// C++11 <type_traits> -*- C++ -*-
	
	// Copyright (C) 2007-2019 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 include/type_traits
	 *  This is a Standard C++ Library header.
	 */
	
	#ifndef _GLIBCXX_TYPE_TRAITS
	#define _GLIBCXX_TYPE_TRAITS 1
	
	#pragma GCC system_header
	
	#if __cplusplus < 201103L
	# include <bits/c++0x_warning.h>
	#else
	
	#include <bits/c++config.h>
	
	namespace std _GLIBCXX_VISIBILITY(default)
	{
	_GLIBCXX_BEGIN_NAMESPACE_VERSION
	
	  /**
	   * @defgroup metaprogramming Metaprogramming
	   * @ingroup utilities
	   *
	   * Template utilities for compile-time introspection and modification,
	   * including type classification traits, type property inspection traits
	   * and type transformation traits.
	   *
	   * @{
	   */
	
	  /// integral_constant
	  template<typename _Tp, _Tp __v>
	    struct integral_constant
	    {
	      static constexpr _Tp                  value = __v;
	      typedef _Tp                           value_type;
	      typedef integral_constant<_Tp, __v>   type;
	      constexpr operator value_type() const noexcept { return value; }
	#if __cplusplus > 201103L
	
	#define __cpp_lib_integral_constant_callable 201304
	
	      constexpr value_type operator()() const noexcept { return value; }
	#endif
	    };
	
	  template<typename _Tp, _Tp __v>
	    constexpr _Tp integral_constant<_Tp, __v>::value;
	
	  /// The type used as a compile-time boolean with true value.
	  typedef integral_constant<bool, true>     true_type;
	
	  /// The type used as a compile-time boolean with false value.
	  typedef integral_constant<bool, false>    false_type;
	
	  template<bool __v>
	    using __bool_constant = integral_constant<bool, __v>;
	
	#if __cplusplus > 201402L
	# define __cpp_lib_bool_constant 201505
	  template<bool __v>
	    using bool_constant = integral_constant<bool, __v>;
	#endif
	
	  // Meta programming helper types.
	
	  template<bool, typename, typename>
	    struct conditional;
	
	  template<typename...>
	    struct __or_;
	
	  template<>
	    struct __or_<>
	    : public false_type
	    { };
	
	  template<typename _B1>
	    struct __or_<_B1>
	    : public _B1
	    { };
	
	  template<typename _B1, typename _B2>
	    struct __or_<_B1, _B2>
	    : public conditional<_B1::value, _B1, _B2>::type
	    { };
	
	  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
	    struct __or_<_B1, _B2, _B3, _Bn...>
	    : public conditional<_B1::value, _B1, __or_<_B2, _B3, _Bn...>>::type
	    { };
	
	  template<typename...>
	    struct __and_;
	
	  template<>
	    struct __and_<>
	    : public true_type
	    { };
	
	  template<typename _B1>
	    struct __and_<_B1>
	    : public _B1
	    { };
	
	  template<typename _B1, typename _B2>
	    struct __and_<_B1, _B2>
	    : public conditional<_B1::value, _B2, _B1>::type
	    { };
	
	  template<typename _B1, typename _B2, typename _B3, typename... _Bn>
	    struct __and_<_B1, _B2, _B3, _Bn...>
	    : public conditional<_B1::value, __and_<_B2, _B3, _Bn...>, _B1>::type
	    { };
	
	  template<typename _Pp>
	    struct __not_
	    : public __bool_constant<!bool(_Pp::value)>
	    { };
	
	#if __cplusplus >= 201703L
	
	  template<typename... _Bn>
	    inline constexpr bool __or_v = __or_<_Bn...>::value;
	  template<typename... _Bn>
	    inline constexpr bool __and_v = __and_<_Bn...>::value;
	
	#define __cpp_lib_logical_traits 201510
	
	  template<typename... _Bn>
	    struct conjunction
	    : __and_<_Bn...>
	    { };
	
	  template<typename... _Bn>
	    struct disjunction
	    : __or_<_Bn...>
	    { };
	
	  template<typename _Pp>
	    struct negation
	    : __not_<_Pp>
	    { };
	
	  template<typename... _Bn>
	    inline constexpr bool conjunction_v = conjunction<_Bn...>::value;
	
	  template<typename... _Bn>
	    inline constexpr bool disjunction_v = disjunction<_Bn...>::value;
	
	  template<typename _Pp>
	    inline constexpr bool negation_v = negation<_Pp>::value;
	
	#endif // C++17
	
	  // For several sfinae-friendly trait implementations we transport both the
	  // result information (as the member type) and the failure information (no
	  // member type). This is very similar to std::enable_if, but we cannot use
	  // them, because we need to derive from them as an implementation detail.
	
	  template<typename _Tp>
	    struct __success_type
	    { typedef _Tp type; };
	
	  struct __failure_type
	  { };
	
	  // Primary type categories.
	
	  template<typename>
	    struct remove_cv;
	
	  template<typename>
	    struct __is_void_helper
	    : public false_type { };
	
	  template<>
	    struct __is_void_helper<void>
	    : public true_type { };
	
	  /// is_void
	  template<typename _Tp>
	    struct is_void
	    : public __is_void_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  template<typename>
	    struct __is_integral_helper
	    : public false_type { };
	
	  template<>
	    struct __is_integral_helper<bool>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<char>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<signed char>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned char>
	    : public true_type { };
	
	#ifdef _GLIBCXX_USE_WCHAR_T
	  template<>
	    struct __is_integral_helper<wchar_t>
	    : public true_type { };
	#endif
	
	#ifdef _GLIBCXX_USE_CHAR8_T
	  template<>
	    struct __is_integral_helper<char8_t>
	    : public true_type { };
	#endif
	
	  template<>
	    struct __is_integral_helper<char16_t>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<char32_t>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<short>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned short>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<int>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned int>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<long>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned long>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<long long>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned long long>
	    : public true_type { };
	
	  // Conditionalizing on __STRICT_ANSI__ here will break any port that
	  // uses one of these types for size_t.
	#if defined(__GLIBCXX_TYPE_INT_N_0)
	  template<>
	    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_0>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_0>
	    : public true_type { };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_1)
	  template<>
	    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_1>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_1>
	    : public true_type { };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_2)
	  template<>
	    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_2>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_2>
	    : public true_type { };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_3)
	  template<>
	    struct __is_integral_helper<__GLIBCXX_TYPE_INT_N_3>
	    : public true_type { };
	
	  template<>
	    struct __is_integral_helper<unsigned __GLIBCXX_TYPE_INT_N_3>
	    : public true_type { };
	#endif
	
	  /// is_integral
	  template<typename _Tp>
	    struct is_integral
	    : public __is_integral_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  template<typename>
	    struct __is_floating_point_helper
	    : public false_type { };
	
	  template<>
	    struct __is_floating_point_helper<float>
	    : public true_type { };
	
	  template<>
	    struct __is_floating_point_helper<double>
	    : public true_type { };
	
	  template<>
	    struct __is_floating_point_helper<long double>
	    : public true_type { };
	
	#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_FLOAT128)
	  template<>
	    struct __is_floating_point_helper<__float128>
	    : public true_type { };
	#endif
	
	  /// is_floating_point
	  template<typename _Tp>
	    struct is_floating_point
	    : public __is_floating_point_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  /// is_array
	  template<typename>
	    struct is_array
	    : public false_type { };
	
	  template<typename _Tp, std::size_t _Size>
	    struct is_array<_Tp[_Size]>
	    : public true_type { };
	
	  template<typename _Tp>
	    struct is_array<_Tp[]>
	    : public true_type { };
	
	  template<typename>
	    struct __is_pointer_helper
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_pointer_helper<_Tp*>
	    : public true_type { };
	
	  /// is_pointer
	  template<typename _Tp>
	    struct is_pointer
	    : public __is_pointer_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  /// is_lvalue_reference
	  template<typename>
	    struct is_lvalue_reference
	    : public false_type { };
	
	  template<typename _Tp>
	    struct is_lvalue_reference<_Tp&>
	    : public true_type { };
	
	  /// is_rvalue_reference
	  template<typename>
	    struct is_rvalue_reference
	    : public false_type { };
	
	  template<typename _Tp>
	    struct is_rvalue_reference<_Tp&&>
	    : public true_type { };
	
	  template<typename>
	    struct is_function;
	
	  template<typename>
	    struct __is_member_object_pointer_helper
	    : public false_type { };
	
	  template<typename _Tp, typename _Cp>
	    struct __is_member_object_pointer_helper<_Tp _Cp::*>
	    : public __not_<is_function<_Tp>>::type { };
	
	  /// is_member_object_pointer
	  template<typename _Tp>
	    struct is_member_object_pointer
	    : public __is_member_object_pointer_helper<
					typename remove_cv<_Tp>::type>::type
	    { };
	
	  template<typename>
	    struct __is_member_function_pointer_helper
	    : public false_type { };
	
	  template<typename _Tp, typename _Cp>
	    struct __is_member_function_pointer_helper<_Tp _Cp::*>
	    : public is_function<_Tp>::type { };
	
