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 //===----------------------------------------------------------------------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef _LIBCPP___CXX03___ALGORITHM_SORT_H
 #define _LIBCPP___CXX03___ALGORITHM_SORT_H
 
 #include <__cxx03/__algorithm/comp.h>
 #include <__cxx03/__algorithm/comp_ref_type.h>
 #include <__cxx03/__algorithm/iter_swap.h>
 #include <__cxx03/__algorithm/iterator_operations.h>
 #include <__cxx03/__algorithm/min_element.h>
 #include <__cxx03/__algorithm/partial_sort.h>
 #include <__cxx03/__algorithm/unwrap_iter.h>
 #include <__cxx03/__assert>
 #include <__cxx03/__bit/blsr.h>
 #include <__cxx03/__bit/countl.h>
 #include <__cxx03/__bit/countr.h>
 #include <__cxx03/__config>
 #include <__cxx03/__debug_utils/randomize_range.h>
 #include <__cxx03/__debug_utils/strict_weak_ordering_check.h>
 #include <__cxx03/__functional/operations.h>
 #include <__cxx03/__functional/ranges_operations.h>
 #include <__cxx03/__iterator/iterator_traits.h>
 #include <__cxx03/__type_traits/conditional.h>
 #include <__cxx03/__type_traits/disjunction.h>
 #include <__cxx03/__type_traits/is_arithmetic.h>
 #include <__cxx03/__type_traits/is_constant_evaluated.h>
 #include <__cxx03/__utility/move.h>
 #include <__cxx03/__utility/pair.h>
 #include <__cxx03/climits>
 #include <__cxx03/cstdint>
 
 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
 #  pragma GCC system_header
 #endif
 
 _LIBCPP_PUSH_MACROS
 #include <__cxx03/__undef_macros>
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 // stable, 2-3 compares, 0-2 swaps
 
 template <class _AlgPolicy, class _Compare, class _ForwardIterator>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 unsigned
 __sort3(_ForwardIterator __x, _ForwardIterator __y, _ForwardIterator __z, _Compare __c) {
   using _Ops = _IterOps<_AlgPolicy>;
 
   unsigned __r = 0;
   if (!__c(*__y, *__x)) // if x <= y
   {
     if (!__c(*__z, *__y))      // if y <= z
       return __r;              // x <= y && y <= z
                                // x <= y && y > z
     _Ops::iter_swap(__y, __z); // x <= z && y < z
     __r = 1;
     if (__c(*__y, *__x)) // if x > y
     {
       _Ops::iter_swap(__x, __y); // x < y && y <= z
       __r = 2;
     }
     return __r; // x <= y && y < z
   }
   if (__c(*__z, *__y)) // x > y, if y > z
   {
     _Ops::iter_swap(__x, __z); // x < y && y < z
     __r = 1;
     return __r;
   }
   _Ops::iter_swap(__x, __y); // x > y && y <= z
   __r = 1;                   // x < y && x <= z
   if (__c(*__z, *__y))       // if y > z
   {
     _Ops::iter_swap(__y, __z); // x <= y && y < z
     __r = 2;
   }
   return __r;
 } // x <= y && y <= z
 
 // stable, 3-6 compares, 0-5 swaps
 
 template <class _AlgPolicy, class _Compare, class _ForwardIterator>
 _LIBCPP_HIDE_FROM_ABI void
 __sort4(_ForwardIterator __x1, _ForwardIterator __x2, _ForwardIterator __x3, _ForwardIterator __x4, _Compare __c) {
   using _Ops = _IterOps<_AlgPolicy>;
   std::__sort3<_AlgPolicy, _Compare>(__x1, __x2, __x3, __c);
   if (__c(*__x4, *__x3)) {
     _Ops::iter_swap(__x3, __x4);
     if (__c(*__x3, *__x2)) {
       _Ops::iter_swap(__x2, __x3);
       if (__c(*__x2, *__x1)) {
         _Ops::iter_swap(__x1, __x2);
       }
     }
   }
 }
 
 // stable, 4-10 compares, 0-9 swaps
 
 template <class _AlgPolicy, class _Comp, class _ForwardIterator>
 _LIBCPP_HIDE_FROM_ABI void
 __sort5(_ForwardIterator __x1,
         _ForwardIterator __x2,
         _ForwardIterator __x3,
         _ForwardIterator __x4,
         _ForwardIterator __x5,
         _Comp __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
 
   std::__sort4<_AlgPolicy, _Comp>(__x1, __x2, __x3, __x4, __comp);
   if (__comp(*__x5, *__x4)) {
     _Ops::iter_swap(__x4, __x5);
     if (__comp(*__x4, *__x3)) {
       _Ops::iter_swap(__x3, __x4);
       if (__comp(*__x3, *__x2)) {
         _Ops::iter_swap(__x2, __x3);
         if (__comp(*__x2, *__x1)) {
           _Ops::iter_swap(__x1, __x2);
         }
       }
     }
   }
 }
 
