// -*- C++ -*-
//===-------------------------- compare -----------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_COMPARE
#define _LIBCPP_COMPARE

/*
    compare synopsis

namespace std {
  // [cmp.categories], comparison category types
  class weak_equality;
  class strong_equality;
  class partial_ordering;
  class weak_ordering;
  class strong_ordering;

  // named comparison functions
  constexpr bool is_eq  (weak_equality cmp) noexcept    { return cmp == 0; }
  constexpr bool is_neq (weak_equality cmp) noexcept    { return cmp != 0; }
  constexpr bool is_lt  (partial_ordering cmp) noexcept { return cmp < 0; }
  constexpr bool is_lteq(partial_ordering cmp) noexcept { return cmp <= 0; }
  constexpr bool is_gt  (partial_ordering cmp) noexcept { return cmp > 0; }
  constexpr bool is_gteq(partial_ordering cmp) noexcept { return cmp >= 0; }

  // [cmp.common], common comparison category type
  template<class... Ts>
  struct common_comparison_category {
    using type = see below;
  };
  template<class... Ts>
    using common_comparison_category_t = typename common_comparison_category<Ts...>::type;

  // [cmp.alg], comparison algorithms
  template<class T> constexpr strong_ordering strong_order(const T& a, const T& b);
  template<class T> constexpr weak_ordering weak_order(const T& a, const T& b);
  template<class T> constexpr partial_ordering partial_order(const T& a, const T& b);
  template<class T> constexpr strong_equality strong_equal(const T& a, const T& b);
  template<class T> constexpr weak_equality weak_equal(const T& a, const T& b);
}
*/

#include <__config>
#include <type_traits>
#include <array>

#ifndef _LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER
#pragma GCC system_header
#endif

_LIBCPP_BEGIN_NAMESPACE_STD

#if _LIBCPP_STD_VER > 17

// exposition only
enum class _LIBCPP_ENUM_VIS _EqResult : unsigned char {
  __zero = 0,
  __equal = __zero,
  __equiv = __equal,
  __nonequal = 1,
  __nonequiv = __nonequal
};

enum class _LIBCPP_ENUM_VIS _OrdResult : signed char {
  __less = -1,
  __greater = 1
};

enum class _LIBCPP_ENUM_VIS _NCmpResult : signed char {
  __unordered = -127
};

struct _CmpUnspecifiedType;
using _CmpUnspecifiedParam = void (_CmpUnspecifiedType::*)();

class  weak_equality {
  _LIBCPP_INLINE_VISIBILITY
  constexpr explicit weak_equality(_EqResult __val) noexcept : __value_(__val) {}

public:
  static const weak_equality equivalent;
  static const weak_equality nonequivalent;

  friend constexpr bool operator==(weak_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator==(_CmpUnspecifiedParam, weak_equality __v) noexcept;
  friend constexpr bool operator!=(weak_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator!=(_CmpUnspecifiedParam, weak_equality __v) noexcept;

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
  friend constexpr weak_equality operator<=>(weak_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr weak_equality operator<=>(_CmpUnspecifiedParam, weak_equality __v) noexcept;
#endif

private:
  _EqResult __value_;
};

_LIBCPP_INLINE_VAR constexpr weak_equality weak_equality::equivalent(_EqResult::__equiv);
_LIBCPP_INLINE_VAR constexpr weak_equality weak_equality::nonequivalent(_EqResult::__nonequiv);

_LIBCPP_INLINE_VISIBILITY
inline constexpr bool operator==(weak_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ == _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
inline constexpr bool operator==(_CmpUnspecifiedParam, weak_equality __v) noexcept {
  return __v.__value_ == _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
inline constexpr bool operator!=(weak_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ != _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
inline constexpr bool operator!=(_CmpUnspecifiedParam, weak_equality __v) noexcept {
  return __v.__value_ != _EqResult::__zero;
}

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
_LIBCPP_INLINE_VISIBILITY
inline constexpr weak_equality operator<=>(weak_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v;
}