	  /// is_member_function_pointer
	  template<typename _Tp>
	    struct is_member_function_pointer
	    : public __is_member_function_pointer_helper<
					typename remove_cv<_Tp>::type>::type
	    { };
	
	  /// is_enum
	  template<typename _Tp>
	    struct is_enum
	    : public integral_constant<bool, __is_enum(_Tp)>
	    { };
	
	  /// is_union
	  template<typename _Tp>
	    struct is_union
	    : public integral_constant<bool, __is_union(_Tp)>
	    { };
	
	  /// is_class
	  template<typename _Tp>
	    struct is_class
	    : public integral_constant<bool, __is_class(_Tp)>
	    { };
	
	  /// is_function
	  template<typename>
	    struct is_function
	    : public false_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) volatile _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) volatile & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) volatile && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) volatile _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) volatile & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) volatile && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const volatile _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const volatile & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes...) const volatile && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const volatile _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const volatile & _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	  template<typename _Res, typename... _ArgTypes _GLIBCXX_NOEXCEPT_PARM>
	    struct is_function<_Res(_ArgTypes......) const volatile && _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type { };
	
	#define __cpp_lib_is_null_pointer 201309
	
	  template<typename>
	    struct __is_null_pointer_helper
	    : public false_type { };
	
	  template<>
	    struct __is_null_pointer_helper<std::nullptr_t>
	    : public true_type { };
	
	  /// is_null_pointer (LWG 2247).
	  template<typename _Tp>
	    struct is_null_pointer
	    : public __is_null_pointer_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  /// __is_nullptr_t (extension).
	  template<typename _Tp>
	    struct __is_nullptr_t
	    : public is_null_pointer<_Tp>
	    { };
	
	  // Composite type categories.
	
	  /// is_reference
	  template<typename _Tp>
	    struct is_reference
	    : public __or_<is_lvalue_reference<_Tp>,
	                   is_rvalue_reference<_Tp>>::type
	    { };
	
	  /// is_arithmetic
	  template<typename _Tp>
	    struct is_arithmetic
	    : public __or_<is_integral<_Tp>, is_floating_point<_Tp>>::type
	    { };
	
	  /// is_fundamental
	  template<typename _Tp>
	    struct is_fundamental
	    : public __or_<is_arithmetic<_Tp>, is_void<_Tp>,
			   is_null_pointer<_Tp>>::type
	    { };
	
	  /// is_object
	  template<typename _Tp>
	    struct is_object
	    : public __not_<__or_<is_function<_Tp>, is_reference<_Tp>,
	                          is_void<_Tp>>>::type
	    { };
	
	  template<typename>
	    struct is_member_pointer;
	
	  /// is_scalar
	  template<typename _Tp>
	    struct is_scalar
	    : public __or_<is_arithmetic<_Tp>, is_enum<_Tp>, is_pointer<_Tp>,
	                   is_member_pointer<_Tp>, is_null_pointer<_Tp>>::type
	    { };
	
	  /// is_compound
	  template<typename _Tp>
	    struct is_compound
	    : public __not_<is_fundamental<_Tp>>::type { };
	
	  template<typename _Tp>
	    struct __is_member_pointer_helper
	    : public false_type { };
	
	  template<typename _Tp, typename _Cp>
	    struct __is_member_pointer_helper<_Tp _Cp::*>
	    : public true_type { };
	
	  /// is_member_pointer
	  template<typename _Tp>
	    struct is_member_pointer
	    : public __is_member_pointer_helper<typename remove_cv<_Tp>::type>::type
	    { };
	
	  // Utility to detect referenceable types ([defns.referenceable]).
	
	  template<typename _Tp>
	    struct __is_referenceable
	    : public __or_<is_object<_Tp>, is_reference<_Tp>>::type
	    { };
	
	  template<typename _Res, typename... _Args _GLIBCXX_NOEXCEPT_PARM>
	    struct __is_referenceable<_Res(_Args...) _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type
	    { };
	
	  template<typename _Res, typename... _Args _GLIBCXX_NOEXCEPT_PARM>
	    struct __is_referenceable<_Res(_Args......) _GLIBCXX_NOEXCEPT_QUAL>
	    : public true_type
	    { };
	
	  // Type properties.
	
	  /// is_const
	  template<typename>
	    struct is_const
	    : public false_type { };
	
	  template<typename _Tp>
	    struct is_const<_Tp const>
	    : public true_type { };
	
	  /// is_volatile
	  template<typename>
	    struct is_volatile
	    : public false_type { };
	
	  template<typename _Tp>
	    struct is_volatile<_Tp volatile>
	    : public true_type { };
	
	  /// is_trivial
	  template<typename _Tp>
	    struct is_trivial
	    : public integral_constant<bool, __is_trivial(_Tp)>
	    { };
	
	  // is_trivially_copyable
	  template<typename _Tp>
	    struct is_trivially_copyable
	    : public integral_constant<bool, __is_trivially_copyable(_Tp)>
	    { };
	
	  /// is_standard_layout
	  template<typename _Tp>
	    struct is_standard_layout
	    : public integral_constant<bool, __is_standard_layout(_Tp)>
	    { };
	
	  /// is_pod
	  // Could use is_standard_layout && is_trivial instead of the builtin.
	  template<typename _Tp>
	    struct is_pod
	    : public integral_constant<bool, __is_pod(_Tp)>
	    { };
	
	  /// is_literal_type
	  template<typename _Tp>
	    struct is_literal_type
	    : public integral_constant<bool, __is_literal_type(_Tp)>
	    { };
	
	  /// is_empty
	  template<typename _Tp>
	    struct is_empty
	    : public integral_constant<bool, __is_empty(_Tp)>
	    { };
	
	  /// is_polymorphic
	  template<typename _Tp>
	    struct is_polymorphic
	    : public integral_constant<bool, __is_polymorphic(_Tp)>
	    { };
	
	#if __cplusplus >= 201402L
	#define __cpp_lib_is_final 201402L
	  /// is_final
	  template<typename _Tp>
	    struct is_final
	    : public integral_constant<bool, __is_final(_Tp)>
	    { };
	#endif
	
	  /// is_abstract
	  template<typename _Tp>
	    struct is_abstract
	    : public integral_constant<bool, __is_abstract(_Tp)>
	    { };
	
	  template<typename _Tp,
		   bool = is_arithmetic<_Tp>::value>
	    struct __is_signed_helper
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_signed_helper<_Tp, true>
	    : public integral_constant<bool, _Tp(-1) < _Tp(0)>
	    { };
	
	  /// is_signed
	  template<typename _Tp>
	    struct is_signed
	    : public __is_signed_helper<_Tp>::type
	    { };
	
	  /// is_unsigned
	  template<typename _Tp>
	    struct is_unsigned
	    : public __and_<is_arithmetic<_Tp>, __not_<is_signed<_Tp>>>
	    { };
	
	
	  // Destructible and constructible type properties.
	
	  /**
	   *  @brief  Utility to simplify expressions used in unevaluated operands
	   *  @ingroup utilities
	   */
	
	  template<typename _Tp, typename _Up = _Tp&&>
	    _Up
	    __declval(int);
	
	  template<typename _Tp>
	    _Tp
	    __declval(long);
	
	  template<typename _Tp>
	    auto declval() noexcept -> decltype(__declval<_Tp>(0));
	
	  template<typename, unsigned = 0>
	    struct extent;
	
	  template<typename>
	    struct remove_all_extents;
	
	  template<typename _Tp>
	    struct __is_array_known_bounds
	    : public integral_constant<bool, (extent<_Tp>::value > 0)>
	    { };
	
	  template<typename _Tp>
	    struct __is_array_unknown_bounds
	    : public __and_<is_array<_Tp>, __not_<extent<_Tp>>>
	    { };
	
	  // In N3290 is_destructible does not say anything about function
	  // types and abstract types, see LWG 2049. This implementation
	  // describes function types as non-destructible and all complete
	  // object types as destructible, iff the explicit destructor
	  // call expression is wellformed.
	  struct __do_is_destructible_impl
	  {
	    template<typename _Tp, typename = decltype(declval<_Tp&>().~_Tp())>
	      static true_type __test(int);
	
	    template<typename>
	      static false_type __test(...);
	  };
	
	  template<typename _Tp>
	    struct __is_destructible_impl
	    : public __do_is_destructible_impl
	    {
	      typedef decltype(__test<_Tp>(0)) type;
	    };
	
	  template<typename _Tp,
	           bool = __or_<is_void<_Tp>,
	                        __is_array_unknown_bounds<_Tp>,
	                        is_function<_Tp>>::value,
	           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
	    struct __is_destructible_safe;
	
	  template<typename _Tp>
	    struct __is_destructible_safe<_Tp, false, false>
	    : public __is_destructible_impl<typename
	               remove_all_extents<_Tp>::type>::type
	    { };
	
	  template<typename _Tp>
	    struct __is_destructible_safe<_Tp, true, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_destructible_safe<_Tp, false, true>
	    : public true_type { };
	
	  /// is_destructible
	  template<typename _Tp>
	    struct is_destructible
	    : public __is_destructible_safe<_Tp>::type
	    { };
	