 // The comparator being simple is a prerequisite for using the branchless optimization.
 template <class _Tp>
 struct __is_simple_comparator : false_type {};
 template <>
 struct __is_simple_comparator<__less<>&> : true_type {};
 template <class _Tp>
 struct __is_simple_comparator<less<_Tp>&> : true_type {};
 template <class _Tp>
 struct __is_simple_comparator<greater<_Tp>&> : true_type {};
 #if _LIBCPP_STD_VER >= 20
 template <>
 struct __is_simple_comparator<ranges::less&> : true_type {};
 template <>
 struct __is_simple_comparator<ranges::greater&> : true_type {};
 #endif
 
 template <class _Compare, class _Iter, class _Tp = typename iterator_traits<_Iter>::value_type>
 using __use_branchless_sort =
     integral_constant<bool,
                       __libcpp_is_contiguous_iterator<_Iter>::value && sizeof(_Tp) <= sizeof(void*) &&
                           is_arithmetic<_Tp>::value && __is_simple_comparator<_Compare>::value>;
 
 namespace __detail {
 
 // Size in bits for the bitset in use.
 enum { __block_size = sizeof(uint64_t) * 8 };
 
 } // namespace __detail
 
 // Ensures that __c(*__x, *__y) is true by swapping *__x and *__y if necessary.
 template <class _Compare, class _RandomAccessIterator>
 inline _LIBCPP_HIDE_FROM_ABI void __cond_swap(_RandomAccessIterator __x, _RandomAccessIterator __y, _Compare __c) {
   // Note: this function behaves correctly even with proxy iterators (because it relies on `value_type`).
   using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
   bool __r         = __c(*__x, *__y);
   value_type __tmp = __r ? *__x : *__y;
   *__y             = __r ? *__y : *__x;
   *__x             = __tmp;
 }
 
 // Ensures that *__x, *__y and *__z are ordered according to the comparator __c,
 // under the assumption that *__y and *__z are already ordered.
 template <class _Compare, class _RandomAccessIterator>
 inline _LIBCPP_HIDE_FROM_ABI void
 __partially_sorted_swap(_RandomAccessIterator __x, _RandomAccessIterator __y, _RandomAccessIterator __z, _Compare __c) {
   // Note: this function behaves correctly even with proxy iterators (because it relies on `value_type`).
   using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
   bool __r         = __c(*__z, *__x);
   value_type __tmp = __r ? *__z : *__x;
   *__z             = __r ? *__x : *__z;
   __r              = __c(__tmp, *__y);
   *__x             = __r ? *__x : *__y;
   *__y             = __r ? *__y : __tmp;
 }
 
 template <class,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort3_maybe_branchless(
     _RandomAccessIterator __x1, _RandomAccessIterator __x2, _RandomAccessIterator __x3, _Compare __c) {
   std::__cond_swap<_Compare>(__x2, __x3, __c);
   std::__partially_sorted_swap<_Compare>(__x1, __x2, __x3, __c);
 }
 
 template <class _AlgPolicy,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<!__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort3_maybe_branchless(
     _RandomAccessIterator __x1, _RandomAccessIterator __x2, _RandomAccessIterator __x3, _Compare __c) {
   std::__sort3<_AlgPolicy, _Compare>(__x1, __x2, __x3, __c);
 }
 
 template <class,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort4_maybe_branchless(
     _RandomAccessIterator __x1,
     _RandomAccessIterator __x2,
     _RandomAccessIterator __x3,
     _RandomAccessIterator __x4,
     _Compare __c) {
   std::__cond_swap<_Compare>(__x1, __x3, __c);
   std::__cond_swap<_Compare>(__x2, __x4, __c);
   std::__cond_swap<_Compare>(__x1, __x2, __c);
   std::__cond_swap<_Compare>(__x3, __x4, __c);
   std::__cond_swap<_Compare>(__x2, __x3, __c);
 }
 
 template <class _AlgPolicy,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<!__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort4_maybe_branchless(
     _RandomAccessIterator __x1,
     _RandomAccessIterator __x2,
     _RandomAccessIterator __x3,
     _RandomAccessIterator __x4,
     _Compare __c) {
   std::__sort4<_AlgPolicy, _Compare>(__x1, __x2, __x3, __x4, __c);
 }
 
 template <class _AlgPolicy,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort5_maybe_branchless(
     _RandomAccessIterator __x1,
     _RandomAccessIterator __x2,
     _RandomAccessIterator __x3,
     _RandomAccessIterator __x4,
     _RandomAccessIterator __x5,
     _Compare __c) {
   std::__cond_swap<_Compare>(__x1, __x2, __c);
   std::__cond_swap<_Compare>(__x4, __x5, __c);
   std::__partially_sorted_swap<_Compare>(__x3, __x4, __x5, __c);
   std::__cond_swap<_Compare>(__x2, __x5, __c);
   std::__partially_sorted_swap<_Compare>(__x1, __x3, __x4, __c);
   std::__partially_sorted_swap<_Compare>(__x2, __x3, __x4, __c);
 }
 
 template <class _AlgPolicy,
           class _Compare,
           class _RandomAccessIterator,
           __enable_if_t<!__use_branchless_sort<_Compare, _RandomAccessIterator>::value, int> = 0>
 inline _LIBCPP_HIDE_FROM_ABI void __sort5_maybe_branchless(
     _RandomAccessIterator __x1,
     _RandomAccessIterator __x2,
     _RandomAccessIterator __x3,
     _RandomAccessIterator __x4,
     _RandomAccessIterator __x5,
     _Compare __c) {
   std::__sort5<_AlgPolicy, _Compare, _RandomAccessIterator>(
       std::move(__x1), std::move(__x2), std::move(__x3), std::move(__x4), std::move(__x5), __c);
 }
 
