::iter_swap(__p, __q);
                        ++__p;
                        ++__q;
                      }
                    __n %= __k;
                    if (__n == 0)
                      return {std::move(__ret), std::move(__lasti)};
                    ranges::swap(__n, __k);
                    __k = __n - __k;
                  }
                else
                  {
                    __k = __n - __k;
                    // TODO: is_pod is deprecated, but this condition is
                    // consistent with the STL implementation.
                    if constexpr (__is_pod(iter_value_t<_Iter>))
                      if (__k == 1)
                        {
                          auto __t = std::move(*(__p + __n - 1));
                          ranges::move_backward(__p, __p + __n - 1, __p + __n);
                          *__p = std::move(__t);
                          return {std::move(__ret), std::move(__lasti)};
                        }
                    auto __q = __p + __n;
                    __p = __q - __k;
                    for (decltype(__n) __i = 0; __i < __n - __k; ++ __i)
                      {
                        --__p;
                        --__q;
                        ranges::iter_swap(__p, __q);
                      }
                    __n %= __k;
                    if (__n == 0)
                      return {std::move(__ret), std::move(__lasti)};
                    std::swap(__n, __k);
                  }
              }
          }
        else if constexpr (bidirectional_iterator<_Iter>)
          {
            auto __tail = __lasti;
 
            ranges::reverse(__first, __middle);
            ranges::reverse(__middle, __tail);
 
            while (__first != __middle && __middle != __tail)
              {
                ranges::iter_swap(__first, --__tail);
                ++__first;
              }
 
            if (__first == __middle)
              {
                ranges::reverse(__middle, __tail);
                return {std::move(__tail), std::move(__lasti)};
              }
            else
              {
                ranges::reverse(__first, __middle);
                return {std::move(__first), std::move(__lasti)};
              }
          }
        else
          {
            auto __first2 = __middle;
            do
              {
                ranges::iter_swap(__first, __first2);
                ++__first;
                ++__first2;
                if (__first == __middle)
                  __middle = __first2;
              } while (__first2 != __last);
 
            auto __ret = __first;
 
            __first2 = __middle;
 
            while (__first2 != __last)
              {
                ranges::iter_swap(__first, __first2);
                ++__first;
                ++__first2;
                if (__first == __middle)
                  __middle = __first2;
                else if (__first2 == __last)
                  __first2 = __middle;
              }
            return {std::move(__ret), std::move(__lasti)};
          }
      }
 
    template<forward_range _Range>
      requires permutable<iterator_t<_Range>>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, iterator_t<_Range> __middle) const
      {
        return (*this)(ranges::begin(__r), std::move(__middle),
                       ranges::end(__r));
      }
  };
 
  inline constexpr __rotate_fn rotate{};
 
  template<typename _Iter, typename _Out>
    using rotate_copy_result = in_out_result<_Iter, _Out>;
 
  struct __rotate_copy_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out>
      requires indirectly_copyable<_Iter, _Out>
      constexpr rotate_copy_result<_Iter, _Out>
      operator()(_Iter __first, _Iter __middle, _Sent __last,
                 _Out __result) const
      {
        auto __copy1 = ranges::copy(__middle,
                                    std::move(__last),
                                    std::move(__result));
        auto __copy2 = ranges::copy(std::move(__first),
                                    std::move(__middle),
                                    std::move(__copy1.out));
        return { std::move(__copy1.in), std::move(__copy2.out) };
      }
 
    template<forward_range _Range, weakly_incrementable _Out>
      requires indirectly_copyable<iterator_t<_Range>, _Out>
      constexpr rotate_copy_result<borrowed_iterator_t<_Range>, _Out>
      operator()(_Range&& __r, iterator_t<_Range> __middle, _Out __result) const
      {
        return (*this)(ranges::begin(__r), std::move(__middle),
                       ranges::end(__r), std::move(__result));
      }
  };
 
  inline constexpr __rotate_copy_fn rotate_copy{};
 
  struct __sample_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out, typename _Gen>
      requires (forward_iterator<_Iter> || random_access_iterator<_Out>)
        && indirectly_copyable<_Iter, _Out>
        && uniform_random_bit_generator<remove_reference_t<_Gen>>
      _Out
      operator()(_Iter __first, _Sent __last, _Out __out,
                 iter_difference_t<_Iter> __n, _Gen&& __g) const
      {
        if constexpr (forward_iterator<_Iter>)
          {
            // FIXME: Forwarding to std::sample here requires computing __lasti
            // which may take linear time.
            auto __lasti = ranges::next(__first, __last);
            return _GLIBCXX_STD_A::
              sample(std::move(__first), std::move(__lasti), std::move(__out),
                     __n, std::forward<_Gen>(__g));
          }
        else
          {
            using __distrib_type
              = uniform_int_distribution<iter_difference_t<_Iter>>;
            using __param_type = typename __distrib_type::param_type;
            __distrib_type __d{};
            iter_difference_t<_Iter> __sample_sz = 0;
            while (__first != __last && __sample_sz != __n)
              {
                __out[__sample_sz++] = *__first;
                ++__first;
              }
            for (auto __pop_sz = __sample_sz; __first != __last;
                ++__first, (void) ++__pop_sz)
              {
                const auto __k = __d(__g, __param_type{0, __pop_sz});
                if (__k < __n)
                  __out[__k] = *__first;
              }
            return __out + __sample_sz;
          }
      }
 
    template<input_range _Range, weakly_incrementable _Out, typename _Gen>
      requires (forward_range<_Range> || random_access_iterator<_Out>)
        && indirectly_copyable<iterator_t<_Range>, _Out>
        && uniform_random_bit_generator<remove_reference_t<_Gen>>
      _Out
      operator()(_Range&& __r, _Out __out,
                 range_difference_t<_Range> __n, _Gen&& __g) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__out), __n,
                       std::forward<_Gen>(__g));
      }
  };
 
  inline constexpr __sample_fn sample{};
 
#ifdef _GLIBCXX_USE_C99_STDINT_TR1
  struct __shuffle_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Gen>
      requires permutable<_Iter>
        && uniform_random_bit_generator<remove_reference_t<_Gen>>
      _Iter
      operator()(_Iter __first, _Sent __last, _Gen&& __g) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::shuffle(std::move(__first), __lasti, std::forward<_Gen>(__g));
        return __lasti;
      }
 
    template<random_access_range _Range, typename _Gen>
      requires permutable<iterator_t<_Range>>
        && uniform_random_bit_generator<remove_reference_t<_Gen>>
      borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Gen&& __g) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::forward<_Gen>(__g));
      }
  };
 
  inline constexpr __shuffle_fn shuffle{};
#endif
 
  struct __push_heap_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::push_heap(__first, __lasti,
                       __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __push_heap_fn push_heap{};
 
  struct __pop_heap_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::pop_heap(__first, __lasti,
                      __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __pop_heap_fn pop_heap{};
 
  struct __make_heap_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::make_heap(__first, __lasti,
                       __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __make_heap_fn make_heap{};
 
  struct __sort_heap_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::sort_heap(__first, __lasti,
                       __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __sort_heap_fn sort_heap{};
 
  struct __is_heap_until_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        iter_difference_t<_Iter> __n = ranges::distance(__first, __last);
        iter_difference_t<_Iter> __parent = 0, __child = 1;
        for (; __child < __n; ++__child)
          if (std::__invoke(__comp,
                            std::__invoke(__proj, *(__first + __parent)),
                            std::__invoke(__proj, *(__first + __child))))
            return __first + __child;
          else if ((__child & 1) == 0)
            ++__parent;
 
        return __first + __n;
      }
 
    template<random_access_range _Range,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __is_heap_until_fn is_heap_until{};
 
  struct __is_heap_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (__last
                == ranges::is_heap_until(__first, __last,
                                         std::move(__comp),
                                         std::move(__proj)));
      }
 
    template<random_access_range _Range,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __is_heap_fn is_heap{};
 
  struct __sort_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        _GLIBCXX_STD_A::sort(std::move(__first), __lasti,
                             __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __sort_fn sort{};
 
  struct __stable_sort_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::stable_sort(std::move(__first), __lasti,
                         __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __stable_sort_fn stable_sort{};
 