	  // is_nothrow_destructible requires that is_destructible is
	  // satisfied as well.  We realize that by mimicing the
	  // implementation of is_destructible but refer to noexcept(expr)
	  // instead of decltype(expr).
	  struct __do_is_nt_destructible_impl
	  {
	    template<typename _Tp>
	      static __bool_constant<noexcept(declval<_Tp&>().~_Tp())>
	      __test(int);
	
	    template<typename>
	      static false_type __test(...);
	  };
	
	  template<typename _Tp>
	    struct __is_nt_destructible_impl
	    : public __do_is_nt_destructible_impl
	    {
	      typedef decltype(__test<_Tp>(0)) type;
	    };
	
	  template<typename _Tp,
	           bool = __or_<is_void<_Tp>,
	                        __is_array_unknown_bounds<_Tp>,
	                        is_function<_Tp>>::value,
	           bool = __or_<is_reference<_Tp>, is_scalar<_Tp>>::value>
	    struct __is_nt_destructible_safe;
	
	  template<typename _Tp>
	    struct __is_nt_destructible_safe<_Tp, false, false>
	    : public __is_nt_destructible_impl<typename
	               remove_all_extents<_Tp>::type>::type
	    { };
	
	  template<typename _Tp>
	    struct __is_nt_destructible_safe<_Tp, true, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_nt_destructible_safe<_Tp, false, true>
	    : public true_type { };
	
	  /// is_nothrow_destructible
	  template<typename _Tp>
	    struct is_nothrow_destructible
	    : public __is_nt_destructible_safe<_Tp>::type
	    { };
	
	  /// is_constructible
	  template<typename _Tp, typename... _Args>
	    struct is_constructible
	      : public __bool_constant<__is_constructible(_Tp, _Args...)>
	    { };
	
	  /// is_default_constructible
	  template<typename _Tp>
	    struct is_default_constructible
	    : public is_constructible<_Tp>::type
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_copy_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_copy_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_copy_constructible_impl<_Tp, true>
	    : public is_constructible<_Tp, const _Tp&>
	    { };
	
	  /// is_copy_constructible
	  template<typename _Tp>
	    struct is_copy_constructible
	    : public __is_copy_constructible_impl<_Tp>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_move_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_move_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_move_constructible_impl<_Tp, true>
	    : public is_constructible<_Tp, _Tp&&>
	    { };
	
	  /// is_move_constructible
	  template<typename _Tp>
	    struct is_move_constructible
	    : public __is_move_constructible_impl<_Tp>
	    { };
	
	  template<typename _Tp>
	    struct __is_nt_default_constructible_atom
	    : public integral_constant<bool, noexcept(_Tp())>
	    { };
	
	  template<typename _Tp, bool = is_array<_Tp>::value>
	    struct __is_nt_default_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_nt_default_constructible_impl<_Tp, true>
	    : public __and_<__is_array_known_bounds<_Tp>,
			    __is_nt_default_constructible_atom<typename
	                      remove_all_extents<_Tp>::type>>
	    { };
	
	  template<typename _Tp>
	    struct __is_nt_default_constructible_impl<_Tp, false>
	    : public __is_nt_default_constructible_atom<_Tp>
	    { };
	
	  /// is_nothrow_default_constructible
	  template<typename _Tp>
	    struct is_nothrow_default_constructible
	    : public __and_<is_default_constructible<_Tp>,
	                    __is_nt_default_constructible_impl<_Tp>>
	    { };
	
	  template<typename _Tp, typename... _Args>
	    struct __is_nt_constructible_impl
	    : public integral_constant<bool, noexcept(_Tp(declval<_Args>()...))>
	    { };
	
	  template<typename _Tp, typename _Arg>
	    struct __is_nt_constructible_impl<_Tp, _Arg>
	    : public integral_constant<bool,
	                               noexcept(static_cast<_Tp>(declval<_Arg>()))>
	    { };
	
	  template<typename _Tp>
	    struct __is_nt_constructible_impl<_Tp>
	    : public is_nothrow_default_constructible<_Tp>
	    { };
	
	  /// is_nothrow_constructible
	  template<typename _Tp, typename... _Args>
	    struct is_nothrow_constructible
	    : public __and_<is_constructible<_Tp, _Args...>,
			    __is_nt_constructible_impl<_Tp, _Args...>>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_nothrow_copy_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_nothrow_copy_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_nothrow_copy_constructible_impl<_Tp, true>
	    : public is_nothrow_constructible<_Tp, const _Tp&>
	    { };
	
	  /// is_nothrow_copy_constructible
	  template<typename _Tp>
	    struct is_nothrow_copy_constructible
	    : public __is_nothrow_copy_constructible_impl<_Tp>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_nothrow_move_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_nothrow_move_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_nothrow_move_constructible_impl<_Tp, true>
	    : public is_nothrow_constructible<_Tp, _Tp&&>
	    { };
	
	  /// is_nothrow_move_constructible
	  template<typename _Tp>
	    struct is_nothrow_move_constructible
	    : public __is_nothrow_move_constructible_impl<_Tp>
	    { };
	
	  /// is_assignable
	  template<typename _Tp, typename _Up>
	    struct is_assignable
	      : public __bool_constant<__is_assignable(_Tp, _Up)>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_copy_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_copy_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_copy_assignable_impl<_Tp, true>
	    : public is_assignable<_Tp&, const _Tp&>
	    { };
	
	  /// is_copy_assignable
	  template<typename _Tp>
	    struct is_copy_assignable
	    : public __is_copy_assignable_impl<_Tp>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_move_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_move_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_move_assignable_impl<_Tp, true>
	    : public is_assignable<_Tp&, _Tp&&>
	    { };
	
	  /// is_move_assignable
	  template<typename _Tp>
	    struct is_move_assignable
	    : public __is_move_assignable_impl<_Tp>
	    { };
	
	  template<typename _Tp, typename _Up>
	    struct __is_nt_assignable_impl
	    : public integral_constant<bool, noexcept(declval<_Tp>() = declval<_Up>())>
	    { };
	
	  /// is_nothrow_assignable
	  template<typename _Tp, typename _Up>
	    struct is_nothrow_assignable
	    : public __and_<is_assignable<_Tp, _Up>,
			    __is_nt_assignable_impl<_Tp, _Up>>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_nt_copy_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_nt_copy_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_nt_copy_assignable_impl<_Tp, true>
	    : public is_nothrow_assignable<_Tp&, const _Tp&>
	    { };
	
	  /// is_nothrow_copy_assignable
	  template<typename _Tp>
	    struct is_nothrow_copy_assignable
	    : public __is_nt_copy_assignable_impl<_Tp>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_nt_move_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_nt_move_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_nt_move_assignable_impl<_Tp, true>
	    : public is_nothrow_assignable<_Tp&, _Tp&&>
	    { };
	
	  /// is_nothrow_move_assignable
	  template<typename _Tp>
	    struct is_nothrow_move_assignable
	    : public __is_nt_move_assignable_impl<_Tp>
	    { };
	
	  /// is_trivially_constructible
	  template<typename _Tp, typename... _Args>
	    struct is_trivially_constructible
	    : public __bool_constant<__is_trivially_constructible(_Tp, _Args...)>
	    { };
	
	  /// is_trivially_default_constructible
	  template<typename _Tp>
	    struct is_trivially_default_constructible
	    : public is_trivially_constructible<_Tp>::type
	    { };
	
	  struct __do_is_implicitly_default_constructible_impl
	  {
	    template <typename _Tp>
	    static void __helper(const _Tp&);
	
	    template <typename _Tp>
	    static true_type __test(const _Tp&,
	                            decltype(__helper<const _Tp&>({}))* = 0);
	
	    static false_type __test(...);
	  };
	
	  template<typename _Tp>
	    struct __is_implicitly_default_constructible_impl
	    : public __do_is_implicitly_default_constructible_impl
	    {
	      typedef decltype(__test(declval<_Tp>())) type;
	    };
	
	  template<typename _Tp>
	    struct __is_implicitly_default_constructible_safe
	    : public __is_implicitly_default_constructible_impl<_Tp>::type
	    { };
	
	  template <typename _Tp>
	    struct __is_implicitly_default_constructible
	    : public __and_<is_default_constructible<_Tp>,
			    __is_implicitly_default_constructible_safe<_Tp>>
	    { };
	
	  /// is_trivially_copy_constructible
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_trivially_copy_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_trivially_copy_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_trivially_copy_constructible_impl<_Tp, true>
	    : public __and_<is_copy_constructible<_Tp>,
			    integral_constant<bool,
				__is_trivially_constructible(_Tp, const _Tp&)>>
	    { };
	
	  template<typename _Tp>
	    struct is_trivially_copy_constructible
	    : public __is_trivially_copy_constructible_impl<_Tp>
	    { };
	
	  /// is_trivially_move_constructible
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_trivially_move_constructible_impl;
	
	  template<typename _Tp>
	    struct __is_trivially_move_constructible_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_trivially_move_constructible_impl<_Tp, true>
	    : public __and_<is_move_constructible<_Tp>,
			    integral_constant<bool,
				__is_trivially_constructible(_Tp, _Tp&&)>>
	    { };
	
	  template<typename _Tp>
	    struct is_trivially_move_constructible
	    : public __is_trivially_move_constructible_impl<_Tp>
	    { };
	