 // Assumes size > 0
 template <class _AlgPolicy, class _Compare, class _BidirectionalIterator>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void
 __selection_sort(_BidirectionalIterator __first, _BidirectionalIterator __last, _Compare __comp) {
   _BidirectionalIterator __lm1 = __last;
   for (--__lm1; __first != __lm1; ++__first) {
     _BidirectionalIterator __i = std::__min_element<_Compare>(__first, __last, __comp);
     if (__i != __first)
       _IterOps<_AlgPolicy>::iter_swap(__first, __i);
   }
 }
 
 // Sort the iterator range [__first, __last) using the comparator __comp using
 // the insertion sort algorithm.
 template <class _AlgPolicy, class _Compare, class _BidirectionalIterator>
 _LIBCPP_HIDE_FROM_ABI void
 __insertion_sort(_BidirectionalIterator __first, _BidirectionalIterator __last, _Compare __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
 
   typedef typename iterator_traits<_BidirectionalIterator>::value_type value_type;
   if (__first == __last)
     return;
   _BidirectionalIterator __i = __first;
   for (++__i; __i != __last; ++__i) {
     _BidirectionalIterator __j = __i;
     --__j;
     if (__comp(*__i, *__j)) {
       value_type __t(_Ops::__iter_move(__i));
       _BidirectionalIterator __k = __j;
       __j                        = __i;
       do {
         *__j = _Ops::__iter_move(__k);
         __j  = __k;
       } while (__j != __first && __comp(__t, *--__k));
       *__j = std::move(__t);
     }
   }
 }
 
 // Sort the iterator range [__first, __last) using the comparator __comp using
 // the insertion sort algorithm.  Insertion sort has two loops, outer and inner.
 // The implementation below has no bounds check (unguarded) for the inner loop.
 // Assumes that there is an element in the position (__first - 1) and that each
 // element in the input range is greater or equal to the element at __first - 1.
 template <class _AlgPolicy, class _Compare, class _RandomAccessIterator>
 _LIBCPP_HIDE_FROM_ABI void
 __insertion_sort_unguarded(_RandomAccessIterator const __first, _RandomAccessIterator __last, _Compare __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
   if (__first == __last)
     return;
   const _RandomAccessIterator __leftmost = __first - difference_type(1);
   (void)__leftmost; // can be unused when assertions are disabled
   for (_RandomAccessIterator __i = __first + difference_type(1); __i != __last; ++__i) {
     _RandomAccessIterator __j = __i - difference_type(1);
     if (__comp(*__i, *__j)) {
       value_type __t(_Ops::__iter_move(__i));
       _RandomAccessIterator __k = __j;
       __j                       = __i;
       do {
         *__j = _Ops::__iter_move(__k);
         __j  = __k;
         _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
             __k != __leftmost,
             "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       } while (__comp(__t, *--__k)); // No need for bounds check due to the assumption stated above.
       *__j = std::move(__t);
     }
   }
 }
 
 template <class _AlgPolicy, class _Comp, class _RandomAccessIterator>
 _LIBCPP_HIDE_FROM_ABI bool
 __insertion_sort_incomplete(_RandomAccessIterator __first, _RandomAccessIterator __last, _Comp __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
 
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   switch (__last - __first) {
   case 0:
   case 1:
     return true;
   case 2:
     if (__comp(*--__last, *__first))
       _Ops::iter_swap(__first, __last);
     return true;
   case 3:
     std::__sort3_maybe_branchless<_AlgPolicy, _Comp>(__first, __first + difference_type(1), --__last, __comp);
     return true;
   case 4:
     std::__sort4_maybe_branchless<_AlgPolicy, _Comp>(
         __first, __first + difference_type(1), __first + difference_type(2), --__last, __comp);
     return true;
   case 5:
     std::__sort5_maybe_branchless<_AlgPolicy, _Comp>(
         __first,
         __first + difference_type(1),
         __first + difference_type(2),
         __first + difference_type(3),
         --__last,
         __comp);
     return true;
   }
   typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
   _RandomAccessIterator __j = __first + difference_type(2);
   std::__sort3_maybe_branchless<_AlgPolicy, _Comp>(__first, __first + difference_type(1), __j, __comp);
   const unsigned __limit = 8;
   unsigned __count       = 0;
   for (_RandomAccessIterator __i = __j + difference_type(1); __i != __last; ++__i) {
     if (__comp(*__i, *__j)) {
       value_type __t(_Ops::__iter_move(__i));
       _RandomAccessIterator __k = __j;
       __j                       = __i;
       do {
         *__j = _Ops::__iter_move(__k);
         __j  = __k;
       } while (__j != __first && __comp(__t, *--__k));
       *__j = std::move(__t);
       if (++__count == __limit)
         return ++__i == __last;
     }
     __j = __i;
   }
   return true;
 }
 