  struct __partial_sort_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Iter __middle, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __middle)
          return ranges::next(__first, __last);
 
        ranges::make_heap(__first, __middle, __comp, __proj);
        auto __i = __middle;
        for (; __i != __last; ++__i)
          if (std::__invoke(__comp,
                            std::__invoke(__proj, *__i),
                            std::__invoke(__proj, *__first)))
            {
              ranges::pop_heap(__first, __middle, __comp, __proj);
              ranges::iter_swap(__middle-1, __i);
              ranges::push_heap(__first, __middle, __comp, __proj);
            }
        ranges::sort_heap(__first, __middle, __comp, __proj);
 
        return __i;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, iterator_t<_Range> __middle,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), std::move(__middle),
                       ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __partial_sort_fn partial_sort{};
 
  template<typename _Iter, typename _Out>
    using partial_sort_copy_result = in_out_result<_Iter, _Out>;
 
  struct __partial_sort_copy_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             random_access_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_copyable<_Iter1, _Iter2>
        && sortable<_Iter2, _Comp, _Proj2>
        && indirect_strict_weak_order<_Comp,
                                      projected<_Iter1, _Proj1>,
                                      projected<_Iter2, _Proj2>>
      constexpr partial_sort_copy_result<_Iter1, _Iter2>
      operator()(_Iter1 __first, _Sent1 __last,
                 _Iter2 __result_first, _Sent2 __result_last,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        if (__result_first == __result_last)
          {
            // TODO: Eliminating the variable __lasti triggers an ICE.
            auto __lasti = ranges::next(std::move(__first),
                                        std::move(__last));
            return {std::move(__lasti), std::move(__result_first)};
          }
 
        auto __result_real_last = __result_first;
        while (__first != __last && __result_real_last != __result_last)
          {
            *__result_real_last = *__first;
            ++__result_real_last;
            ++__first;
          }
 
        ranges::make_heap(__result_first, __result_real_last, __comp, __proj2);
        for (; __first != __last; ++__first)
          if (std::__invoke(__comp,
                            std::__invoke(__proj1, *__first),
                            std::__invoke(__proj2, *__result_first)))
            {
              ranges::pop_heap(__result_first, __result_real_last,
                               __comp, __proj2);
              *(__result_real_last-1) = *__first;
              ranges::push_heap(__result_first, __result_real_last,
                                __comp, __proj2);
            }
        ranges::sort_heap(__result_first, __result_real_last, __comp, __proj2);
 
        return {std::move(__first), std::move(__result_real_last)};
      }
 
    template<input_range _Range1, random_access_range _Range2,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_copyable<iterator_t<_Range1>, iterator_t<_Range2>>
        && sortable<iterator_t<_Range2>, _Comp, _Proj2>
        && indirect_strict_weak_order<_Comp,
                                      projected<iterator_t<_Range1>, _Proj1>,
                                      projected<iterator_t<_Range2>, _Proj2>>
      constexpr partial_sort_copy_result<borrowed_iterator_t<_Range1>,
                                         borrowed_iterator_t<_Range2>>
      operator()(_Range1&& __r, _Range2&& __out, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       ranges::begin(__out), ranges::end(__out),
                       std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __partial_sort_copy_fn partial_sort_copy{};
 
  struct __is_sorted_until_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return __first;
 
        auto __next = __first;
        for (++__next; __next != __last; __first = __next, (void)++__next)
          if (std::__invoke(__comp,
                            std::__invoke(__proj, *__next),
                            std::__invoke(__proj, *__first)))
            return __next;
        return __next;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __is_sorted_until_fn is_sorted_until{};
 
  struct __is_sorted_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return true;
 
        auto __next = __first;
        for (++__next; __next != __last; __first = __next, (void)++__next)
          if (std::__invoke(__comp,
                            std::__invoke(__proj, *__next),
                            std::__invoke(__proj, *__first)))
            return false;
        return true;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __is_sorted_fn is_sorted{};
 
  struct __nth_element_fn
  {
    template<random_access_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr _Iter
      operator()(_Iter __first, _Iter __nth, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        _GLIBCXX_STD_A::nth_element(std::move(__first), std::move(__nth),
                                    __lasti,
                                    __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<random_access_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, iterator_t<_Range> __nth,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), std::move(__nth),
                       ranges::end(__r), std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __nth_element_fn nth_element{};
 
  struct __lower_bound_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*, projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __len = ranges::distance(__first, __last);
 
        while (__len > 0)
          {
            auto __half = __len / 2;
            auto __middle = __first;
            ranges::advance(__middle, __half);
            if (std::__invoke(__comp, std::__invoke(__proj, *__middle), __value))
              {
                __first = __middle;
                ++__first;
                __len = __len - __half - 1;
              }
            else
              __len = __half;
          }
        return __first;
      }
 
    template<forward_range _Range, typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*,
                                        projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __lower_bound_fn lower_bound{};
 
  struct __upper_bound_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*, projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __len = ranges::distance(__first, __last);
 
        while (__len > 0)
          {
            auto __half = __len / 2;
            auto __middle = __first;
            ranges::advance(__middle, __half);
            if (std::__invoke(__comp, __value, std::__invoke(__proj, *__middle)))
              __len = __half;
            else
              {
                __first = __middle;
                ++__first;
                __len = __len - __half - 1;
              }
          }
        return __first;
      }
 
    template<forward_range _Range, typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*,
                                        projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __upper_bound_fn upper_bound{};
 
  struct __equal_range_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*, projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __len = ranges::distance(__first, __last);
 
        while (__len > 0)
          {
            auto __half = __len / 2;
            auto __middle = __first;
            ranges::advance(__middle, __half);
            if (std::__invoke(__comp,
                              std::__invoke(__proj, *__middle),
                              __value))
              {
                __first = __middle;
                ++__first;
                __len = __len - __half - 1;
              }
            else if (std::__invoke(__comp,
                                   __value,
                                   std::__invoke(__proj, *__middle)))
              __len = __half;
            else
              {
                auto __left
                  = ranges::lower_bound(__first, __middle,
                                        __value, __comp, __proj);
                ranges::advance(__first, __len);
                auto __right
                  = ranges::upper_bound(++__middle, __first,
                                        __value, __comp, __proj);
                return {__left, __right};
              }
          }
        return {__first, __first};
      }
 
    template<forward_range _Range,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*,
                                        projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, const _Tp& __value,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __equal_range_fn equal_range{};
 
  struct __binary_search_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*, projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 const _Tp& __value, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __i = ranges::lower_bound(__first, __last, __value, __comp, __proj);
        if (__i == __last)
          return false;
        return !(bool)std::__invoke(__comp, __value,
                                    std::__invoke(__proj, *__i));
      }
 
    template<forward_range _Range,
             typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<const _Tp*,
                                        projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Range&& __r, const _Tp& __value, _Comp __comp = {},
                 _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       __value, std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __binary_search_fn binary_search{};
 
  struct __is_partitioned_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr bool
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        __first = ranges::find_if_not(std::move(__first), __last,
                                      __pred, __proj);
        if (__first == __last)
          return true;
        ++__first;
        return ranges::none_of(std::move(__first), std::move(__last),
                               std::move(__pred), std::move(__proj));
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr bool
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __is_partitioned_fn is_partitioned{};
 
  struct __partition_fn
  {
    template<permutable _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        if constexpr (bidirectional_iterator<_Iter>)
          {
            auto __lasti = ranges::next(__first, __last);
            auto __tail = __lasti;
            for (;;)
              {
                for (;;)
                  if (__first == __tail)
                    return {std::move(__first), std::move(__lasti)};
                  else if (std::__invoke(__pred,
                                         std::__invoke(__proj, *__first)))
                    ++__first;
                  else
                    break;
                --__tail;
                for (;;)
                  if (__first == __tail)
                    return {std::move(__first), std::move(__lasti)};
                  else if (!(bool)std::__invoke(__pred,
                                                std::__invoke(__proj, *__tail)))
                    --__tail;
                  else
                    break;
                ranges::iter_swap(__first, __tail);
                ++__first;
              }
          }
        else
          {
            if (__first == __last)
              return {__first, __first};
 
            while (std::__invoke(__pred, std::__invoke(__proj, *__first)))
              if (++__first == __last)
                return {__first, __first};
 
            auto __next = __first;
            while (++__next != __last)
              if (std::__invoke(__pred, std::__invoke(__proj, *__next)))
                {
                  ranges::iter_swap(__first, __next);
                  ++__first;
                }
 
            return {std::move(__first), std::move(__next)};
          }
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires permutable<iterator_t<_Range>>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __partition_fn partition{};
 