	  /// is_trivially_assignable
	  template<typename _Tp, typename _Up>
	    struct is_trivially_assignable
	    : public __bool_constant<__is_trivially_assignable(_Tp, _Up)>
	    { };
	
	  /// is_trivially_copy_assignable
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_trivially_copy_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_trivially_copy_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_trivially_copy_assignable_impl<_Tp, true>
	    : public __bool_constant<__is_trivially_assignable(_Tp&, const _Tp&)>
	    { };
	
	  template<typename _Tp>
	    struct is_trivially_copy_assignable
	    : public __is_trivially_copy_assignable_impl<_Tp>
	    { };
	
	  /// is_trivially_move_assignable
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __is_trivially_move_assignable_impl;
	
	  template<typename _Tp>
	    struct __is_trivially_move_assignable_impl<_Tp, false>
	    : public false_type { };
	
	  template<typename _Tp>
	    struct __is_trivially_move_assignable_impl<_Tp, true>
	    : public __bool_constant<__is_trivially_assignable(_Tp&, _Tp&&)>
	    { };
	
	  template<typename _Tp>
	    struct is_trivially_move_assignable
	    : public __is_trivially_move_assignable_impl<_Tp>
	    { };
	
	  /// is_trivially_destructible
	  template<typename _Tp>
	    struct is_trivially_destructible
	    : public __and_<is_destructible<_Tp>,
			    __bool_constant<__has_trivial_destructor(_Tp)>>
	    { };
	
	
	  /// has_virtual_destructor
	  template<typename _Tp>
	    struct has_virtual_destructor
	    : public integral_constant<bool, __has_virtual_destructor(_Tp)>
	    { };
	
	
	  // type property queries.
	
	  /// alignment_of
	  template<typename _Tp>
	    struct alignment_of
	    : public integral_constant<std::size_t, alignof(_Tp)> { };
	
	  /// rank
	  template<typename>
	    struct rank
	    : public integral_constant<std::size_t, 0> { };
	
	  template<typename _Tp, std::size_t _Size>
	    struct rank<_Tp[_Size]>
	    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
	
	  template<typename _Tp>
	    struct rank<_Tp[]>
	    : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
	
	  /// extent
	  template<typename, unsigned _Uint>
	    struct extent
	    : public integral_constant<std::size_t, 0> { };
	
	  template<typename _Tp, unsigned _Uint, std::size_t _Size>
	    struct extent<_Tp[_Size], _Uint>
	    : public integral_constant<std::size_t,
				       _Uint == 0 ? _Size : extent<_Tp,
								   _Uint - 1>::value>
	    { };
	
	  template<typename _Tp, unsigned _Uint>
	    struct extent<_Tp[], _Uint>
	    : public integral_constant<std::size_t,
				       _Uint == 0 ? 0 : extent<_Tp,
							       _Uint - 1>::value>
	    { };
	
	
	  // Type relations.
	
	  /// is_same
	  template<typename, typename>
	    struct is_same
	    : public false_type { };
	
	  template<typename _Tp>
	    struct is_same<_Tp, _Tp>
	    : public true_type { };
	
	  /// is_base_of
	  template<typename _Base, typename _Derived>
	    struct is_base_of
	    : public integral_constant<bool, __is_base_of(_Base, _Derived)>
	    { };
	
	  template<typename _From, typename _To,
	           bool = __or_<is_void<_From>, is_function<_To>,
	                        is_array<_To>>::value>
	    struct __is_convertible_helper
	    {
	      typedef typename is_void<_To>::type type;
	    };
	
	  template<typename _From, typename _To>
	    class __is_convertible_helper<_From, _To, false>
	    {
	      template<typename _To1>
		static void __test_aux(_To1) noexcept;
	
	      template<typename _From1, typename _To1,
		       typename = decltype(__test_aux<_To1>(std::declval<_From1>()))>
		static true_type
		__test(int);
	
	      template<typename, typename>
		static false_type
		__test(...);
	
	    public:
	      typedef decltype(__test<_From, _To>(0)) type;
	    };
	
	
	  /// is_convertible
	  template<typename _From, typename _To>
	    struct is_convertible

	    : public __is_convertible_helper<_From, _To>::type
	    { };
	
	#if __cplusplus > 201703L
	    template<typename _From, typename _To,
	           bool = __or_<is_void<_From>, is_function<_To>,
	                        is_array<_To>>::value>
	    struct __is_nt_convertible_helper
	    : is_void<_To>
	    { };
	
	  template<typename _From, typename _To>
	    class __is_nt_convertible_helper<_From, _To, false>
	    {
	      template<typename _To1>
		static void __test_aux(_To1) noexcept;
	
	      template<typename _From1, typename _To1>
		static bool_constant<noexcept(__test_aux<_To1>(std::declval<_From1>()))>
		__test(int);
	
	      template<typename, typename>
		static false_type
		__test(...);
	
	    public:
	      using type = decltype(__test<_From, _To>(0));
	    };
	
	  /// is_nothrow_convertible
	  template<typename _From, typename _To>
	    struct is_nothrow_convertible
	    : public __is_nt_convertible_helper<_From, _To>::type
	    { };
	
	  /// is_nothrow_convertible_v
	  template<typename _From, typename _To>
	    inline constexpr bool is_nothrow_convertible_v
	      = is_nothrow_convertible<_From, _To>::value;
	#endif // C++2a
	
	  // Const-volatile modifications.
	
	  /// remove_const
	  template<typename _Tp>
	    struct remove_const
	    { typedef _Tp     type; };
	
	  template<typename _Tp>
	    struct remove_const<_Tp const>
	    { typedef _Tp     type; };
	
	  /// remove_volatile
	  template<typename _Tp>
	    struct remove_volatile
	    { typedef _Tp     type; };
	
	  template<typename _Tp>
	    struct remove_volatile<_Tp volatile>
	    { typedef _Tp     type; };
	
	  /// remove_cv
	  template<typename _Tp>
	    struct remove_cv
	    {
	      typedef typename
	      remove_const<typename remove_volatile<_Tp>::type>::type     type;
	    };
	
	  /// add_const
	  template<typename _Tp>
	    struct add_const
	    { typedef _Tp const     type; };
	
	  /// add_volatile
	  template<typename _Tp>
	    struct add_volatile
	    { typedef _Tp volatile     type; };
	
	  /// add_cv
	  template<typename _Tp>
	    struct add_cv
	    {
	      typedef typename
	      add_const<typename add_volatile<_Tp>::type>::type     type;
	    };
	
	#if __cplusplus > 201103L
	
	#define __cpp_lib_transformation_trait_aliases 201304
	
	  /// Alias template for remove_const
	  template<typename _Tp>
	    using remove_const_t = typename remove_const<_Tp>::type;
	
	  /// Alias template for remove_volatile
	  template<typename _Tp>
	    using remove_volatile_t = typename remove_volatile<_Tp>::type;
	
	  /// Alias template for remove_cv
	  template<typename _Tp>
	    using remove_cv_t = typename remove_cv<_Tp>::type;
	
	  /// Alias template for add_const
	  template<typename _Tp>
	    using add_const_t = typename add_const<_Tp>::type;
	
	  /// Alias template for add_volatile
	  template<typename _Tp>
	    using add_volatile_t = typename add_volatile<_Tp>::type;
	
	  /// Alias template for add_cv
	  template<typename _Tp>
	    using add_cv_t = typename add_cv<_Tp>::type;
	#endif
	
	  // Reference transformations.
	
	  /// remove_reference
	  template<typename _Tp>
	    struct remove_reference
	    { typedef _Tp   type; };
	
	  template<typename _Tp>
	    struct remove_reference<_Tp&>
	    { typedef _Tp   type; };
	
	  template<typename _Tp>
	    struct remove_reference<_Tp&&>
	    { typedef _Tp   type; };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __add_lvalue_reference_helper
	    { typedef _Tp   type; };
	
	  template<typename _Tp>
	    struct __add_lvalue_reference_helper<_Tp, true>
	    { typedef _Tp&   type; };
	
	  /// add_lvalue_reference
	  template<typename _Tp>
	    struct add_lvalue_reference
	    : public __add_lvalue_reference_helper<_Tp>
	    { };
	
	  template<typename _Tp, bool = __is_referenceable<_Tp>::value>
	    struct __add_rvalue_reference_helper
	    { typedef _Tp   type; };
	
	  template<typename _Tp>
	    struct __add_rvalue_reference_helper<_Tp, true>
	    { typedef _Tp&&   type; };
	
	  /// add_rvalue_reference
	  template<typename _Tp>
	    struct add_rvalue_reference
	    : public __add_rvalue_reference_helper<_Tp>
	    { };
	
	#if __cplusplus > 201103L
	  /// Alias template for remove_reference
	  template<typename _Tp>
	    using remove_reference_t = typename remove_reference<_Tp>::type;
	
	  /// Alias template for add_lvalue_reference
	  template<typename _Tp>
	    using add_lvalue_reference_t = typename add_lvalue_reference<_Tp>::type;
	
	  /// Alias template for add_rvalue_reference
	  template<typename _Tp>
	    using add_rvalue_reference_t = typename add_rvalue_reference<_Tp>::type;
	#endif
	
	  // Sign modifications.
	