 template <class _AlgPolicy, class _RandomAccessIterator>
 inline _LIBCPP_HIDE_FROM_ABI void __swap_bitmap_pos(
     _RandomAccessIterator __first, _RandomAccessIterator __last, uint64_t& __left_bitset, uint64_t& __right_bitset) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename std::iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   // Swap one pair on each iteration as long as both bitsets have at least one
   // element for swapping.
   while (__left_bitset != 0 && __right_bitset != 0) {
     difference_type __tz_left  = __libcpp_ctz(__left_bitset);
     __left_bitset              = __libcpp_blsr(__left_bitset);
     difference_type __tz_right = __libcpp_ctz(__right_bitset);
     __right_bitset             = __libcpp_blsr(__right_bitset);
     _Ops::iter_swap(__first + __tz_left, __last - __tz_right);
   }
 }
 
 template <class _Compare,
           class _RandomAccessIterator,
           class _ValueType = typename iterator_traits<_RandomAccessIterator>::value_type>
 inline _LIBCPP_HIDE_FROM_ABI void
 __populate_left_bitset(_RandomAccessIterator __first, _Compare __comp, _ValueType& __pivot, uint64_t& __left_bitset) {
   // Possible vectorization. With a proper "-march" flag, the following loop
   // will be compiled into a set of SIMD instructions.
   _RandomAccessIterator __iter = __first;
   for (int __j = 0; __j < __detail::__block_size;) {
     bool __comp_result = !__comp(*__iter, __pivot);
     __left_bitset |= (static_cast<uint64_t>(__comp_result) << __j);
     __j++;
     ++__iter;
   }
 }
 
 template <class _Compare,
           class _RandomAccessIterator,
           class _ValueType = typename iterator_traits<_RandomAccessIterator>::value_type>
 inline _LIBCPP_HIDE_FROM_ABI void
 __populate_right_bitset(_RandomAccessIterator __lm1, _Compare __comp, _ValueType& __pivot, uint64_t& __right_bitset) {
   // Possible vectorization. With a proper "-march" flag, the following loop
   // will be compiled into a set of SIMD instructions.
   _RandomAccessIterator __iter = __lm1;
   for (int __j = 0; __j < __detail::__block_size;) {
     bool __comp_result = __comp(*__iter, __pivot);
     __right_bitset |= (static_cast<uint64_t>(__comp_result) << __j);
     __j++;
     --__iter;
   }
 }
 
 template <class _AlgPolicy,
           class _Compare,
           class _RandomAccessIterator,
           class _ValueType = typename iterator_traits<_RandomAccessIterator>::value_type>
 inline _LIBCPP_HIDE_FROM_ABI void __bitset_partition_partial_blocks(
     _RandomAccessIterator& __first,
     _RandomAccessIterator& __lm1,
     _Compare __comp,
     _ValueType& __pivot,
     uint64_t& __left_bitset,
     uint64_t& __right_bitset) {
   typedef typename std::iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   difference_type __remaining_len = __lm1 - __first + 1;
   difference_type __l_size;
   difference_type __r_size;
   if (__left_bitset == 0 && __right_bitset == 0) {
     __l_size = __remaining_len / 2;
     __r_size = __remaining_len - __l_size;
   } else if (__left_bitset == 0) {
     // We know at least one side is a full block.
     __l_size = __remaining_len - __detail::__block_size;
     __r_size = __detail::__block_size;
   } else { // if (__right_bitset == 0)
     __l_size = __detail::__block_size;
     __r_size = __remaining_len - __detail::__block_size;
   }
   // Record the comparison outcomes for the elements currently on the left side.
   if (__left_bitset == 0) {
     _RandomAccessIterator __iter = __first;
     for (int __j = 0; __j < __l_size; __j++) {
       bool __comp_result = !__comp(*__iter, __pivot);
       __left_bitset |= (static_cast<uint64_t>(__comp_result) << __j);
       ++__iter;
     }
   }
   // Record the comparison outcomes for the elements currently on the right
   // side.
   if (__right_bitset == 0) {
     _RandomAccessIterator __iter = __lm1;
     for (int __j = 0; __j < __r_size; __j++) {
       bool __comp_result = __comp(*__iter, __pivot);
       __right_bitset |= (static_cast<uint64_t>(__comp_result) << __j);
       --__iter;
     }
   }
   std::__swap_bitmap_pos<_AlgPolicy, _RandomAccessIterator>(__first, __lm1, __left_bitset, __right_bitset);
   __first += (__left_bitset == 0) ? __l_size : 0;
   __lm1 -= (__right_bitset == 0) ? __r_size : 0;
 }
 
 template <class _AlgPolicy, class _RandomAccessIterator>
 inline _LIBCPP_HIDE_FROM_ABI void __swap_bitmap_pos_within(
     _RandomAccessIterator& __first, _RandomAccessIterator& __lm1, uint64_t& __left_bitset, uint64_t& __right_bitset) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename std::iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   if (__left_bitset) {
     // Swap within the left side.  Need to find set positions in the reverse
     // order.
     while (__left_bitset != 0) {
       difference_type __tz_left = __detail::__block_size - 1 - __libcpp_clz(__left_bitset);
       __left_bitset &= (static_cast<uint64_t>(1) << __tz_left) - 1;
       _RandomAccessIterator __it = __first + __tz_left;
       if (__it != __lm1) {
         _Ops::iter_swap(__it, __lm1);
       }
       --__lm1;
     }
     __first = __lm1 + difference_type(1);
   } else if (__right_bitset) {
     // Swap within the right side.  Need to find set positions in the reverse
     // order.
     while (__right_bitset != 0) {
       difference_type __tz_right = __detail::__block_size - 1 - __libcpp_clz(__right_bitset);
       __right_bitset &= (static_cast<uint64_t>(1) << __tz_right) - 1;
       _RandomAccessIterator __it = __lm1 - __tz_right;
       if (__it != __first) {
         _Ops::iter_swap(__it, __first);
       }
       ++__first;
     }
   }
 }
 