#if _GLIBCXX_HOSTED
  struct __stable_partition_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires permutable<_Iter>
      subrange<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        auto __middle
          = std::stable_partition(std::move(__first), __lasti,
                                  __detail::__make_pred_proj(__pred, __proj));
        return {std::move(__middle), std::move(__lasti)};
      }
 
    template<bidirectional_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires permutable<iterator_t<_Range>>
      borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __stable_partition_fn stable_partition{};
#endif
 
  template<typename _Iter, typename _Out1, typename _Out2>
    struct in_out_out_result
    {
      [[no_unique_address]] _Iter  in;
      [[no_unique_address]] _Out1 out1;
      [[no_unique_address]] _Out2 out2;
 
      template<typename _IIter, typename _OOut1, typename _OOut2>
        requires convertible_to<const _Iter&, _IIter>
          && convertible_to<const _Out1&, _OOut1>
          && convertible_to<const _Out2&, _OOut2>
        constexpr
        operator in_out_out_result<_IIter, _OOut1, _OOut2>() const &
        { return {in, out1, out2}; }
 
      template<typename _IIter, typename _OOut1, typename _OOut2>
        requires convertible_to<_Iter, _IIter>
          && convertible_to<_Out1, _OOut1>
          && convertible_to<_Out2, _OOut2>
        constexpr
        operator in_out_out_result<_IIter, _OOut1, _OOut2>() &&
        { return {std::move(in), std::move(out1), std::move(out2)}; }
    };
 
  template<typename _Iter, typename _Out1, typename _Out2>
    using partition_copy_result = in_out_out_result<_Iter, _Out1, _Out2>;
 
  struct __partition_copy_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             weakly_incrementable _Out1, weakly_incrementable _Out2,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      requires indirectly_copyable<_Iter, _Out1>
        && indirectly_copyable<_Iter, _Out2>
      constexpr partition_copy_result<_Iter, _Out1, _Out2>
      operator()(_Iter __first, _Sent __last,
                 _Out1 __out_true, _Out2 __out_false,
                 _Pred __pred, _Proj __proj = {}) const
      {
        for (; __first != __last; ++__first)
          if (std::__invoke(__pred, std::__invoke(__proj, *__first)))
            {
              *__out_true = *__first;
              ++__out_true;
            }
          else
            {
              *__out_false = *__first;
              ++__out_false;
            }
 
        return {std::move(__first),
                std::move(__out_true), std::move(__out_false)};
      }
 
    template<input_range _Range, weakly_incrementable _Out1,
             weakly_incrementable _Out2,
             typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      requires indirectly_copyable<iterator_t<_Range>, _Out1>
        && indirectly_copyable<iterator_t<_Range>, _Out2>
      constexpr partition_copy_result<borrowed_iterator_t<_Range>, _Out1, _Out2>
      operator()(_Range&& __r, _Out1 __out_true, _Out2 __out_false,
                 _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__out_true), std::move(__out_false),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __partition_copy_fn partition_copy{};
 
  struct __partition_point_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Pred __pred, _Proj __proj = {}) const
      {
        auto __len = ranges::distance(__first, __last);
 
        while (__len > 0)
          {
            auto __half = __len / 2;
            auto __middle = __first;
            ranges::advance(__middle, __half);
            if (std::__invoke(__pred, std::__invoke(__proj, *__middle)))
              {
                __first = __middle;
                ++__first;
                __len = __len - __half - 1;
              }
            else
              __len = __half;
          }
        return __first;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>>
               _Pred>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__pred), std::move(__proj));
      }
  };
 
  inline constexpr __partition_point_fn partition_point{};
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    using merge_result = in_in_out_result<_Iter1, _Iter2, _Out>;
 
  struct __merge_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<_Iter1, _Iter2, _Out, _Comp, _Proj1, _Proj2>
      constexpr merge_result<_Iter1, _Iter2, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          {
            if (std::__invoke(__comp,
                              std::__invoke(__proj2, *__first2),
                              std::__invoke(__proj1, *__first1)))
              {
                *__result = *__first2;
                ++__first2;
              }
            else
              {
                *__result = *__first1;
                ++__first1;
              }
            ++__result;
          }
        auto __copy1 = ranges::copy(std::move(__first1), std::move(__last1),
                                    std::move(__result));
        auto __copy2 = ranges::copy(std::move(__first2), std::move(__last2),
                                    std::move(__copy1.out));
        return { std::move(__copy1.in), std::move(__copy2.in),
                 std::move(__copy2.out) };
      }
 
    template<input_range _Range1, input_range _Range2, weakly_incrementable _Out,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<iterator_t<_Range1>, iterator_t<_Range2>, _Out,
                         _Comp, _Proj1, _Proj2>
      constexpr merge_result<borrowed_iterator_t<_Range1>,
                             borrowed_iterator_t<_Range2>,
                             _Out>
      operator()(_Range1&& __r1, _Range2&& __r2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __merge_fn merge{};
 
  struct __inplace_merge_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less,
             typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      _Iter
      operator()(_Iter __first, _Iter __middle, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __lasti = ranges::next(__first, __last);
        std::inplace_merge(std::move(__first), std::move(__middle), __lasti,
                           __detail::__make_comp_proj(__comp, __proj));
        return __lasti;
      }
 
    template<bidirectional_range _Range,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      borrowed_iterator_t<_Range>
      operator()(_Range&& __r, iterator_t<_Range> __middle,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), std::move(__middle),
                       ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __inplace_merge_fn inplace_merge{};
 
  struct __includes_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_strict_weak_order<projected<_Iter1, _Proj1>,
                                        projected<_Iter2, _Proj2>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          if (std::__invoke(__comp,
                            std::__invoke(__proj2, *__first2),
                            std::__invoke(__proj1, *__first1)))
            return false;
          else if (std::__invoke(__comp,
                                 std::__invoke(__proj1, *__first1),
                                 std::__invoke(__proj2, *__first2)))
            ++__first1;
          else
            {
              ++__first1;
              ++__first2;
            }
 
        return __first2 == __last2;
      }
 
    template<input_range _Range1, input_range _Range2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range1>, _Proj1>,
                                        projected<iterator_t<_Range2>, _Proj2>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Range1&& __r1, _Range2&& __r2, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __includes_fn includes{};
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    using set_union_result = in_in_out_result<_Iter1, _Iter2, _Out>;
 
  struct __set_union_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<_Iter1, _Iter2, _Out, _Comp, _Proj1, _Proj2>
      constexpr set_union_result<_Iter1, _Iter2, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2,
                 _Out __result, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          {
            if (std::__invoke(__comp,
                              std::__invoke(__proj1, *__first1),
                              std::__invoke(__proj2, *__first2)))
              {
                *__result = *__first1;
                ++__first1;
              }
            else if (std::__invoke(__comp,
                                   std::__invoke(__proj2, *__first2),
                                   std::__invoke(__proj1, *__first1)))
              {
                *__result = *__first2;
                ++__first2;
              }
            else
              {
                *__result = *__first1;
                ++__first1;
                ++__first2;
              }
            ++__result;
          }
        auto __copy1 = ranges::copy(std::move(__first1), std::move(__last1),
                                    std::move(__result));
        auto __copy2 = ranges::copy(std::move(__first2), std::move(__last2),
                                    std::move(__copy1.out));
        return {std::move(__copy1.in), std::move(__copy2.in),
                std::move(__copy2.out)};
      }
 
    template<input_range _Range1, input_range _Range2, weakly_incrementable _Out,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<iterator_t<_Range1>, iterator_t<_Range2>, _Out,
                         _Comp, _Proj1, _Proj2>
      constexpr set_union_result<borrowed_iterator_t<_Range1>,
                                 borrowed_iterator_t<_Range2>, _Out>
      operator()(_Range1&& __r1, _Range2&& __r2,
                 _Out __result, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __set_union_fn set_union{};
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    using set_intersection_result = in_in_out_result<_Iter1, _Iter2, _Out>;
 