	  // Utility for constructing identically cv-qualified types.
	  template<typename _Unqualified, bool _IsConst, bool _IsVol>
	    struct __cv_selector;
	
	  template<typename _Unqualified>
	    struct __cv_selector<_Unqualified, false, false>
	    { typedef _Unqualified __type; };
	
	  template<typename _Unqualified>
	    struct __cv_selector<_Unqualified, false, true>
	    { typedef volatile _Unqualified __type; };
	
	  template<typename _Unqualified>
	    struct __cv_selector<_Unqualified, true, false>
	    { typedef const _Unqualified __type; };
	
	  template<typename _Unqualified>
	    struct __cv_selector<_Unqualified, true, true>
	    { typedef const volatile _Unqualified __type; };
	
	  template<typename _Qualified, typename _Unqualified,
		   bool _IsConst = is_const<_Qualified>::value,
		   bool _IsVol = is_volatile<_Qualified>::value>
	    class __match_cv_qualifiers
	    {
	      typedef __cv_selector<_Unqualified, _IsConst, _IsVol> __match;
	
	    public:
	      typedef typename __match::__type __type;
	    };
	
	  // Utility for finding the unsigned versions of signed integral types.
	  template<typename _Tp>
	    struct __make_unsigned
	    { typedef _Tp __type; };
	
	  template<>
	    struct __make_unsigned<char>
	    { typedef unsigned char __type; };
	
	  template<>
	    struct __make_unsigned<signed char>
	    { typedef unsigned char __type; };
	
	  template<>
	    struct __make_unsigned<short>
	    { typedef unsigned short __type; };
	
	  template<>
	    struct __make_unsigned<int>
	    { typedef unsigned int __type; };
	
	  template<>
	    struct __make_unsigned<long>
	    { typedef unsigned long __type; };
	
	  template<>
	    struct __make_unsigned<long long>
	    { typedef unsigned long long __type; };
	
	#if defined(__GLIBCXX_TYPE_INT_N_0)
	  template<>
	    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_0>
	    { typedef unsigned __GLIBCXX_TYPE_INT_N_0 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_1)
	  template<>
	    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_1>
	    { typedef unsigned __GLIBCXX_TYPE_INT_N_1 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_2)
	  template<>
	    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_2>
	    { typedef unsigned __GLIBCXX_TYPE_INT_N_2 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_3)
	  template<>
	    struct __make_unsigned<__GLIBCXX_TYPE_INT_N_3>
	    { typedef unsigned __GLIBCXX_TYPE_INT_N_3 __type; };
	#endif
	
	  // Select between integral and enum: not possible to be both.
	  template<typename _Tp,
		   bool _IsInt = is_integral<_Tp>::value,
		   bool _IsEnum = is_enum<_Tp>::value>
	    class __make_unsigned_selector;
	
	  template<typename _Tp>
	    class __make_unsigned_selector<_Tp, true, false>
	    {
	      using __unsigned_type
		= typename __make_unsigned<typename remove_cv<_Tp>::type>::__type;
	
	    public:
	      using __type
		= typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
	    };
	
	  class __make_unsigned_selector_base
	  {
	  protected:
	    template<typename...> struct _List { };
	
	    template<typename _Tp, typename... _Up>
	      struct _List<_Tp, _Up...> : _List<_Up...>
	      { static constexpr size_t __size = sizeof(_Tp); };
	
	    template<size_t _Sz, typename _Tp, bool = (_Sz <= _Tp::__size)>
	      struct __select;
	
	    template<size_t _Sz, typename _Uint, typename... _UInts>
	      struct __select<_Sz, _List<_Uint, _UInts...>, true>
	      { using __type = _Uint; };
	
	    template<size_t _Sz, typename _Uint, typename... _UInts>
	      struct __select<_Sz, _List<_Uint, _UInts...>, false>
	      : __select<_Sz, _List<_UInts...>>
	      { };
	  };
	
	  // Choose unsigned integer type with the smallest rank and same size as _Tp
	  template<typename _Tp>
	    class __make_unsigned_selector<_Tp, false, true>
	    : __make_unsigned_selector_base
	    {
	      // With -fshort-enums, an enum may be as small as a char.
	      using _UInts = _List<unsigned char, unsigned short, unsigned int,
				   unsigned long, unsigned long long>;
	
	      using __unsigned_type = typename __select<sizeof(_Tp), _UInts>::__type;
	
	    public:
	      using __type
		= typename __match_cv_qualifiers<_Tp, __unsigned_type>::__type;
	    };
	
	  // wchar_t, char8_t, char16_t and char32_t are integral types but are
	  // neither signed integer types nor unsigned integer types, so must be
	  // transformed to the unsigned integer type with the smallest rank.
	  // Use the partial specialization for enumeration types to do that.
	#if defined(_GLIBCXX_USE_WCHAR_T)
	  template<>
	    struct __make_unsigned<wchar_t>
	    {
	      using __type
		= typename __make_unsigned_selector<wchar_t, false, true>::__type;
	    };
	#endif
	
	#ifdef _GLIBCXX_USE_CHAR8_T
	  template<>
	    struct __make_unsigned<char8_t>
	    {
	      using __type
		= typename __make_unsigned_selector<char8_t, false, true>::__type;
	    };
	#endif
	
	  template<>
	    struct __make_unsigned<char16_t>
	    {
	      using __type
		= typename __make_unsigned_selector<char16_t, false, true>::__type;
	    };
	
	  template<>
	    struct __make_unsigned<char32_t>
	    {
	      using __type
		= typename __make_unsigned_selector<char32_t, false, true>::__type;
	    };
	
	  // Given an integral/enum type, return the corresponding unsigned
	  // integer type.
	  // Primary template.
	  /// make_unsigned
	  template<typename _Tp>
	    struct make_unsigned
	    { typedef typename __make_unsigned_selector<_Tp>::__type type; };
	
	  // Integral, but don't define.
	  template<>
	    struct make_unsigned<bool>;
	
	
	  // Utility for finding the signed versions of unsigned integral types.
	  template<typename _Tp>
	    struct __make_signed
	    { typedef _Tp __type; };
	
	  template<>
	    struct __make_signed<char>
	    { typedef signed char __type; };
	
	  template<>
	    struct __make_signed<unsigned char>
	    { typedef signed char __type; };
	
	  template<>
	    struct __make_signed<unsigned short>
	    { typedef signed short __type; };
	
	  template<>
	    struct __make_signed<unsigned int>
	    { typedef signed int __type; };
	
	  template<>
	    struct __make_signed<unsigned long>
	    { typedef signed long __type; };
	
	  template<>
	    struct __make_signed<unsigned long long>
	    { typedef signed long long __type; };
	
	#if defined(__GLIBCXX_TYPE_INT_N_0)
	  template<>
	    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_0>
	    { typedef __GLIBCXX_TYPE_INT_N_0 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_1)
	  template<>
	    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_1>
	    { typedef __GLIBCXX_TYPE_INT_N_1 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_2)
	  template<>
	    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_2>
	    { typedef __GLIBCXX_TYPE_INT_N_2 __type; };
	#endif
	#if defined(__GLIBCXX_TYPE_INT_N_3)
	  template<>
	    struct __make_signed<unsigned __GLIBCXX_TYPE_INT_N_3>
	    { typedef __GLIBCXX_TYPE_INT_N_3 __type; };
	#endif
	
	  // Select between integral and enum: not possible to be both.
	  template<typename _Tp,
		   bool _IsInt = is_integral<_Tp>::value,
		   bool _IsEnum = is_enum<_Tp>::value>
	    class __make_signed_selector;
	
	  template<typename _Tp>
	    class __make_signed_selector<_Tp, true, false>
	    {
	      using __signed_type
		= typename __make_signed<typename remove_cv<_Tp>::type>::__type;
	
	    public:
	      using __type
		= typename __match_cv_qualifiers<_Tp, __signed_type>::__type;
	    };
	
	  // Choose signed integer type with the smallest rank and same size as _Tp
	  template<typename _Tp>
	    class __make_signed_selector<_Tp, false, true>
	    {
	      typedef typename __make_unsigned_selector<_Tp>::__type __unsigned_type;
	
	    public:
	      typedef typename __make_signed_selector<__unsigned_type>::__type __type;
	    };
	
	  // wchar_t, char16_t and char32_t are integral types but are neither
	  // signed integer types nor unsigned integer types, so must be
	  // transformed to the signed integer type with the smallest rank.
	  // Use the partial specialization for enumeration types to do that.
	#if defined(_GLIBCXX_USE_WCHAR_T)
	  template<>
	    struct __make_signed<wchar_t>
	    {
	      using __type
		= typename __make_signed_selector<wchar_t, false, true>::__type;
	    };
	#endif
	
	#if defined(_GLIBCXX_USE_CHAR8_T)
	  template<>
	    struct __make_signed<char8_t>
	    {
	      using __type
		= typename __make_signed_selector<char8_t, false, true>::__type;
	    };
	#endif
	
	  template<>
	    struct __make_signed<char16_t>
	    {
	      using __type
		= typename __make_signed_selector<char16_t, false, true>::__type;
	    };
	
	  template<>
	    struct __make_signed<char32_t>
	    {
	      using __type
		= typename __make_signed_selector<char32_t, false, true>::__type;
	    };
	
	  // Given an integral/enum type, return the corresponding signed
	  // integer type.
	  // Primary template.
	  /// make_signed
	  template<typename _Tp>
	    struct make_signed
	    { typedef typename __make_signed_selector<_Tp>::__type type; };
	
	  // Integral, but don't define.
	  template<>
	    struct make_signed<bool>;
	
	#if __cplusplus > 201103L
	  /// Alias template for make_signed
	  template<typename _Tp>
	    using make_signed_t = typename make_signed<_Tp>::type;
	
	  /// Alias template for make_unsigned
	  template<typename _Tp>
	    using make_unsigned_t = typename make_unsigned<_Tp>::type;
	#endif
	
	  // Array modifications.
	