 // Partition [__first, __last) using the comparator __comp.  *__first has the
 // chosen pivot.  Elements that are equivalent are kept to the left of the
 // pivot.  Returns the iterator for the pivot and a bool value which is true if
 // the provided range is already sorted, false otherwise.  We assume that the
 // length of the range is at least three elements.
 //
 // __bitset_partition uses bitsets for storing outcomes of the comparisons
 // between the pivot and other elements.
 template <class _AlgPolicy, class _RandomAccessIterator, class _Compare>
 _LIBCPP_HIDE_FROM_ABI std::pair<_RandomAccessIterator, bool>
 __bitset_partition(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename std::iterator_traits<_RandomAccessIterator>::value_type value_type;
   typedef typename std::iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   _LIBCPP_ASSERT_INTERNAL(__last - __first >= difference_type(3), "");
   const _RandomAccessIterator __begin = __first; // used for bounds checking, those are not moved around
   const _RandomAccessIterator __end   = __last;
   (void)__end; //
 
   value_type __pivot(_Ops::__iter_move(__first));
   // Find the first element greater than the pivot.
   if (__comp(__pivot, *(__last - difference_type(1)))) {
     // Not guarded since we know the last element is greater than the pivot.
     do {
       ++__first;
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __first != __end,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
     } while (!__comp(__pivot, *__first));
   } else {
     while (++__first < __last && !__comp(__pivot, *__first)) {
     }
   }
   // Find the last element less than or equal to the pivot.
   if (__first < __last) {
     // It will be always guarded because __introsort will do the median-of-three
     // before calling this.
     do {
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __last != __begin,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       --__last;
     } while (__comp(__pivot, *__last));
   }
   // If the first element greater than the pivot is at or after the
   // last element less than or equal to the pivot, then we have covered the
   // entire range without swapping elements.  This implies the range is already
   // partitioned.
   bool __already_partitioned = __first >= __last;
   if (!__already_partitioned) {
     _Ops::iter_swap(__first, __last);
     ++__first;
   }
 
   // In [__first, __last) __last is not inclusive. From now on, it uses last
   // minus one to be inclusive on both sides.
   _RandomAccessIterator __lm1 = __last - difference_type(1);
   uint64_t __left_bitset      = 0;
   uint64_t __right_bitset     = 0;
 
   // Reminder: length = __lm1 - __first + 1.
   while (__lm1 - __first >= 2 * __detail::__block_size - 1) {
     // Record the comparison outcomes for the elements currently on the left
     // side.
     if (__left_bitset == 0)
       std::__populate_left_bitset<_Compare>(__first, __comp, __pivot, __left_bitset);
     // Record the comparison outcomes for the elements currently on the right
     // side.
     if (__right_bitset == 0)
       std::__populate_right_bitset<_Compare>(__lm1, __comp, __pivot, __right_bitset);
     // Swap the elements recorded to be the candidates for swapping in the
     // bitsets.
     std::__swap_bitmap_pos<_AlgPolicy, _RandomAccessIterator>(__first, __lm1, __left_bitset, __right_bitset);
     // Only advance the iterator if all the elements that need to be moved to
     // other side were moved.
     __first += (__left_bitset == 0) ? difference_type(__detail::__block_size) : difference_type(0);
     __lm1 -= (__right_bitset == 0) ? difference_type(__detail::__block_size) : difference_type(0);
   }
   // Now, we have a less-than a block worth of elements on at least one of the
   // sides.
   std::__bitset_partition_partial_blocks<_AlgPolicy, _Compare>(
       __first, __lm1, __comp, __pivot, __left_bitset, __right_bitset);
   // At least one the bitsets would be empty.  For the non-empty one, we need to
   // properly partition the elements that appear within that bitset.
   std::__swap_bitmap_pos_within<_AlgPolicy>(__first, __lm1, __left_bitset, __right_bitset);
 
   // Move the pivot to its correct position.
   _RandomAccessIterator __pivot_pos = __first - difference_type(1);
   if (__begin != __pivot_pos) {
     *__begin = _Ops::__iter_move(__pivot_pos);
   }
   *__pivot_pos = std::move(__pivot);
   return std::make_pair(__pivot_pos, __already_partitioned);
 }
 