_LIBCPP_INLINE_VISIBILITY
inline constexpr weak_equality operator<=>(_CmpUnspecifiedParam, weak_equality __v) noexcept {
  return __v;
}
#endif

class strong_equality {
  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr strong_equality(_EqResult __val) noexcept : __value_(__val) {}

public:
  static const strong_equality equal;
  static const strong_equality nonequal;
  static const strong_equality equivalent;
  static const strong_equality nonequivalent;

  // conversion
  constexpr operator weak_equality() const noexcept {
    return __value_ == _EqResult::__zero ? weak_equality::equivalent
          : weak_equality::nonequivalent;
  }

  // comparisons
  friend constexpr bool operator==(strong_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator!=(strong_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator==(_CmpUnspecifiedParam, strong_equality __v) noexcept;
  friend constexpr bool operator!=(_CmpUnspecifiedParam, strong_equality __v) noexcept;

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
  friend constexpr strong_equality operator<=>(strong_equality __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr strong_equality operator<=>(_CmpUnspecifiedParam, strong_equality __v) noexcept;
#endif
private:
  _EqResult __value_;
};

_LIBCPP_INLINE_VAR constexpr strong_equality strong_equality::equal(_EqResult::__equal);
_LIBCPP_INLINE_VAR constexpr strong_equality strong_equality::nonequal(_EqResult::__nonequal);
_LIBCPP_INLINE_VAR constexpr strong_equality strong_equality::equivalent(_EqResult::__equiv);
_LIBCPP_INLINE_VAR constexpr strong_equality strong_equality::nonequivalent(_EqResult::__nonequiv);

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(strong_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ == _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(_CmpUnspecifiedParam, strong_equality __v) noexcept {
  return __v.__value_ == _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(strong_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ != _EqResult::__zero;
}

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(_CmpUnspecifiedParam, strong_equality __v) noexcept {
  return __v.__value_ != _EqResult::__zero;
}

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
_LIBCPP_INLINE_VISIBILITY
constexpr strong_equality operator<=>(strong_equality __v, _CmpUnspecifiedParam) noexcept {
  return __v;
}

_LIBCPP_INLINE_VISIBILITY
constexpr strong_equality operator<=>(_CmpUnspecifiedParam, strong_equality __v) noexcept {
  return __v;
}
#endif // _LIBCPP_HAS_NO_SPACESHIP_OPERATOR

class partial_ordering {
  using _ValueT = signed char;

  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr partial_ordering(_EqResult __v) noexcept
      : __value_(_ValueT(__v)) {}

  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr partial_ordering(_OrdResult __v) noexcept
      : __value_(_ValueT(__v)) {}

  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr partial_ordering(_NCmpResult __v) noexcept
      : __value_(_ValueT(__v)) {}

  constexpr bool __is_ordered() const noexcept {
    return __value_ != _ValueT(_NCmpResult::__unordered);
  }
public:
  // valid values
  static const partial_ordering less;
  static const partial_ordering equivalent;
  static const partial_ordering greater;
  static const partial_ordering unordered;

  // conversion
  constexpr operator weak_equality() const noexcept {
    return __value_ == 0 ? weak_equality::equivalent : weak_equality::nonequivalent;
  }

  // comparisons
  friend constexpr bool operator==(partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator!=(partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator< (partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator<=(partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator> (partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator>=(partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator==(_CmpUnspecifiedParam, partial_ordering __v) noexcept;
  friend constexpr bool operator!=(_CmpUnspecifiedParam, partial_ordering __v) noexcept;
  friend constexpr bool operator< (_CmpUnspecifiedParam, partial_ordering __v) noexcept;
  friend constexpr bool operator<=(_CmpUnspecifiedParam, partial_ordering __v) noexcept;
  friend constexpr bool operator> (_CmpUnspecifiedParam, partial_ordering __v) noexcept;
  friend constexpr bool operator>=(_CmpUnspecifiedParam, partial_ordering __v) noexcept;

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
  friend constexpr partial_ordering operator<=>(partial_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr partial_ordering operator<=>(_CmpUnspecifiedParam, partial_ordering __v) noexcept;
#endif

private:
  _ValueT __value_;
};