  struct __set_intersection_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<_Iter1, _Iter2, _Out, _Comp, _Proj1, _Proj2>
      constexpr set_intersection_result<_Iter1, _Iter2, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          if (std::__invoke(__comp,
                            std::__invoke(__proj1, *__first1),
                            std::__invoke(__proj2, *__first2)))
            ++__first1;
          else if (std::__invoke(__comp,
                                 std::__invoke(__proj2, *__first2),
                                 std::__invoke(__proj1, *__first1)))
            ++__first2;
          else
            {
              *__result = *__first1;
              ++__first1;
              ++__first2;
              ++__result;
            }
        // TODO: Eliminating these variables triggers an ICE.
        auto __last1i = ranges::next(std::move(__first1), std::move(__last1));
        auto __last2i = ranges::next(std::move(__first2), std::move(__last2));
        return {std::move(__last1i), std::move(__last2i), std::move(__result)};
      }
 
    template<input_range _Range1, input_range _Range2, weakly_incrementable _Out,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<iterator_t<_Range1>, iterator_t<_Range2>, _Out,
                         _Comp, _Proj1, _Proj2>
      constexpr set_intersection_result<borrowed_iterator_t<_Range1>,
                                        borrowed_iterator_t<_Range2>, _Out>
      operator()(_Range1&& __r1, _Range2&& __r2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __set_intersection_fn set_intersection{};
 
  template<typename _Iter, typename _Out>
    using set_difference_result = in_out_result<_Iter, _Out>;
 
  struct __set_difference_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<_Iter1, _Iter2, _Out, _Comp, _Proj1, _Proj2>
      constexpr set_difference_result<_Iter1, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          if (std::__invoke(__comp,
                            std::__invoke(__proj1, *__first1),
                            std::__invoke(__proj2, *__first2)))
            {
              *__result = *__first1;
              ++__first1;
              ++__result;
            }
          else if (std::__invoke(__comp,
                                 std::__invoke(__proj2, *__first2),
                                 std::__invoke(__proj1, *__first1)))
            ++__first2;
          else
            {
              ++__first1;
              ++__first2;
            }
        return ranges::copy(std::move(__first1), std::move(__last1),
                            std::move(__result));
      }
 
    template<input_range _Range1, input_range _Range2, weakly_incrementable _Out,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<iterator_t<_Range1>, iterator_t<_Range2>, _Out,
                         _Comp, _Proj1, _Proj2>
      constexpr set_difference_result<borrowed_iterator_t<_Range1>, _Out>
      operator()(_Range1&& __r1, _Range2&& __r2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __set_difference_fn set_difference{};
 
  template<typename _Iter1, typename _Iter2, typename _Out>
    using set_symmetric_difference_result
      = in_in_out_result<_Iter1, _Iter2, _Out>;
 
  struct __set_symmetric_difference_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             weakly_incrementable _Out, typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<_Iter1, _Iter2, _Out, _Comp, _Proj1, _Proj2>
      constexpr set_symmetric_difference_result<_Iter1, _Iter2, _Out>
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2,
                 _Out __result, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        while (__first1 != __last1 && __first2 != __last2)
          if (std::__invoke(__comp,
                            std::__invoke(__proj1, *__first1),
                            std::__invoke(__proj2, *__first2)))
            {
              *__result = *__first1;
              ++__first1;
              ++__result;
            }
          else if (std::__invoke(__comp,
                                 std::__invoke(__proj2, *__first2),
                                 std::__invoke(__proj1, *__first1)))
            {
              *__result = *__first2;
              ++__first2;
              ++__result;
            }
          else
            {
              ++__first1;
              ++__first2;
            }
        auto __copy1 = ranges::copy(std::move(__first1), std::move(__last1),
                                    std::move(__result));
        auto __copy2 = ranges::copy(std::move(__first2), std::move(__last2),
                                    std::move(__copy1.out));
        return {std::move(__copy1.in), std::move(__copy2.in),
                std::move(__copy2.out)};
      }
 
    template<input_range _Range1, input_range _Range2, weakly_incrementable _Out,
             typename _Comp = ranges::less,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires mergeable<iterator_t<_Range1>, iterator_t<_Range2>, _Out,
                         _Comp, _Proj1, _Proj2>
      constexpr set_symmetric_difference_result<borrowed_iterator_t<_Range1>,
                                                borrowed_iterator_t<_Range2>,
                                                _Out>
      operator()(_Range1&& __r1, _Range2&& __r2, _Out __result,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__result), std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __set_symmetric_difference_fn set_symmetric_difference{};
 
  // min is defined in <bits/ranges_util.h>.
 
  struct __max_fn
  {
    template<typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<projected<const _Tp*, _Proj>>
               _Comp = ranges::less>
      constexpr const _Tp&
      operator()(const _Tp& __a, const _Tp& __b,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (std::__invoke(__comp,
                          std::__invoke(__proj, __a),
                          std::__invoke(__proj, __b)))
          return __b;
        else
          return __a;
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      requires indirectly_copyable_storable<iterator_t<_Range>,
                                            range_value_t<_Range>*>
      constexpr range_value_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __first = ranges::begin(__r);
        auto __last = ranges::end(__r);
        __glibcxx_assert(__first != __last);
        auto __result = *__first;
        while (++__first != __last)
          {
            auto __tmp = *__first;
            if (std::__invoke(__comp,
                              std::__invoke(__proj, __result),
                              std::__invoke(__proj, __tmp)))
              __result = std::move(__tmp);
          }
        return __result;
      }
 
    template<copyable _Tp, typename _Proj = identity,
             indirect_strict_weak_order<projected<const _Tp*, _Proj>>
               _Comp = ranges::less>
      constexpr _Tp
      operator()(initializer_list<_Tp> __r,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::subrange(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __max_fn max{};
 
  struct __clamp_fn
  {
    template<typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<projected<const _Tp*, _Proj>> _Comp
               = ranges::less>
      constexpr const _Tp&
      operator()(const _Tp& __val, const _Tp& __lo, const _Tp& __hi,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        __glibcxx_assert(!(std::__invoke(__comp,
                                         std::__invoke(__proj, __hi),
                                         std::__invoke(__proj, __lo))));
        auto&& __proj_val = std::__invoke(__proj, __val);
        if (std::__invoke(__comp, __proj_val, std::__invoke(__proj, __lo)))
          return __lo;
        else if (std::__invoke(__comp, std::__invoke(__proj, __hi), __proj_val))
          return __hi;
        else
          return __val;
      }
  };
 
  inline constexpr __clamp_fn clamp{};
 
  template<typename _Tp>
    struct min_max_result
    {
      [[no_unique_address]] _Tp min;
      [[no_unique_address]] _Tp max;
 
      template<typename _Tp2>
        requires convertible_to<const _Tp&, _Tp2>
        constexpr
        operator min_max_result<_Tp2>() const &
        { return {min, max}; }
 
      template<typename _Tp2>
        requires convertible_to<_Tp, _Tp2>
        constexpr
        operator min_max_result<_Tp2>() &&
        { return {std::move(min), std::move(max)}; }
    };
 
  template<typename _Tp>
    using minmax_result = min_max_result<_Tp>;
 
  struct __minmax_fn
  {
    template<typename _Tp, typename _Proj = identity,
             indirect_strict_weak_order<projected<const _Tp*, _Proj>>
               _Comp = ranges::less>
      constexpr minmax_result<const _Tp&>
      operator()(const _Tp& __a, const _Tp& __b,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (std::__invoke(__comp,
                          std::__invoke(__proj, __b),
                          std::__invoke(__proj, __a)))
          return {__b, __a};
        else
          return {__a, __b};
      }
 