 // Partition [__first, __last) using the comparator __comp.  *__first has the
 // chosen pivot.  Elements that are equivalent are kept to the right of the
 // pivot.  Returns the iterator for the pivot and a bool value which is true if
 // the provided range is already sorted, false otherwise.  We assume that the
 // length of the range is at least three elements.
 template <class _AlgPolicy, class _RandomAccessIterator, class _Compare>
 _LIBCPP_HIDE_FROM_ABI std::pair<_RandomAccessIterator, bool>
 __partition_with_equals_on_right(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   typedef typename std::iterator_traits<_RandomAccessIterator>::value_type value_type;
   _LIBCPP_ASSERT_INTERNAL(__last - __first >= difference_type(3), "");
   const _RandomAccessIterator __begin = __first; // used for bounds checking, those are not moved around
   const _RandomAccessIterator __end   = __last;
   (void)__end; //
   value_type __pivot(_Ops::__iter_move(__first));
   // Find the first element greater or equal to the pivot.  It will be always
   // guarded because __introsort will do the median-of-three before calling
   // this.
   do {
     ++__first;
     _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
         __first != __end,
         "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
   } while (__comp(*__first, __pivot));
 
   // Find the last element less than the pivot.
   if (__begin == __first - difference_type(1)) {
     while (__first < __last && !__comp(*--__last, __pivot))
       ;
   } else {
     // Guarded.
     do {
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __last != __begin,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       --__last;
     } while (!__comp(*__last, __pivot));
   }
 
   // If the first element greater than or equal to the pivot is at or after the
   // last element less than the pivot, then we have covered the entire range
   // without swapping elements.  This implies the range is already partitioned.
   bool __already_partitioned = __first >= __last;
   // Go through the remaining elements.  Swap pairs of elements (one to the
   // right of the pivot and the other to left of the pivot) that are not on the
   // correct side of the pivot.
   while (__first < __last) {
     _Ops::iter_swap(__first, __last);
     do {
       ++__first;
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __first != __end,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
     } while (__comp(*__first, __pivot));
     do {
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __last != __begin,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       --__last;
     } while (!__comp(*__last, __pivot));
   }
   // Move the pivot to its correct position.
   _RandomAccessIterator __pivot_pos = __first - difference_type(1);
   if (__begin != __pivot_pos) {
     *__begin = _Ops::__iter_move(__pivot_pos);
   }
   *__pivot_pos = std::move(__pivot);
   return std::make_pair(__pivot_pos, __already_partitioned);
 }
 
 // Similar to the above function.  Elements equivalent to the pivot are put to
 // the left of the pivot.  Returns the iterator to the pivot element.
 template <class _AlgPolicy, class _RandomAccessIterator, class _Compare>
 _LIBCPP_HIDE_FROM_ABI _RandomAccessIterator
 __partition_with_equals_on_left(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   typedef typename std::iterator_traits<_RandomAccessIterator>::value_type value_type;
   const _RandomAccessIterator __begin = __first; // used for bounds checking, those are not moved around
   const _RandomAccessIterator __end   = __last;
   (void)__end; //
   value_type __pivot(_Ops::__iter_move(__first));
   if (__comp(__pivot, *(__last - difference_type(1)))) {
     // Guarded.
     do {
       ++__first;
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __first != __end,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
     } while (!__comp(__pivot, *__first));
   } else {
     while (++__first < __last && !__comp(__pivot, *__first)) {
     }
   }
 
   if (__first < __last) {
     // It will be always guarded because __introsort will do the
     // median-of-three before calling this.
     do {
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __last != __begin,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       --__last;
     } while (__comp(__pivot, *__last));
   }
   while (__first < __last) {
     _Ops::iter_swap(__first, __last);
     do {
       ++__first;
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __first != __end,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
     } while (!__comp(__pivot, *__first));
     do {
       _LIBCPP_ASSERT_VALID_ELEMENT_ACCESS(
           __last != __begin,
           "Would read out of bounds, does your comparator satisfy the strict-weak ordering requirement?");
       --__last;
     } while (__comp(__pivot, *__last));
   }
   _RandomAccessIterator __pivot_pos = __first - difference_type(1);
   if (__begin != __pivot_pos) {
     *__begin = _Ops::__iter_move(__pivot_pos);
   }
   *__pivot_pos = std::move(__pivot);
   return __first;
 }
 