	  /// remove_extent
	  template<typename _Tp>
	    struct remove_extent
	    { typedef _Tp     type; };
	
	  template<typename _Tp, std::size_t _Size>
	    struct remove_extent<_Tp[_Size]>
	    { typedef _Tp     type; };
	
	  template<typename _Tp>
	    struct remove_extent<_Tp[]>
	    { typedef _Tp     type; };
	
	  /// remove_all_extents
	  template<typename _Tp>
	    struct remove_all_extents
	    { typedef _Tp     type; };
	
	  template<typename _Tp, std::size_t _Size>
	    struct remove_all_extents<_Tp[_Size]>
	    { typedef typename remove_all_extents<_Tp>::type     type; };
	
	  template<typename _Tp>
	    struct remove_all_extents<_Tp[]>
	    { typedef typename remove_all_extents<_Tp>::type     type; };
	
	#if __cplusplus > 201103L
	  /// Alias template for remove_extent
	  template<typename _Tp>
	    using remove_extent_t = typename remove_extent<_Tp>::type;
	
	  /// Alias template for remove_all_extents
	  template<typename _Tp>
	    using remove_all_extents_t = typename remove_all_extents<_Tp>::type;
	#endif
	
	  // Pointer modifications.
	
	  template<typename _Tp, typename>
	    struct __remove_pointer_helper
	    { typedef _Tp     type; };
	
	  template<typename _Tp, typename _Up>
	    struct __remove_pointer_helper<_Tp, _Up*>
	    { typedef _Up     type; };
	
	  /// remove_pointer
	  template<typename _Tp>
	    struct remove_pointer
	    : public __remove_pointer_helper<_Tp, typename remove_cv<_Tp>::type>
	    { };
	
	  /// add_pointer
	  template<typename _Tp, bool = __or_<__is_referenceable<_Tp>,
					      is_void<_Tp>>::value>
	    struct __add_pointer_helper
	    { typedef _Tp     type; };
	
	  template<typename _Tp>
	    struct __add_pointer_helper<_Tp, true>
	    { typedef typename remove_reference<_Tp>::type*     type; };
	
	  template<typename _Tp>
	    struct add_pointer
	    : public __add_pointer_helper<_Tp>
	    { };
	
	#if __cplusplus > 201103L
	  /// Alias template for remove_pointer
	  template<typename _Tp>
	    using remove_pointer_t = typename remove_pointer<_Tp>::type;
	
	  /// Alias template for add_pointer
	  template<typename _Tp>
	    using add_pointer_t = typename add_pointer<_Tp>::type;
	#endif
	
	  template<std::size_t _Len>
	    struct __aligned_storage_msa
	    {
	      union __type
	      {
		unsigned char __data[_Len];
		struct __attribute__((__aligned__)) { } __align;
	      };
	    };
	
	  /**
	   *  @brief Alignment type.
	   *
	   *  The value of _Align is a default-alignment which shall be the
	   *  most stringent alignment requirement for any C++ object type
	   *  whose size is no greater than _Len (3.9). The member typedef
	   *  type shall be a POD type suitable for use as uninitialized
	   *  storage for any object whose size is at most _Len and whose
	   *  alignment is a divisor of _Align.
	  */
	  template<std::size_t _Len, std::size_t _Align =
		   __alignof__(typename __aligned_storage_msa<_Len>::__type)>
	    struct aligned_storage
	    {
	      union type
	      {
		unsigned char __data[_Len];
		struct __attribute__((__aligned__((_Align)))) { } __align;
	      };
	    };
	
	  template <typename... _Types>
	    struct __strictest_alignment
	    {
	      static const size_t _S_alignment = 0;
	      static const size_t _S_size = 0;
	    };
	
	  template <typename _Tp, typename... _Types>
	    struct __strictest_alignment<_Tp, _Types...>
	    {
	      static const size_t _S_alignment =
	        alignof(_Tp) > __strictest_alignment<_Types...>::_S_alignment
		? alignof(_Tp) : __strictest_alignment<_Types...>::_S_alignment;
	      static const size_t _S_size =
	        sizeof(_Tp) > __strictest_alignment<_Types...>::_S_size
		? sizeof(_Tp) : __strictest_alignment<_Types...>::_S_size;
	    };
	
	  /**
	   *  @brief Provide aligned storage for types.
	   *
	   *  [meta.trans.other]
	   *
	   *  Provides aligned storage for any of the provided types of at
	   *  least size _Len.
	   *
	   *  @see aligned_storage
	   */
	  template <size_t _Len, typename... _Types>
	    struct aligned_union
	    {
	    private:
	      static_assert(sizeof...(_Types) != 0, "At least one type is required");
	
	      using __strictest = __strictest_alignment<_Types...>;
	      static const size_t _S_len = _Len > __strictest::_S_size
		? _Len : __strictest::_S_size;
	    public:
	      /// The value of the strictest alignment of _Types.
	      static const size_t alignment_value = __strictest::_S_alignment;
	      /// The storage.
	      typedef typename aligned_storage<_S_len, alignment_value>::type type;
	    };
	
	  template <size_t _Len, typename... _Types>
	    const size_t aligned_union<_Len, _Types...>::alignment_value;
	
	  // Decay trait for arrays and functions, used for perfect forwarding
	  // in make_pair, make_tuple, etc.
	  template<typename _Up,
		   bool _IsArray = is_array<_Up>::value,
		   bool _IsFunction = is_function<_Up>::value>
	    struct __decay_selector;
	
	  // NB: DR 705.
	  template<typename _Up>
	    struct __decay_selector<_Up, false, false>
	    { typedef typename remove_cv<_Up>::type __type; };
	
	  template<typename _Up>
	    struct __decay_selector<_Up, true, false>
	    { typedef typename remove_extent<_Up>::type* __type; };
	
	  template<typename _Up>
	    struct __decay_selector<_Up, false, true>
	    { typedef typename add_pointer<_Up>::type __type; };
	
	  /// decay
	  template<typename _Tp>
	    class decay
	    {
	      typedef typename remove_reference<_Tp>::type __remove_type;
	
	    public:
	      typedef typename __decay_selector<__remove_type>::__type type;
	    };
	
	  template<typename _Tp>
	    class reference_wrapper;
	
	  // Helper which adds a reference to a type when given a reference_wrapper
	  template<typename _Tp>
	    struct __strip_reference_wrapper
	    {
	      typedef _Tp __type;
	    };
	
	  template<typename _Tp>
	    struct __strip_reference_wrapper<reference_wrapper<_Tp> >
	    {
	      typedef _Tp& __type;
	    };
	
	  template<typename _Tp>
	    struct __decay_and_strip
	    {
	      typedef typename __strip_reference_wrapper<
		typename decay<_Tp>::type>::__type __type;
	    };
	
	
	  // Primary template.
	  /// Define a member typedef @c type only if a boolean constant is true.
	  template<bool, typename _Tp = void>
	    struct enable_if
	    { };
	
	  // Partial specialization for true.
	  template<typename _Tp>
	    struct enable_if<true, _Tp>
	    { typedef _Tp type; };
	
	  template<typename... _Cond>
	    using _Require = typename enable_if<__and_<_Cond...>::value>::type;
	
	  // Primary template.
	  /// Define a member typedef @c type to one of two argument types.
	  template<bool _Cond, typename _Iftrue, typename _Iffalse>
	    struct conditional
	    { typedef _Iftrue type; };
	
	  // Partial specialization for false.
	  template<typename _Iftrue, typename _Iffalse>
	    struct conditional<false, _Iftrue, _Iffalse>
	    { typedef _Iffalse type; };
	
	  /// common_type
	  template<typename... _Tp>
	    struct common_type;
	