_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::less(_OrdResult::__less);
_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::equivalent(_EqResult::__equiv);
_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::greater(_OrdResult::__greater);
_LIBCPP_INLINE_VAR constexpr partial_ordering partial_ordering::unordered(_NCmpResult ::__unordered);

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__is_ordered() && __v.__value_ == 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__is_ordered() && __v.__value_ < 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__is_ordered() && __v.__value_ <= 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__is_ordered() && __v.__value_ > 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__is_ordered() && __v.__value_ >= 0;
}

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v.__is_ordered() && 0 == __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v.__is_ordered() && 0 < __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v.__is_ordered() && 0 <= __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v.__is_ordered() && 0 > __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v.__is_ordered() && 0 >= __v.__value_;
}

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return !__v.__is_ordered() || __v.__value_ != 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return !__v.__is_ordered() || __v.__value_ != 0;
}

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
_LIBCPP_INLINE_VISIBILITY
constexpr partial_ordering operator<=>(partial_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v;
}
_LIBCPP_INLINE_VISIBILITY
constexpr partial_ordering operator<=>(_CmpUnspecifiedParam, partial_ordering __v) noexcept {
  return __v < 0 ? partial_ordering::greater : (__v > 0 ? partial_ordering::less : __v);
}
#endif // _LIBCPP_HAS_NO_SPACESHIP_OPERATOR

class weak_ordering {
  using _ValueT = signed char;

  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr weak_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr weak_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}

public:
  static const weak_ordering less;
  static const weak_ordering equivalent;
  static const weak_ordering greater;

  // conversions
  _LIBCPP_INLINE_VISIBILITY
  constexpr operator weak_equality() const noexcept {
    return __value_ == 0 ? weak_equality::equivalent
                         : weak_equality::nonequivalent;
  }

  _LIBCPP_INLINE_VISIBILITY
  constexpr operator partial_ordering() const noexcept {
    return __value_ == 0 ? partial_ordering::equivalent
        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
  }

  // comparisons
  friend constexpr bool operator==(weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator!=(weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator< (weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator<=(weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator> (weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator>=(weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator==(_CmpUnspecifiedParam, weak_ordering __v) noexcept;
  friend constexpr bool operator!=(_CmpUnspecifiedParam, weak_ordering __v) noexcept;
  friend constexpr bool operator< (_CmpUnspecifiedParam, weak_ordering __v) noexcept;
  friend constexpr bool operator<=(_CmpUnspecifiedParam, weak_ordering __v) noexcept;
  friend constexpr bool operator> (_CmpUnspecifiedParam, weak_ordering __v) noexcept;
  friend constexpr bool operator>=(_CmpUnspecifiedParam, weak_ordering __v) noexcept;

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
  friend constexpr weak_ordering operator<=>(weak_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr weak_ordering operator<=>(_CmpUnspecifiedParam, weak_ordering __v) noexcept;
#endif

private:
  _ValueT __value_;
};

_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::less(_OrdResult::__less);
_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::equivalent(_EqResult::__equiv);
_LIBCPP_INLINE_VAR constexpr weak_ordering weak_ordering::greater(_OrdResult::__greater);

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ == 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ != 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ < 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ <= 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ > 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ >= 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 == __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 != __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 < __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 <= __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 > __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return 0 >= __v.__value_;
}

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
_LIBCPP_INLINE_VISIBILITY
constexpr weak_ordering operator<=>(weak_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v;
}
_LIBCPP_INLINE_VISIBILITY
constexpr weak_ordering operator<=>(_CmpUnspecifiedParam, weak_ordering __v) noexcept {
  return __v < 0 ? weak_ordering::greater : (__v > 0 ? weak_ordering::less : __v);
}
#endif // _LIBCPP_HAS_NO_SPACESHIP_OPERATOR

class strong_ordering {
  using _ValueT = signed char;