 // The main sorting function.  Implements introsort combined with other ideas:
 //  - option of using block quick sort for partitioning,
 //  - guarded and unguarded insertion sort for small lengths,
 //  - Tuckey's ninther technique for computing the pivot,
 //  - check on whether partition was not required.
 // The implementation is partly based on Orson Peters' pattern-defeating
 // quicksort, published at: <https://github.com/orlp/pdqsort>.
 template <class _AlgPolicy, class _Compare, class _RandomAccessIterator, bool _UseBitSetPartition>
 void __introsort(_RandomAccessIterator __first,
                  _RandomAccessIterator __last,
                  _Compare __comp,
                  typename iterator_traits<_RandomAccessIterator>::difference_type __depth,
                  bool __leftmost = true) {
   using _Ops = _IterOps<_AlgPolicy>;
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   using _Comp_ref = __comp_ref_type<_Compare>;
   // Upper bound for using insertion sort for sorting.
   _LIBCPP_CONSTEXPR difference_type __limit = 24;
   // Lower bound for using Tuckey's ninther technique for median computation.
   _LIBCPP_CONSTEXPR difference_type __ninther_threshold = 128;
   while (true) {
     difference_type __len = __last - __first;
     switch (__len) {
     case 0:
     case 1:
       return;
     case 2:
       if (__comp(*--__last, *__first))
         _Ops::iter_swap(__first, __last);
       return;
     case 3:
       std::__sort3_maybe_branchless<_AlgPolicy, _Compare>(__first, __first + difference_type(1), --__last, __comp);
       return;
     case 4:
       std::__sort4_maybe_branchless<_AlgPolicy, _Compare>(
           __first, __first + difference_type(1), __first + difference_type(2), --__last, __comp);
       return;
     case 5:
       std::__sort5_maybe_branchless<_AlgPolicy, _Compare>(
           __first,
           __first + difference_type(1),
           __first + difference_type(2),
           __first + difference_type(3),
           --__last,
           __comp);
       return;
     }
     // Use insertion sort if the length of the range is below the specified limit.
     if (__len < __limit) {
       if (__leftmost) {
         std::__insertion_sort<_AlgPolicy, _Compare>(__first, __last, __comp);
       } else {
         std::__insertion_sort_unguarded<_AlgPolicy, _Compare>(__first, __last, __comp);
       }
       return;
     }
     if (__depth == 0) {
       // Fallback to heap sort as Introsort suggests.
       std::__partial_sort<_AlgPolicy, _Compare>(__first, __last, __last, __comp);
       return;
     }
     --__depth;
     {
       difference_type __half_len = __len / 2;
       // Use Tuckey's ninther technique or median of 3 for pivot selection
       // depending on the length of the range being sorted.
       if (__len > __ninther_threshold) {
         std::__sort3<_AlgPolicy, _Compare>(__first, __first + __half_len, __last - difference_type(1), __comp);
         std::__sort3<_AlgPolicy, _Compare>(
             __first + difference_type(1), __first + (__half_len - 1), __last - difference_type(2), __comp);
         std::__sort3<_AlgPolicy, _Compare>(
             __first + difference_type(2), __first + (__half_len + 1), __last - difference_type(3), __comp);
         std::__sort3<_AlgPolicy, _Compare>(
             __first + (__half_len - 1), __first + __half_len, __first + (__half_len + 1), __comp);
         _Ops::iter_swap(__first, __first + __half_len);
       } else {
         std::__sort3<_AlgPolicy, _Compare>(__first + __half_len, __first, __last - difference_type(1), __comp);
       }
     }
     // The elements to the left of the current iterator range are already
     // sorted.  If the current iterator range to be sorted is not the
     // leftmost part of the entire iterator range and the pivot is same as
     // the highest element in the range to the left, then we know that all
     // the elements in the range [first, pivot] would be equal to the pivot,
     // assuming the equal elements are put on the left side when
     // partitioned.  This also means that we do not need to sort the left
     // side of the partition.
     if (!__leftmost && !__comp(*(__first - difference_type(1)), *__first)) {
       __first = std::__partition_with_equals_on_left<_AlgPolicy, _RandomAccessIterator, _Comp_ref>(
           __first, __last, _Comp_ref(__comp));
       continue;
     }
     // Use bitset partition only if asked for.
     auto __ret                = _UseBitSetPartition
                                   ? std::__bitset_partition<_AlgPolicy, _RandomAccessIterator, _Compare>(__first, __last, __comp)
                                   : std::__partition_with_equals_on_right<_AlgPolicy, _RandomAccessIterator, _Compare>(
                          __first, __last, __comp);
     _RandomAccessIterator __i = __ret.first;
     // [__first, __i) < *__i and *__i <= [__i+1, __last)
     // If we were given a perfect partition, see if insertion sort is quick...
     if (__ret.second) {
       bool __fs = std::__insertion_sort_incomplete<_AlgPolicy, _Compare>(__first, __i, __comp);
       if (std::__insertion_sort_incomplete<_AlgPolicy, _Compare>(__i + difference_type(1), __last, __comp)) {
         if (__fs)
           return;
         __last = __i;
         continue;
       } else {
         if (__fs) {
           __first = ++__i;
           continue;
         }
       }
     }
     // Sort the left partiton recursively and the right partition with tail recursion elimination.
     std::__introsort<_AlgPolicy, _Compare, _RandomAccessIterator, _UseBitSetPartition>(
         __first, __i, __comp, __depth, __leftmost);
     __leftmost = false;
     __first    = ++__i;
   }
 }
 
 template <typename _Number>
 inline _LIBCPP_HIDE_FROM_ABI _Number __log2i(_Number __n) {
   if (__n == 0)
     return 0;
   if (sizeof(__n) <= sizeof(unsigned))
     return sizeof(unsigned) * CHAR_BIT - 1 - __libcpp_clz(static_cast<unsigned>(__n));
   if (sizeof(__n) <= sizeof(unsigned long))
     return sizeof(unsigned long) * CHAR_BIT - 1 - __libcpp_clz(static_cast<unsigned long>(__n));
   if (sizeof(__n) <= sizeof(unsigned long long))
     return sizeof(unsigned long long) * CHAR_BIT - 1 - __libcpp_clz(static_cast<unsigned long long>(__n));
 
   _Number __log2 = 0;
   while (__n > 1) {
     __log2++;
     __n >>= 1;
   }
   return __log2;
 }
 
 template <class _Comp, class _RandomAccessIterator>
 void __sort(_RandomAccessIterator, _RandomAccessIterator, _Comp);
 