    template<input_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      requires indirectly_copyable_storable<iterator_t<_Range>, range_value_t<_Range>*>
      constexpr minmax_result<range_value_t<_Range>>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __first = ranges::begin(__r);
        auto __last = ranges::end(__r);
        __glibcxx_assert(__first != __last);
        auto __comp_proj = __detail::__make_comp_proj(__comp, __proj);
        minmax_result<range_value_t<_Range>> __result = {*__first, __result.min};
        if (++__first == __last)
          return __result;
        else
          {
            // At this point __result.min == __result.max, so a single
            // comparison with the next element suffices.
            auto&& __val = *__first;
            if (__comp_proj(__val, __result.min))
              __result.min = std::forward<decltype(__val)>(__val);
            else
              __result.max = std::forward<decltype(__val)>(__val);
          }
        while (++__first != __last)
          {
            // Now process two elements at a time so that we perform at most
            // 1 + 3*(N-2)/2 comparisons in total (each of the (N-2)/2
            // iterations of this loop performs three comparisons).
            range_value_t<_Range> __val1 = *__first;
            if (++__first == __last)
              {
                // N is odd; in this final iteration, we perform at most two
                // comparisons, for a total of 1 + 3*(N-3)/2 + 2 comparisons,
                // which is not more than 3*N/2, as required.
                if (__comp_proj(__val1, __result.min))
                  __result.min = std::move(__val1);
                else if (!__comp_proj(__val1, __result.max))
                  __result.max = std::move(__val1);
                break;
              }
            auto&& __val2 = *__first;
            if (!__comp_proj(__val2, __val1))
              {
                if (__comp_proj(__val1, __result.min))
                  __result.min = std::move(__val1);
                if (!__comp_proj(__val2, __result.max))
                  __result.max = std::forward<decltype(__val2)>(__val2);
              }
            else
              {
                if (__comp_proj(__val2, __result.min))
                  __result.min = std::forward<decltype(__val2)>(__val2);
                if (!__comp_proj(__val1, __result.max))
                  __result.max = std::move(__val1);
              }
          }
        return __result;
      }
 
    template<copyable _Tp, typename _Proj = identity,
             indirect_strict_weak_order<projected<const _Tp*, _Proj>>
               _Comp = ranges::less>
      constexpr minmax_result<_Tp>
      operator()(initializer_list<_Tp> __r,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::subrange(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __minmax_fn minmax{};
 
  struct __min_element_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return __first;
 
        auto __i = __first;
        while (++__i != __last)
          {
            if (std::__invoke(__comp,
                              std::__invoke(__proj, *__i),
                              std::__invoke(__proj, *__first)))
              __first = __i;
          }
        return __first;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __min_element_fn min_element{};
 
  struct __max_element_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr _Iter
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return __first;
 
        auto __i = __first;
        while (++__i != __last)
          {
            if (std::__invoke(__comp,
                              std::__invoke(__proj, *__first),
                              std::__invoke(__proj, *__i)))
              __first = __i;
          }
        return __first;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr borrowed_iterator_t<_Range>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __max_element_fn max_element{};
 
  template<typename _Iter>
    using minmax_element_result = min_max_result<_Iter>;
 
  struct __minmax_element_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Proj = identity,
             indirect_strict_weak_order<projected<_Iter, _Proj>>
               _Comp = ranges::less>
      constexpr minmax_element_result<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        auto __comp_proj = __detail::__make_comp_proj(__comp, __proj);
        minmax_element_result<_Iter> __result = {__first, __first};
        if (__first == __last || ++__first == __last)
          return __result;
        else
          {
            // At this point __result.min == __result.max, so a single
            // comparison with the next element suffices.
            if (__comp_proj(*__first, *__result.min))
              __result.min = __first;
            else
              __result.max = __first;
          }
        while (++__first != __last)
          {
            // Now process two elements at a time so that we perform at most
            // 1 + 3*(N-2)/2 comparisons in total (each of the (N-2)/2
            // iterations of this loop performs three comparisons).
            auto __prev = __first;
            if (++__first == __last)
              {
                // N is odd; in this final iteration, we perform at most two
                // comparisons, for a total of 1 + 3*(N-3)/2 + 2 comparisons,
                // which is not more than 3*N/2, as required.
                if (__comp_proj(*__prev, *__result.min))
                  __result.min = __prev;
                else if (!__comp_proj(*__prev, *__result.max))
                  __result.max = __prev;
                break;
              }
            if (!__comp_proj(*__first, *__prev))
              {
                if (__comp_proj(*__prev, *__result.min))
                  __result.min = __prev;
                if (!__comp_proj(*__first, *__result.max))
                  __result.max = __first;
              }
            else
              {
                if (__comp_proj(*__first, *__result.min))
                  __result.min = __first;
                if (!__comp_proj(*__prev, *__result.max))
                  __result.max = __prev;
              }
          }
        return __result;
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range>, _Proj>>
               _Comp = ranges::less>
      constexpr minmax_element_result<borrowed_iterator_t<_Range>>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __minmax_element_fn minmax_element{};
 
  struct __lexicographical_compare_fn
  {
    template<input_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             input_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_strict_weak_order<projected<_Iter1, _Proj1>,
                                        projected<_Iter2, _Proj2>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Iter1 __first1, _Sent1 __last1,
                 _Iter2 __first2, _Sent2 __last2,
                 _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        if constexpr (__detail::__is_normal_iterator<_Iter1>
                      && same_as<_Iter1, _Sent1>)
          return (*this)(__first1.base(), __last1.base(),
                         std::move(__first2), std::move(__last2),
                         std::move(__comp),
                         std::move(__proj1), std::move(__proj2));
        else if constexpr (__detail::__is_normal_iterator<_Iter2>
                           && same_as<_Iter2, _Sent2>)
          return (*this)(std::move(__first1), std::move(__last1),
                         __first2.base(), __last2.base(),
                         std::move(__comp),
                         std::move(__proj1), std::move(__proj2));
        else
          {
            constexpr bool __sized_iters
              = (sized_sentinel_for<_Sent1, _Iter1>
                 && sized_sentinel_for<_Sent2, _Iter2>);
            if constexpr (__sized_iters)
              {
                using _ValueType1 = iter_value_t<_Iter1>;
                using _ValueType2 = iter_value_t<_Iter2>;
                // This condition is consistent with the one in
                // __lexicographical_compare_aux in <bits/stl_algobase.h>.
                constexpr bool __use_memcmp
                  = (__is_memcmp_ordered_with<_ValueType1, _ValueType2>::__value
                     && __ptr_to_nonvolatile<_Iter1>
                     && __ptr_to_nonvolatile<_Iter2>
                     && (is_same_v<_Comp, ranges::less>
                         || is_same_v<_Comp, ranges::greater>)
                     && is_same_v<_Proj1, identity>
                     && is_same_v<_Proj2, identity>);
                if constexpr (__use_memcmp)
                  {
                    const auto __d1 = __last1 - __first1;
                    const auto __d2 = __last2 - __first2;
 
                    if (const auto __len = std::min(__d1, __d2))
                      {
                        const auto __c
                          = std::__memcmp(__first1, __first2, __len);
                        if constexpr (is_same_v<_Comp, ranges::less>)
                          {
                            if (__c < 0)
                              return true;
                            if (__c > 0)
                              return false;
                          }
                        else if constexpr (is_same_v<_Comp, ranges::greater>)
                          {
                            if (__c > 0)
                              return true;
                            if (__c < 0)
                              return false;
                          }
                      }
                    return __d1 < __d2;
                  }
              }
 
            for (; __first1 != __last1 && __first2 != __last2;
                 ++__first1, (void) ++__first2)
              {
                if (std::__invoke(__comp,
                                  std::__invoke(__proj1, *__first1),
                                  std::__invoke(__proj2, *__first2)))
                  return true;
                if (std::__invoke(__comp,
                                  std::__invoke(__proj2, *__first2),
                                  std::__invoke(__proj1, *__first1)))
                  return false;
              }
            return __first1 == __last1 && __first2 != __last2;
          }
      }
 
    template<input_range _Range1, input_range _Range2,
             typename _Proj1 = identity, typename _Proj2 = identity,
             indirect_strict_weak_order<projected<iterator_t<_Range1>, _Proj1>,
                                        projected<iterator_t<_Range2>, _Proj2>>
               _Comp = ranges::less>
      constexpr bool
      operator()(_Range1&& __r1, _Range2&& __r2, _Comp __comp = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__comp),
                       std::move(__proj1), std::move(__proj2));
      }
 