  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr strong_ordering(_EqResult __v) noexcept : __value_(_ValueT(__v)) {}
  _LIBCPP_INLINE_VISIBILITY
  explicit constexpr strong_ordering(_OrdResult __v) noexcept : __value_(_ValueT(__v)) {}

public:
  static const strong_ordering less;
  static const strong_ordering equal;
  static const strong_ordering equivalent;
  static const strong_ordering greater;

  // conversions
  _LIBCPP_INLINE_VISIBILITY
  constexpr operator weak_equality() const noexcept {
    return __value_ == 0 ? weak_equality::equivalent
                         : weak_equality::nonequivalent;
  }

  _LIBCPP_INLINE_VISIBILITY
  constexpr operator strong_equality() const noexcept {
    return __value_ == 0 ? strong_equality::equal
                         : strong_equality::nonequal;
  }

  _LIBCPP_INLINE_VISIBILITY
  constexpr operator partial_ordering() const noexcept {
    return __value_ == 0 ? partial_ordering::equivalent
        : (__value_ < 0 ? partial_ordering::less : partial_ordering::greater);
  }

  _LIBCPP_INLINE_VISIBILITY
  constexpr operator weak_ordering() const noexcept {
    return __value_ == 0 ? weak_ordering::equivalent
        : (__value_ < 0 ? weak_ordering::less : weak_ordering::greater);
  }

  // comparisons
  friend constexpr bool operator==(strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator!=(strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator< (strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator<=(strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator> (strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator>=(strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr bool operator==(_CmpUnspecifiedParam, strong_ordering __v) noexcept;
  friend constexpr bool operator!=(_CmpUnspecifiedParam, strong_ordering __v) noexcept;
  friend constexpr bool operator< (_CmpUnspecifiedParam, strong_ordering __v) noexcept;
  friend constexpr bool operator<=(_CmpUnspecifiedParam, strong_ordering __v) noexcept;
  friend constexpr bool operator> (_CmpUnspecifiedParam, strong_ordering __v) noexcept;
  friend constexpr bool operator>=(_CmpUnspecifiedParam, strong_ordering __v) noexcept;

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
  friend constexpr strong_ordering operator<=>(strong_ordering __v, _CmpUnspecifiedParam) noexcept;
  friend constexpr strong_ordering operator<=>(_CmpUnspecifiedParam, strong_ordering __v) noexcept;
#endif

private:
  _ValueT __value_;
};

_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::less(_OrdResult::__less);
_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equal(_EqResult::__equal);
_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::equivalent(_EqResult::__equiv);
_LIBCPP_INLINE_VAR constexpr strong_ordering strong_ordering::greater(_OrdResult::__greater);

_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ == 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ != 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ < 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ <= 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ > 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v.__value_ >= 0;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator==(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 == __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator!=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 != __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator< (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 < __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator<=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 <= __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator> (_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 > __v.__value_;
}
_LIBCPP_INLINE_VISIBILITY
constexpr bool operator>=(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return 0 >= __v.__value_;
}

#ifndef _LIBCPP_HAS_NO_SPACESHIP_OPERATOR
_LIBCPP_INLINE_VISIBILITY
constexpr strong_ordering operator<=>(strong_ordering __v, _CmpUnspecifiedParam) noexcept {
  return __v;
}
_LIBCPP_INLINE_VISIBILITY
constexpr strong_ordering operator<=>(_CmpUnspecifiedParam, strong_ordering __v) noexcept {
  return __v < 0 ? strong_ordering::greater : (__v > 0 ? strong_ordering::less : __v);
}
#endif // _LIBCPP_HAS_NO_SPACESHIP_OPERATOR

// named comparison functions
_LIBCPP_INLINE_VISIBILITY
constexpr bool is_eq(weak_equality __cmp) noexcept    { return __cmp == 0; }

_LIBCPP_INLINE_VISIBILITY
constexpr bool is_neq(weak_equality __cmp) noexcept    { return __cmp != 0; }

_LIBCPP_INLINE_VISIBILITY
constexpr bool is_lt(partial_ordering __cmp) noexcept { return __cmp < 0; }