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<char>&, char*>(char*, char*, __less<char>&);
 #ifndef _LIBCPP_HAS_NO_WIDE_CHARACTERS
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<wchar_t>&, wchar_t*>(wchar_t*, wchar_t*, __less<wchar_t>&);
 #endif
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<signed char>&, signed char*>(signed char*, signed char*, __less<signed char>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<unsigned char>&, unsigned char*>(unsigned char*, unsigned char*, __less<unsigned char>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<short>&, short*>(short*, short*, __less<short>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<unsigned short>&, unsigned short*>(unsigned short*, unsigned short*, __less<unsigned short>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<int>&, int*>(int*, int*, __less<int>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<unsigned>&, unsigned*>(unsigned*, unsigned*, __less<unsigned>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<long>&, long*>(long*, long*, __less<long>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<unsigned long>&, unsigned long*>(unsigned long*, unsigned long*, __less<unsigned long>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<long long>&, long long*>(long long*, long long*, __less<long long>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<unsigned long long>&, unsigned long long*>(
     unsigned long long*, unsigned long long*, __less<unsigned long long>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<float>&, float*>(float*, float*, __less<float>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void __sort<__less<double>&, double*>(double*, double*, __less<double>&);
 extern template _LIBCPP_EXPORTED_FROM_ABI void
 __sort<__less<long double>&, long double*>(long double*, long double*, __less<long double>&);
 
 template <class _AlgPolicy, class _RandomAccessIterator, class _Comp>
 _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void
 __sort_dispatch(_RandomAccessIterator __first, _RandomAccessIterator __last, _Comp& __comp) {
   typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
   difference_type __depth_limit = 2 * std::__log2i(__last - __first);
 
   // Only use bitset partitioning for arithmetic types.  We should also check
   // that the default comparator is in use so that we are sure that there are no
   // branches in the comparator.
   std::__introsort<_AlgPolicy,
                    _Comp&,
                    _RandomAccessIterator,
                    __use_branchless_sort<_Comp, _RandomAccessIterator>::value>(__first, __last, __comp, __depth_limit);
 }
 
 template <class _Type, class... _Options>
 using __is_any_of = _Or<is_same<_Type, _Options>...>;
 
 template <class _Type>
 using __sort_is_specialized_in_library = __is_any_of<
     _Type,
     char,
 #ifndef _LIBCPP_HAS_NO_WIDE_CHARACTERS
     wchar_t,
 #endif
     signed char,
     unsigned char,
     short,
     unsigned short,
     int,
     unsigned int,
     long,
     unsigned long,
     long long,
     unsigned long long,
     float,
     double,
     long double>;
 
 template <class _AlgPolicy, class _Type, __enable_if_t<__sort_is_specialized_in_library<_Type>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI void __sort_dispatch(_Type* __first, _Type* __last, __less<>&) {
   __less<_Type> __comp;
   std::__sort<__less<_Type>&, _Type*>(__first, __last, __comp);
 }
 
 template <class _AlgPolicy, class _Type, __enable_if_t<__sort_is_specialized_in_library<_Type>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI void __sort_dispatch(_Type* __first, _Type* __last, less<_Type>&) {
   __less<_Type> __comp;
   std::__sort<__less<_Type>&, _Type*>(__first, __last, __comp);
 }
 
 #if _LIBCPP_STD_VER >= 14
 template <class _AlgPolicy, class _Type, __enable_if_t<__sort_is_specialized_in_library<_Type>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI void __sort_dispatch(_Type* __first, _Type* __last, less<>&) {
   __less<_Type> __comp;
   std::__sort<__less<_Type>&, _Type*>(__first, __last, __comp);
 }
 #endif
 
 #if _LIBCPP_STD_VER >= 20
 template <class _AlgPolicy, class _Type, __enable_if_t<__sort_is_specialized_in_library<_Type>::value, int> = 0>
 _LIBCPP_HIDE_FROM_ABI void __sort_dispatch(_Type* __first, _Type* __last, ranges::less&) {
   __less<_Type> __comp;
   std::__sort<__less<_Type>&, _Type*>(__first, __last, __comp);
 }
 #endif
 
 template <class _AlgPolicy, class _RandomAccessIterator, class _Comp>
 inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void
 __sort_impl(_RandomAccessIterator __first, _RandomAccessIterator __last, _Comp& __comp) {
   std::__debug_randomize_range<_AlgPolicy>(__first, __last);
 
   if (__libcpp_is_constant_evaluated()) {
     std::__partial_sort<_AlgPolicy>(
         std::__unwrap_iter(__first), std::__unwrap_iter(__last), std::__unwrap_iter(__last), __comp);
   } else {
     std::__sort_dispatch<_AlgPolicy>(std::__unwrap_iter(__first), std::__unwrap_iter(__last), __comp);
   }
   std::__check_strict_weak_ordering_sorted(std::__unwrap_iter(__first), std::__unwrap_iter(__last), __comp);
 }
 
 template <class _RandomAccessIterator, class _Comp>
 inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void
 sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Comp __comp) {
   std::__sort_impl<_ClassicAlgPolicy>(std::move(__first), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
 inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 void
 sort(_RandomAccessIterator __first, _RandomAccessIterator __last) {
   std::sort(__first, __last, __less<>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
 
 _LIBCPP_POP_MACROS
 
 #endif // _LIBCPP___CXX03___ALGORITHM_SORT_H

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