  private:
    template<typename _Iter, typename _Ref = iter_reference_t<_Iter>>
      static constexpr bool __ptr_to_nonvolatile
        = is_pointer_v<_Iter> && !is_volatile_v<remove_reference_t<_Ref>>;
  };
 
  inline constexpr __lexicographical_compare_fn lexicographical_compare;
 
  template<typename _Iter>
    struct in_found_result
    {
      [[no_unique_address]] _Iter in;
      bool found;
 
      template<typename _Iter2>
        requires convertible_to<const _Iter&, _Iter2>
        constexpr
        operator in_found_result<_Iter2>() const &
        { return {in, found}; }
 
      template<typename _Iter2>
        requires convertible_to<_Iter, _Iter2>
        constexpr
        operator in_found_result<_Iter2>() &&
        { return {std::move(in), found}; }
    };
 
  template<typename _Iter>
    using next_permutation_result = in_found_result<_Iter>;
 
  struct __next_permutation_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr next_permutation_result<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return {std::move(__first), false};
 
        auto __i = __first;
        ++__i;
        if (__i == __last)
          return {std::move(__i), false};
 
        auto __lasti = ranges::next(__first, __last);
        __i = __lasti;
        --__i;
 
        for (;;)
          {
            auto __ii = __i;
            --__i;
            if (std::__invoke(__comp,
                              std::__invoke(__proj, *__i),
                              std::__invoke(__proj, *__ii)))
              {
                auto __j = __lasti;
                while (!(bool)std::__invoke(__comp,
                                            std::__invoke(__proj, *__i),
                                            std::__invoke(__proj, *--__j)))
                  ;
                ranges::iter_swap(__i, __j);
                ranges::reverse(__ii, __last);
                return {std::move(__lasti), true};
              }
            if (__i == __first)
              {
                ranges::reverse(__first, __last);
                return {std::move(__lasti), false};
              }
          }
      }
 
    template<bidirectional_range _Range, typename _Comp = ranges::less,
             typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr next_permutation_result<borrowed_iterator_t<_Range>>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __next_permutation_fn next_permutation{};
 
  template<typename _Iter>
    using prev_permutation_result = in_found_result<_Iter>;
 
  struct __prev_permutation_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             typename _Comp = ranges::less, typename _Proj = identity>
      requires sortable<_Iter, _Comp, _Proj>
      constexpr prev_permutation_result<_Iter>
      operator()(_Iter __first, _Sent __last,
                 _Comp __comp = {}, _Proj __proj = {}) const
      {
        if (__first == __last)
          return {std::move(__first), false};
 
        auto __i = __first;
        ++__i;
        if (__i == __last)
          return {std::move(__i), false};
 
        auto __lasti = ranges::next(__first, __last);
        __i = __lasti;
        --__i;
 
        for (;;)
          {
            auto __ii = __i;
            --__i;
            if (std::__invoke(__comp,
                              std::__invoke(__proj, *__ii),
                              std::__invoke(__proj, *__i)))
              {
                auto __j = __lasti;
                while (!(bool)std::__invoke(__comp,
                                            std::__invoke(__proj, *--__j),
                                            std::__invoke(__proj, *__i)))
                  ;
                ranges::iter_swap(__i, __j);
                ranges::reverse(__ii, __last);
                return {std::move(__lasti), true};
              }
            if (__i == __first)
              {
                ranges::reverse(__first, __last);
                return {std::move(__lasti), false};
              }
          }
      }
 
    template<bidirectional_range _Range, typename _Comp = ranges::less,
             typename _Proj = identity>
      requires sortable<iterator_t<_Range>, _Comp, _Proj>
      constexpr prev_permutation_result<borrowed_iterator_t<_Range>>
      operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const
      {
        return (*this)(ranges::begin(__r), ranges::end(__r),
                       std::move(__comp), std::move(__proj));
      }
  };
 
  inline constexpr __prev_permutation_fn prev_permutation{};
 
#if __cplusplus > 202002L
 
#define __cpp_lib_ranges_contains 202207L
 
  struct __contains_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
            typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<_Iter, _Proj>, const _Tp*>
      constexpr bool
      operator()(_Iter __first, _Sent __last, const _Tp& __value, _Proj __proj = {}) const
      { return ranges::find(std::move(__first), __last, __value, std::move(__proj)) != __last; }
 
    template<input_range _Range, typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to,
                                         projected<iterator_t<_Range>, _Proj>, const _Tp*>
      constexpr bool
      operator()(_Range&& __r, const _Tp& __value, _Proj __proj = {}) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), __value, std::move(__proj)); }
  };
 
  inline constexpr __contains_fn contains{};
 
  struct __contains_subrange_fn
  {
    template<forward_iterator _Iter1, sentinel_for<_Iter1> _Sent1,
             forward_iterator _Iter2, sentinel_for<_Iter2> _Sent2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<_Iter1, _Iter2, _Pred, _Proj1, _Proj2>
      constexpr bool
      operator()(_Iter1 __first1, _Sent1 __last1, _Iter2 __first2, _Sent2 __last2,
                 _Pred __pred = {}, _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return __first2 == __last2
          || !ranges::search(__first1, __last1, __first2, __last2,
                             std::move(__pred), std::move(__proj1), std::move(__proj2)).empty();
      }
 
    template<forward_range _Range1, forward_range _Range2,
             typename _Pred = ranges::equal_to,
             typename _Proj1 = identity, typename _Proj2 = identity>
      requires indirectly_comparable<iterator_t<_Range1>, iterator_t<_Range2>,
                                     _Pred, _Proj1, _Proj2>
      constexpr bool
      operator()(_Range1&& __r1, _Range2&& __r2, _Pred __pred = {},
                 _Proj1 __proj1 = {}, _Proj2 __proj2 = {}) const
      {
        return (*this)(ranges::begin(__r1), ranges::end(__r1),
                       ranges::begin(__r2), ranges::end(__r2),
                       std::move(__pred), std::move(__proj1), std::move(__proj2));
      }
  };
 
  inline constexpr __contains_subrange_fn contains_subrange{};
 
#define __cpp_lib_ranges_iota 202202L
 
  template<typename _Out, typename _Tp>
    struct out_value_result
    {
      [[no_unique_address]] _Out out;
      [[no_unique_address]] _Tp value;
 
      template<typename _Out2, typename _Tp2>
        requires convertible_to<const _Out&, _Out2>
          && convertible_to<const _Tp&, _Tp2>
        constexpr
        operator out_value_result<_Out2, _Tp2>() const &
        { return {out, value}; }
 
      template<typename _Out2, typename _Tp2>
        requires convertible_to<_Out, _Out2>
          && convertible_to<_Tp, _Tp2>
        constexpr
        operator out_value_result<_Out2, _Tp2>() &&
        { return {std::move(out), std::move(value)}; }
    };
 
  template<typename _Out, typename _Tp>
    using iota_result = out_value_result<_Out, _Tp>;
 
  struct __iota_fn
  {
    template<input_or_output_iterator _Out, sentinel_for<_Out> _Sent, weakly_incrementable _Tp>
      requires indirectly_writable<_Out, const _Tp&>
      constexpr iota_result<_Out, _Tp>
      operator()(_Out __first, _Sent __last, _Tp __value) const
      {
        while (__first != __last)
          {
            *__first = static_cast<const _Tp&>(__value);
            ++__first;
            ++__value;
          }
        return {std::move(__first), std::move(__value)};
      }
 
    template<weakly_incrementable _Tp, output_range<const _Tp&> _Range>
      constexpr iota_result<borrowed_iterator_t<_Range>, _Tp>
      operator()(_Range&& __r, _Tp __value) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__value)); }
  };
 
  inline constexpr __iota_fn iota{};
 