_LIBCPP_INLINE_VISIBILITY
constexpr bool is_lteq(partial_ordering __cmp) noexcept { return __cmp <= 0; }

_LIBCPP_INLINE_VISIBILITY
constexpr bool is_gt(partial_ordering __cmp) noexcept { return __cmp > 0; }

_LIBCPP_INLINE_VISIBILITY
constexpr bool is_gteq(partial_ordering __cmp) noexcept { return __cmp >= 0; }

namespace __comp_detail {

enum _ClassifyCompCategory : unsigned{
  _None,
  _WeakEq,
  _StrongEq,
  _PartialOrd,
  _WeakOrd,
  _StrongOrd,
  _CCC_Size
};

template <class _Tp>
_LIBCPP_INLINE_VISIBILITY
constexpr _ClassifyCompCategory __type_to_enum() noexcept {
  if (is_same_v<_Tp, weak_equality>)
    return _WeakEq;
  if (is_same_v<_Tp, strong_equality>)
    return _StrongEq;
  if (is_same_v<_Tp, partial_ordering>)
    return _PartialOrd;
  if (is_same_v<_Tp, weak_ordering>)
    return _WeakOrd;
  if (is_same_v<_Tp, strong_ordering>)
    return _StrongOrd;
  return _None;
}

template <size_t _Size>
constexpr _ClassifyCompCategory
__compute_comp_type(std::array<_ClassifyCompCategory, _Size> __types) {
  std::array<int, _CCC_Size> __seen = {};
  for (auto __type : __types)
    ++__seen[__type];
  if (__seen[_None])
    return _None;
  if (__seen[_WeakEq])
    return _WeakEq;
  if (__seen[_StrongEq] && (__seen[_PartialOrd] || __seen[_WeakOrd]))
    return _WeakEq;
  if (__seen[_StrongEq])
    return _StrongEq;
  if (__seen[_PartialOrd])
    return _PartialOrd;
  if (__seen[_WeakOrd])
    return _WeakOrd;
  return _StrongOrd;
}

template <class ..._Ts>
constexpr auto __get_comp_type() {
  using _CCC = _ClassifyCompCategory;
  constexpr array<_CCC, sizeof...(_Ts)> __type_kinds{{__comp_detail::__type_to_enum<_Ts>()...}};
  constexpr _CCC _Cat = sizeof...(_Ts) == 0 ? _StrongOrd
      : __compute_comp_type(__type_kinds);
  if constexpr (_Cat == _None)
    return void();
  else if constexpr (_Cat == _WeakEq)
    return weak_equality::equivalent;
  else if constexpr (_Cat == _StrongEq)
    return strong_equality::equivalent;
  else if constexpr (_Cat == _PartialOrd)
    return partial_ordering::equivalent;
  else if constexpr (_Cat == _WeakOrd)
    return weak_ordering::equivalent;
  else if constexpr (_Cat == _StrongOrd)
    return strong_ordering::equivalent;
  else
    static_assert(_Cat != _Cat, "unhandled case");
}
} // namespace __comp_detail

// [cmp.common], common comparison category type
template<class... _Ts>
struct _LIBCPP_TEMPLATE_VIS common_comparison_category {
  using type = decltype(__comp_detail::__get_comp_type<_Ts...>());
};

template<class... _Ts>
using common_comparison_category_t = typename common_comparison_category<_Ts...>::type;

// [cmp.alg], comparison algorithms
// TODO: unimplemented
template<class _Tp> constexpr strong_ordering strong_order(const _Tp& __lhs, const _Tp& __rhs);
template<class _Tp> constexpr weak_ordering weak_order(const _Tp& __lhs, const _Tp& __rhs);
template<class _Tp> constexpr partial_ordering partial_order(const _Tp& __lhs, const _Tp& __rhs);
template<class _Tp> constexpr strong_equality strong_equal(const _Tp& __lhs, const _Tp& __rhs);
template<class _Tp> constexpr weak_equality weak_equal(const _Tp& __lhs, const _Tp& __rhs);

#endif // _LIBCPP_STD_VER > 17

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP_COMPARE