	  // Sfinae-friendly common_type implementation:
	
	  struct __do_common_type_impl
	  {
	    template<typename _Tp, typename _Up>
	      static __success_type<typename decay<decltype
				    (true ? std::declval<_Tp>()
				     : std::declval<_Up>())>::type> _S_test(int);
	
	    template<typename, typename>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _Tp, typename _Up>
	    struct __common_type_impl
	    : private __do_common_type_impl
	    {
	      typedef decltype(_S_test<_Tp, _Up>(0)) type;
	    };
	
	  struct __do_member_type_wrapper
	  {
	    template<typename _Tp>
	      static __success_type<typename _Tp::type> _S_test(int);
	
	    template<typename>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _Tp>
	    struct __member_type_wrapper
	    : private __do_member_type_wrapper
	    {
	      typedef decltype(_S_test<_Tp>(0)) type;
	    };
	
	  template<typename _CTp, typename... _Args>
	    struct __expanded_common_type_wrapper
	    {
	      typedef common_type<typename _CTp::type, _Args...> type;
	    };
	
	  template<typename... _Args>
	    struct __expanded_common_type_wrapper<__failure_type, _Args...>
	    { typedef __failure_type type; };
	
	  template<>
	    struct common_type<>
	    { };
	
	  template<typename _Tp>
	    struct common_type<_Tp>
	    : common_type<_Tp, _Tp>
	    { };
	
	  template<typename _Tp, typename _Up>
	    struct common_type<_Tp, _Up>
	    : public __common_type_impl<_Tp, _Up>::type
	    { };
	
	  template<typename _Tp, typename _Up, typename... _Vp>
	    struct common_type<_Tp, _Up, _Vp...>
	    : public __expanded_common_type_wrapper<typename __member_type_wrapper<
	               common_type<_Tp, _Up>>::type, _Vp...>::type
	    { };
	
	  template<typename _Tp, bool = is_enum<_Tp>::value>
	    struct __underlying_type_impl
	    {
	      using type = __underlying_type(_Tp);
	    };
	
	  template<typename _Tp>
	    struct __underlying_type_impl<_Tp, false>
	    { };
	
	  /// The underlying type of an enum.
	  template<typename _Tp>
	    struct underlying_type
	    : public __underlying_type_impl<_Tp>
	    { };
	
	  template<typename _Tp>
	    struct __declval_protector
	    {
	      static const bool __stop = false;
	    };
	
	  template<typename _Tp>
	    auto declval() noexcept -> decltype(__declval<_Tp>(0))
	    {
	      static_assert(__declval_protector<_Tp>::__stop,
			    "declval() must not be used!");
	      return __declval<_Tp>(0);
	    }
	
	  // __remove_cvref_t (std::remove_cvref_t for C++11).
	  template<typename _Tp>
	    using __remove_cvref_t
	     = typename remove_cv<typename remove_reference<_Tp>::type>::type;
	
	  /// result_of
	  template<typename _Signature>
	    class result_of;
	
	  // Sfinae-friendly result_of implementation:
	
	#define __cpp_lib_result_of_sfinae 201210
	
	  struct __invoke_memfun_ref { };
	  struct __invoke_memfun_deref { };
	  struct __invoke_memobj_ref { };
	  struct __invoke_memobj_deref { };
	  struct __invoke_other { };
	
	  // Associate a tag type with a specialization of __success_type.
	  template<typename _Tp, typename _Tag>
	    struct __result_of_success : __success_type<_Tp>
	    { using __invoke_type = _Tag; };
	
	  // [func.require] paragraph 1 bullet 1:
	  struct __result_of_memfun_ref_impl
	  {
	    template<typename _Fp, typename _Tp1, typename... _Args>
	      static __result_of_success<decltype(
	      (std::declval<_Tp1>().*std::declval<_Fp>())(std::declval<_Args>()...)
	      ), __invoke_memfun_ref> _S_test(int);
	
	    template<typename...>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _MemPtr, typename _Arg, typename... _Args>
	    struct __result_of_memfun_ref
	    : private __result_of_memfun_ref_impl
	    {
	      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
	    };
	
	  // [func.require] paragraph 1 bullet 2:
	  struct __result_of_memfun_deref_impl
	  {
	    template<typename _Fp, typename _Tp1, typename... _Args>
	      static __result_of_success<decltype(
	      ((*std::declval<_Tp1>()).*std::declval<_Fp>())(std::declval<_Args>()...)
	      ), __invoke_memfun_deref> _S_test(int);
	
	    template<typename...>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _MemPtr, typename _Arg, typename... _Args>
	    struct __result_of_memfun_deref
	    : private __result_of_memfun_deref_impl
	    {
	      typedef decltype(_S_test<_MemPtr, _Arg, _Args...>(0)) type;
	    };
	
	  // [func.require] paragraph 1 bullet 3:
	  struct __result_of_memobj_ref_impl
	  {
	    template<typename _Fp, typename _Tp1>
	      static __result_of_success<decltype(
	      std::declval<_Tp1>().*std::declval<_Fp>()
	      ), __invoke_memobj_ref> _S_test(int);
	
	    template<typename, typename>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _MemPtr, typename _Arg>
	    struct __result_of_memobj_ref
	    : private __result_of_memobj_ref_impl
	    {
	      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
	    };
	
	  // [func.require] paragraph 1 bullet 4:
	  struct __result_of_memobj_deref_impl
	  {
	    template<typename _Fp, typename _Tp1>
	      static __result_of_success<decltype(
	      (*std::declval<_Tp1>()).*std::declval<_Fp>()
	      ), __invoke_memobj_deref> _S_test(int);
	
	    template<typename, typename>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _MemPtr, typename _Arg>
	    struct __result_of_memobj_deref
	    : private __result_of_memobj_deref_impl
	    {
	      typedef decltype(_S_test<_MemPtr, _Arg>(0)) type;
	    };
	
	  template<typename _MemPtr, typename _Arg>
	    struct __result_of_memobj;
	
	  template<typename _Res, typename _Class, typename _Arg>
	    struct __result_of_memobj<_Res _Class::*, _Arg>
	    {
	      typedef __remove_cvref_t<_Arg> _Argval;
	      typedef _Res _Class::* _MemPtr;
	      typedef typename conditional<__or_<is_same<_Argval, _Class>,
	        is_base_of<_Class, _Argval>>::value,
	        __result_of_memobj_ref<_MemPtr, _Arg>,
	        __result_of_memobj_deref<_MemPtr, _Arg>
	      >::type::type type;
	    };
	
	  template<typename _MemPtr, typename _Arg, typename... _Args>
	    struct __result_of_memfun;
	
	  template<typename _Res, typename _Class, typename _Arg, typename... _Args>
	    struct __result_of_memfun<_Res _Class::*, _Arg, _Args...>
	    {
	      typedef typename remove_reference<_Arg>::type _Argval;
	      typedef _Res _Class::* _MemPtr;
	      typedef typename conditional<is_base_of<_Class, _Argval>::value,
	        __result_of_memfun_ref<_MemPtr, _Arg, _Args...>,
	        __result_of_memfun_deref<_MemPtr, _Arg, _Args...>
	      >::type::type type;
	    };
	
	  // _GLIBCXX_RESOLVE_LIB_DEFECTS
	  // 2219.  INVOKE-ing a pointer to member with a reference_wrapper
	  //        as the object expression
	
	  // Used by result_of, invoke etc. to unwrap a reference_wrapper.
	  template<typename _Tp, typename _Up = __remove_cvref_t<_Tp>>
	    struct __inv_unwrap
	    {
	      using type = _Tp;
	    };
	
	  template<typename _Tp, typename _Up>
	    struct __inv_unwrap<_Tp, reference_wrapper<_Up>>
	    {
	      using type = _Up&;
	    };
	
	  template<bool, bool, typename _Functor, typename... _ArgTypes>
	    struct __result_of_impl
	    {
	      typedef __failure_type type;
	    };
	
	  template<typename _MemPtr, typename _Arg>
	    struct __result_of_impl<true, false, _MemPtr, _Arg>
	    : public __result_of_memobj<typename decay<_MemPtr>::type,
					typename __inv_unwrap<_Arg>::type>
	    { };
	
	  template<typename _MemPtr, typename _Arg, typename... _Args>
	    struct __result_of_impl<false, true, _MemPtr, _Arg, _Args...>
	    : public __result_of_memfun<typename decay<_MemPtr>::type,
					typename __inv_unwrap<_Arg>::type, _Args...>
	    { };
	
	  // [func.require] paragraph 1 bullet 5:
	  struct __result_of_other_impl
	  {
	    template<typename _Fn, typename... _Args>
	      static __result_of_success<decltype(
	      std::declval<_Fn>()(std::declval<_Args>()...)
	      ), __invoke_other> _S_test(int);
	
	    template<typename...>
	      static __failure_type _S_test(...);
	  };
	
	  template<typename _Functor, typename... _ArgTypes>
	    struct __result_of_impl<false, false, _Functor, _ArgTypes...>
	    : private __result_of_other_impl
	    {
	      typedef decltype(_S_test<_Functor, _ArgTypes...>(0)) type;
	    };
	
	  // __invoke_result (std::invoke_result for C++11)
	  template<typename _Functor, typename... _ArgTypes>
	    struct __invoke_result
	    : public __result_of_impl<
	        is_member_object_pointer<
	          typename remove_reference<_Functor>::type
	        >::value,
	        is_member_function_pointer<
	          typename remove_reference<_Functor>::type
	        >::value,
		_Functor, _ArgTypes...
	      >::type
	    { };
	
	  template<typename _Functor, typename... _ArgTypes>
	    struct result_of<_Functor(_ArgTypes...)>
	    : public __invoke_result<_Functor, _ArgTypes...>
	    { };
	