#define __cpp_lib_ranges_find_last 202207L
 
  struct __find_last_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to, projected<_Iter, _Proj>, const _Tp*>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last, const _Tp& __value, _Proj __proj = {}) const
      {
        if constexpr (same_as<_Iter, _Sent> && bidirectional_iterator<_Iter>)
          {
            _Iter __found = ranges::find(reverse_iterator<_Iter>{__last},
                                         reverse_iterator<_Iter>{__first},
                                         __value, std::move(__proj)).base();
            if (__found == __first)
              return {__last, __last};
            else
              return {ranges::prev(__found), __last};
          }
        else
          {
            _Iter __found = ranges::find(__first, __last, __value, __proj);
            if (__found == __last)
              return {__found, __found};
            __first = __found;
            for (;;)
              {
                __first = ranges::find(ranges::next(__first), __last, __value, __proj);
                if (__first == __last)
                  return {__found, __first};
                __found = __first;
              }
          }
      }
 
    template<forward_range _Range, typename _Tp, typename _Proj = identity>
      requires indirect_binary_predicate<ranges::equal_to, projected<iterator_t<_Range>, _Proj>, const _Tp*>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, const _Tp& __value, _Proj __proj = {}) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), __value, std::move(__proj)); }
  };
 
  inline constexpr __find_last_fn find_last{};
 
  struct __find_last_if_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last, _Pred __pred, _Proj __proj = {}) const
      {
        if constexpr (same_as<_Iter, _Sent> && bidirectional_iterator<_Iter>)
          {
            _Iter __found = ranges::find_if(reverse_iterator<_Iter>{__last},
                                            reverse_iterator<_Iter>{__first},
                                            std::move(__pred), std::move(__proj)).base();
            if (__found == __first)
              return {__last, __last};
            else
              return {ranges::prev(__found), __last};
          }
        else
          {
            _Iter __found = ranges::find_if(__first, __last, __pred, __proj);
            if (__found == __last)
              return {__found, __found};
            __first = __found;
            for (;;)
              {
                __first = ranges::find_if(ranges::next(__first), __last, __pred, __proj);
                if (__first == __last)
                  return {__found, __first};
                __found = __first;
              }
          }
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>> _Pred>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__pred), std::move(__proj)); }
  };
 
  inline constexpr __find_last_if_fn find_last_if{};
 
  struct __find_last_if_not_fn
  {
    template<forward_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Proj = identity,
             indirect_unary_predicate<projected<_Iter, _Proj>> _Pred>
      constexpr subrange<_Iter>
      operator()(_Iter __first, _Sent __last, _Pred __pred, _Proj __proj = {}) const
      {
        if constexpr (same_as<_Iter, _Sent> && bidirectional_iterator<_Iter>)
          {
            _Iter __found = ranges::find_if_not(reverse_iterator<_Iter>{__last},
                                                reverse_iterator<_Iter>{__first},
                                                std::move(__pred), std::move(__proj)).base();
            if (__found == __first)
              return {__last, __last};
            else
              return {ranges::prev(__found), __last};
          }
        else
          {
            _Iter __found = ranges::find_if_not(__first, __last, __pred, __proj);
            if (__found == __last)
              return {__found, __found};
            __first = __found;
            for (;;)
              {
                __first = ranges::find_if_not(ranges::next(__first), __last, __pred, __proj);
                if (__first == __last)
                  return {__found, __first};
                __found = __first;
              }
          }
      }
 
    template<forward_range _Range, typename _Proj = identity,
             indirect_unary_predicate<projected<iterator_t<_Range>, _Proj>> _Pred>
      constexpr borrowed_subrange_t<_Range>
      operator()(_Range&& __r, _Pred __pred, _Proj __proj = {}) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__pred), std::move(__proj)); }
  };
 
  inline constexpr __find_last_if_not_fn find_last_if_not{};
 
#define __cpp_lib_ranges_fold 202207L
 
  template<typename _Iter, typename _Tp>
    struct in_value_result
    {
      [[no_unique_address]] _Iter in;
      [[no_unique_address]] _Tp value;
 
      template<typename _Iter2, typename _Tp2>
        requires convertible_to<const _Iter&, _Iter2>
          && convertible_to<const _Tp&, _Tp2>
      constexpr
      operator in_value_result<_Iter2, _Tp2>() const &
      { return {in, value}; }
 
      template<typename _Iter2, typename _Tp2>
        requires convertible_to<_Iter, _Iter2>
          && convertible_to<_Tp, _Tp2>
      constexpr
      operator in_value_result<_Iter2, _Tp2>() &&
      { return {std::move(in), std::move(value)}; }
    };
 
  namespace __detail
  {
    template<typename _Fp>
      class __flipped
      {
        _Fp _M_f;
 
      public:
        template<typename _Tp, typename _Up>
          requires invocable<_Fp&, _Up, _Tp>
        invoke_result_t<_Fp&, _Up, _Tp>
        operator()(_Tp&&, _Up&&); // not defined
      };
 
      template<typename _Fp, typename _Tp, typename _Iter, typename _Up>
      concept __indirectly_binary_left_foldable_impl = movable<_Tp> && movable<_Up>
        && convertible_to<_Tp, _Up>
        && invocable<_Fp&, _Up, iter_reference_t<_Iter>>
        && assignable_from<_Up&, invoke_result_t<_Fp&, _Up, iter_reference_t<_Iter>>>;
 
      template<typename _Fp, typename _Tp, typename _Iter>
      concept __indirectly_binary_left_foldable = copy_constructible<_Fp>
        && indirectly_readable<_Iter>
        && invocable<_Fp&, _Tp, iter_reference_t<_Iter>>
        && convertible_to<invoke_result_t<_Fp&, _Tp, iter_reference_t<_Iter>>,
                          decay_t<invoke_result_t<_Fp&, _Tp, iter_reference_t<_Iter>>>>
        && __indirectly_binary_left_foldable_impl
            <_Fp, _Tp, _Iter, decay_t<invoke_result_t<_Fp&, _Tp, iter_reference_t<_Iter>>>>;
 
      template <typename _Fp, typename _Tp, typename _Iter>
      concept __indirectly_binary_right_foldable
        = __indirectly_binary_left_foldable<__flipped<_Fp>, _Tp, _Iter>;
  } // namespace __detail
 
  template<typename _Iter, typename _Tp>
    using fold_left_with_iter_result = in_value_result<_Iter, _Tp>;
 
  struct __fold_left_with_iter_fn
  {
    template<typename _Ret_iter,
             typename _Iter, typename _Sent, typename _Tp, typename _Fp>
      static constexpr auto
      _S_impl(_Iter __first, _Sent __last, _Tp __init, _Fp __f)
      {
        using _Up = decay_t<invoke_result_t<_Fp&, _Tp, iter_reference_t<_Iter>>>;
        using _Ret = fold_left_with_iter_result<_Ret_iter, _Up>;
 
        if (__first == __last)
          return _Ret{std::move(__first), _Up(std::move(__init))};
 
        _Up __accum = std::__invoke(__f, std::move(__init), *__first);
        for (++__first; __first != __last; ++__first)
          __accum = std::__invoke(__f, std::move(__accum), *__first);
        return _Ret{std::move(__first), std::move(__accum)};
      }
 
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Tp,
             __detail::__indirectly_binary_left_foldable<_Tp, _Iter> _Fp>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Tp __init, _Fp __f) const
      {
        using _Ret_iter = _Iter;
        return _S_impl<_Ret_iter>(std::move(__first), __last,
                                  std::move(__init), std::move(__f));
      }
 
    template<input_range _Range, typename _Tp,
             __detail::__indirectly_binary_left_foldable<_Tp, iterator_t<_Range>> _Fp>
      constexpr auto
      operator()(_Range&& __r, _Tp __init, _Fp __f) const
      {
        using _Ret_iter = borrowed_iterator_t<_Range>;
        return _S_impl<_Ret_iter>(ranges::begin(__r), ranges::end(__r),
                                  std::move(__init), std::move(__f));
      }
  };
 
  inline constexpr __fold_left_with_iter_fn fold_left_with_iter{};
 
  struct __fold_left_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Tp,
             __detail::__indirectly_binary_left_foldable<_Tp, _Iter> _Fp>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Tp __init, _Fp __f) const
      {
        return ranges::fold_left_with_iter(std::move(__first), __last,
                                           std::move(__init), std::move(__f)).value;
      }
 
    template<input_range _Range, typename _Tp,
             __detail::__indirectly_binary_left_foldable<_Tp, iterator_t<_Range>> _Fp>
      constexpr auto
      operator()(_Range&& __r, _Tp __init, _Fp __f) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__init), std::move(__f)); }
  };
 
  inline constexpr __fold_left_fn fold_left{};
 
  template<typename _Iter, typename _Tp>
    using fold_left_first_with_iter_result = in_value_result<_Iter, _Tp>;
 
  struct __fold_left_first_with_iter_fn
  {
    template<typename _Ret_iter, typename _Iter, typename _Sent, typename _Fp>
      static constexpr auto
      _S_impl(_Iter __first, _Sent __last, _Fp __f)
      {
        using _Up = decltype(ranges::fold_left(std::move(__first), __last,
                                               iter_value_t<_Iter>(*__first), __f));
        using _Ret = fold_left_first_with_iter_result<_Ret_iter, optional<_Up>>;
 
        if (__first == __last)
          return _Ret{std::move(__first), optional<_Up>()};
 
        optional<_Up> __init(in_place, *__first);
        for (++__first; __first != __last; ++__first)
          *__init = std::__invoke(__f, std::move(*__init), *__first);
        return _Ret{std::move(__first), std::move(__init)};
      }
 
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             __detail::__indirectly_binary_left_foldable<iter_value_t<_Iter>, _Iter> _Fp>
      requires constructible_from<iter_value_t<_Iter>, iter_reference_t<_Iter>>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Fp __f) const
      {
        using _Ret_iter = _Iter;
        return _S_impl<_Ret_iter>(std::move(__first), __last, std::move(__f));
      }
 
    template<input_range _Range,
             __detail::__indirectly_binary_left_foldable<range_value_t<_Range>, iterator_t<_Range>> _Fp>
      requires constructible_from<range_value_t<_Range>, range_reference_t<_Range>>
      constexpr auto
      operator()(_Range&& __r, _Fp __f) const
      {
        using _Ret_iter = borrowed_iterator_t<_Range>;
        return _S_impl<_Ret_iter>(ranges::begin(__r), ranges::end(__r), std::move(__f));
      }
  };
 
  inline constexpr __fold_left_first_with_iter_fn fold_left_first_with_iter{};
 
  struct __fold_left_first_fn
  {
    template<input_iterator _Iter, sentinel_for<_Iter> _Sent,
             __detail::__indirectly_binary_left_foldable<iter_value_t<_Iter>, _Iter> _Fp>
      requires constructible_from<iter_value_t<_Iter>, iter_reference_t<_Iter>>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Fp __f) const
      {
        return ranges::fold_left_first_with_iter(std::move(__first), __last,
                                                 std::move(__f)).value;
      }
 
    template<input_range _Range,
             __detail::__indirectly_binary_left_foldable<range_value_t<_Range>, iterator_t<_Range>> _Fp>
      requires constructible_from<range_value_t<_Range>, range_reference_t<_Range>>
      constexpr auto
      operator()(_Range&& __r, _Fp __f) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__f)); }
  };
 
  inline constexpr __fold_left_first_fn fold_left_first{};
 
  struct __fold_right_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent, typename _Tp,
             __detail::__indirectly_binary_right_foldable<_Tp, _Iter> _Fp>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Tp __init, _Fp __f) const
      {
        using _Up = decay_t<invoke_result_t<_Fp&, iter_reference_t<_Iter>, _Tp>>;
 
        if (__first == __last)
          return _Up(std::move(__init));
 
        _Iter __tail = ranges::next(__first, __last);
        _Up __accum = std::__invoke(__f, *--__tail, std::move(__init));
        while (__first != __tail)
          __accum = std::__invoke(__f, *--__tail, std::move(__accum));
        return __accum;
      }
 
    template<bidirectional_range _Range, typename _Tp,
             __detail::__indirectly_binary_right_foldable<_Tp, iterator_t<_Range>> _Fp>
      constexpr auto
      operator()(_Range&& __r, _Tp __init, _Fp __f) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__init), std::move(__f)); }
  };
 
  inline constexpr __fold_right_fn fold_right{};
 
  struct __fold_right_last_fn
  {
    template<bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent,
             __detail::__indirectly_binary_right_foldable<iter_value_t<_Iter>, _Iter> _Fp>
      requires constructible_from<iter_value_t<_Iter>, iter_reference_t<_Iter>>
      constexpr auto
      operator()(_Iter __first, _Sent __last, _Fp __f) const
      {
        using _Up = decltype(ranges::fold_right(__first, __last,
                                                iter_value_t<_Iter>(*__first), __f));
 
        if (__first == __last)
          return optional<_Up>();
 
        _Iter __tail = ranges::prev(ranges::next(__first, std::move(__last)));
        return optional<_Up>(in_place,
                             ranges::fold_right(std::move(__first), __tail,
                                                iter_value_t<_Iter>(*__tail),
                                                std::move(__f)));
      }
 
    template<bidirectional_range _Range,
             __detail::__indirectly_binary_right_foldable<range_value_t<_Range>, iterator_t<_Range>> _Fp>
      requires constructible_from<range_value_t<_Range>, range_reference_t<_Range>>
      constexpr auto
      operator()(_Range&& __r, _Fp __f) const
      { return (*this)(ranges::begin(__r), ranges::end(__r), std::move(__f)); }
  };
 
  inline constexpr __fold_right_last_fn fold_right_last{};
#endif // C++23
} // namespace ranges
 
#define __cpp_lib_shift 201806L
  template<typename _ForwardIterator>
    constexpr _ForwardIterator
    shift_left(_ForwardIterator __first, _ForwardIterator __last,
               typename iterator_traits<_ForwardIterator>::difference_type __n)
    {
      __glibcxx_assert(__n >= 0);
      if (__n == 0)
        return __last;
 
      auto __mid = ranges::next(__first, __n, __last);
      if (__mid == __last)
        return __first;
      return std::move(std::move(__mid), std::move(__last), std::move(__first));
    }
 
  template<typename _ForwardIterator>
    constexpr _ForwardIterator
    shift_right(_ForwardIterator __first, _ForwardIterator __last,
                typename iterator_traits<_ForwardIterator>::difference_type __n)
    {
      __glibcxx_assert(__n >= 0);
      if (__n == 0)
        return __first;
 
      using _Cat
        = typename iterator_traits<_ForwardIterator>::iterator_category;
      if constexpr (derived_from<_Cat, bidirectional_iterator_tag>)
        {
          auto __mid = ranges::next(__last, -__n, __first);
          if (__mid == __first)
            return __last;
 
          return std::move_backward(std::move(__first), std::move(__mid),
                                    std::move(__last));
        }
      else
        {
          auto __result = ranges::next(__first, __n, __last);
          if (__result == __last)
            return __last;
 
          auto __dest_head = __first, __dest_tail = __result;
          while (__dest_head != __result)
            {
              if (__dest_tail == __last)
                {
                  // If we get here, then we must have
                  //     2*n >= distance(__first, __last)
                  // i.e. we are shifting out at least half of the range.  In
                  // this case we can safely perform the shift with a single
                  // move.
                  std::move(std::move(__first), std::move(__dest_head), __result);
                  return __result;
                }
              ++__dest_head;
              ++__dest_tail;
            }
 
          for (;;)
            {
              // At the start of each iteration of this outer loop, the range
              // [__first, __result) contains those elements that after shifting
              // the whole range right by __n, should end up in
              // [__dest_head, __dest_tail) in order.
 
              // The below inner loop swaps the elements of [__first, __result)
              // and [__dest_head, __dest_tail), while simultaneously shifting
              // the latter range by __n.
              auto __cursor = __first;
              while (__cursor != __result)
                {
                  if (__dest_tail == __last)
                    {
                      // At this point the ranges [__first, result) and
                      // [__dest_head, dest_tail) are disjoint, so we can safely
                      // move the remaining elements.
                      __dest_head = std::move(__cursor, __result,
                                              std::move(__dest_head));
                      std::move(std::move(__first), std::move(__cursor),
                                std::move(__dest_head));
                      return __result;
                    }
                  std::iter_swap(__cursor, __dest_head);
                  ++__dest_head;
                  ++__dest_tail;
                  ++__cursor;
                }
            }
        }
    }
 
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace std
#endif // concepts
#endif // C++20
#endif // _RANGES_ALGO_H