	#if __cplusplus >= 201402L
	  /// Alias template for aligned_storage
	  template<size_t _Len, size_t _Align =
		    __alignof__(typename __aligned_storage_msa<_Len>::__type)>
	    using aligned_storage_t = typename aligned_storage<_Len, _Align>::type;
	
	  template <size_t _Len, typename... _Types>
	    using aligned_union_t = typename aligned_union<_Len, _Types...>::type;
	
	  /// Alias template for decay
	  template<typename _Tp>
	    using decay_t = typename decay<_Tp>::type;
	
	  /// Alias template for enable_if
	  template<bool _Cond, typename _Tp = void>
	    using enable_if_t = typename enable_if<_Cond, _Tp>::type;
	
	  /// Alias template for conditional
	  template<bool _Cond, typename _Iftrue, typename _Iffalse>
	    using conditional_t = typename conditional<_Cond, _Iftrue, _Iffalse>::type;
	
	  /// Alias template for common_type
	  template<typename... _Tp>
	    using common_type_t = typename common_type<_Tp...>::type;
	
	  /// Alias template for underlying_type
	  template<typename _Tp>
	    using underlying_type_t = typename underlying_type<_Tp>::type;
	
	  /// Alias template for result_of
	  template<typename _Tp>
	    using result_of_t = typename result_of<_Tp>::type;
	#endif // C++14
	
	  // __enable_if_t (std::enable_if_t for C++11)
	  template<bool _Cond, typename _Tp = void>
	    using __enable_if_t = typename enable_if<_Cond, _Tp>::type;
	
	  // __void_t (std::void_t for C++11)
	  template<typename...> using __void_t = void;
	
	#if __cplusplus >= 201703L || !defined(__STRICT_ANSI__) // c++17 or gnu++11
	#define __cpp_lib_void_t 201411
	  /// A metafunction that always yields void, used for detecting valid types.
	  template<typename...> using void_t = void;
	#endif
	
	  /// Implementation of the detection idiom (negative case).
	  template<typename _Default, typename _AlwaysVoid,
		   template<typename...> class _Op, typename... _Args>
	    struct __detector
	    {
	      using value_t = false_type;
	      using type = _Default;
	    };
	
	  /// Implementation of the detection idiom (positive case).
	  template<typename _Default, template<typename...> class _Op,
		    typename... _Args>
	    struct __detector<_Default, __void_t<_Op<_Args...>>, _Op, _Args...>
	    {
	      using value_t = true_type;
	      using type = _Op<_Args...>;
	    };
	
	  // Detect whether _Op<_Args...> is a valid type, use _Default if not.
	  template<typename _Default, template<typename...> class _Op,
		   typename... _Args>
	    using __detected_or = __detector<_Default, void, _Op, _Args...>;
	
	  // _Op<_Args...> if that is a valid type, otherwise _Default.
	  template<typename _Default, template<typename...> class _Op,
		   typename... _Args>
	    using __detected_or_t
	      = typename __detected_or<_Default, _Op, _Args...>::type;
	
	  /// @} group metaprogramming
	
	  /**
	   *  Use SFINAE to determine if the type _Tp has a publicly-accessible
	   *  member type _NTYPE.
	   */
	#define _GLIBCXX_HAS_NESTED_TYPE(_NTYPE)				\
	  template<typename _Tp, typename = __void_t<>>				\
	    struct __has_##_NTYPE						\
	    : false_type							\
	    { };								\
	  template<typename _Tp>						\
	    struct __has_##_NTYPE<_Tp, __void_t<typename _Tp::_NTYPE>>		\
	    : true_type								\
	    { };
	
	  template <typename _Tp>
	    struct __is_swappable;
	
	  template <typename _Tp>
	    struct __is_nothrow_swappable;
	
	  template<typename... _Elements>
	    class tuple;
	
	  template<typename>
	    struct __is_tuple_like_impl : false_type
	    { };
	
	  template<typename... _Tps>
	    struct __is_tuple_like_impl<tuple<_Tps...>> : true_type
	    { };
	
	  // Internal type trait that allows us to sfinae-protect tuple_cat.
	  template<typename _Tp>
	    struct __is_tuple_like
	    : public __is_tuple_like_impl<__remove_cvref_t<_Tp>>::type
	    { };
	
	  template<typename _Tp>
	    inline
	    typename enable_if<__and_<__not_<__is_tuple_like<_Tp>>,
				      is_move_constructible<_Tp>,
				      is_move_assignable<_Tp>>::value>::type
	    swap(_Tp&, _Tp&)
	    noexcept(__and_<is_nothrow_move_constructible<_Tp>,
		            is_nothrow_move_assignable<_Tp>>::value);
	
	  template<typename _Tp, size_t _Nm>
	    inline
	    typename enable_if<__is_swappable<_Tp>::value>::type
	    swap(_Tp (&__a)[_Nm], _Tp (&__b)[_Nm])
	    noexcept(__is_nothrow_swappable<_Tp>::value);
	
	  namespace __swappable_details {
	    using std::swap;
	
	    struct __do_is_swappable_impl
	    {
	      template<typename _Tp, typename
	               = decltype(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))>
	        static true_type __test(int);
	
	      template<typename>
	        static false_type __test(...);
	    };
	
	    struct __do_is_nothrow_swappable_impl
	    {
	      template<typename _Tp>
	        static __bool_constant<
	          noexcept(swap(std::declval<_Tp&>(), std::declval<_Tp&>()))
	        > __test(int);
	
	      template<typename>
	        static false_type __test(...);
	    };
	
	  } // namespace __swappable_details
	
	  template<typename _Tp>
	    struct __is_swappable_impl
	    : public __swappable_details::__do_is_swappable_impl
	    {
	      typedef decltype(__test<_Tp>(0)) type;
	    };
	
	  template<typename _Tp>
	    struct __is_nothrow_swappable_impl
	    : public __swappable_details::__do_is_nothrow_swappable_impl
	    {
	      typedef decltype(__test<_Tp>(0)) type;
	    };
	
	  template<typename _Tp>
	    struct __is_swappable
	    : public __is_swappable_impl<_Tp>::type
	    { };
	
	  template<typename _Tp>
	    struct __is_nothrow_swappable
	    : public __is_nothrow_swappable_impl<_Tp>::type
	    { };
	
	#if __cplusplus > 201402L || !defined(__STRICT_ANSI__) // c++1z or gnu++11
	#define __cpp_lib_is_swappable 201603
	  /// Metafunctions used for detecting swappable types: p0185r1
	
	  /// is_swappable
	  template<typename _Tp>
	    struct is_swappable
	    : public __is_swappable_impl<_Tp>::type
	    { };
	
	  /// is_nothrow_swappable
	  template<typename _Tp>
	    struct is_nothrow_swappable
	    : public __is_nothrow_swappable_impl<_Tp>::type
	    { };
	
	#if __cplusplus >= 201402L
	  /// is_swappable_v
	  template<typename _Tp>
	    _GLIBCXX17_INLINE constexpr bool is_swappable_v =
	      is_swappable<_Tp>::value;
	
	  /// is_nothrow_swappable_v
	  template<typename _Tp>
	    _GLIBCXX17_INLINE constexpr bool is_nothrow_swappable_v =
	      is_nothrow_swappable<_Tp>::value;
	#endif // __cplusplus >= 201402L
	
	  namespace __swappable_with_details {
	    using std::swap;
	
	    struct __do_is_swappable_with_impl
	    {
	      template<typename _Tp, typename _Up, typename
	               = decltype(swap(std::declval<_Tp>(), std::declval<_Up>())),
	               typename
	               = decltype(swap(std::declval<_Up>(), std::declval<_Tp>()))>
	        static true_type __test(int);
	
	      template<typename, typename>
	        static false_type __test(...);
	    };
	
	    struct __do_is_nothrow_swappable_with_impl
	    {
	      template<typename _Tp, typename _Up>
	        static __bool_constant<
	          noexcept(swap(std::declval<_Tp>(), std::declval<_Up>()))
	          &&
	          noexcept(swap(std::declval<_Up>(), std::declval<_Tp>()))
	        > __test(int);
	
	      template<typename, typename>
	        static false_type __test(...);
	    };
	
	  } // namespace __swappable_with_details
	
	  template<typename _Tp, typename _Up>
	    struct __is_swappable_with_impl
	    : public __swappable_with_details::__do_is_swappable_with_impl
	    {
	      typedef decltype(__test<_Tp, _Up>(0)) type;
	    };
	
	  // Optimization for the homogenous lvalue case, not required:
	  template<typename _Tp>
	    struct __is_swappable_with_impl<_Tp&, _Tp&>
	    : public __swappable_details::__do_is_swappable_impl
	    {
	      typedef decltype(__test<_Tp&>(0)) type;
	    };
	
	  template<typename _Tp, typename _Up>
	    struct __is_nothrow_swappable_with_impl
	    : public __swappable_with_details::__do_is_nothrow_swappable_with_impl
	    {
	      typedef decltype(__test<_Tp, _Up>(0)) type;
	    };
	
	  // Optimization for the homogenous lvalue case, not required:
	  template<typename _Tp>
	    struct __is_nothrow_swappable_with_impl<_Tp&, _Tp&>
	    : public __swappable_details::__do_is_nothrow_swappable_impl
	    {
	      typedef decltype(__test<_Tp&>(0)) type;
	    };
	
	  /// is_swappable_with
	  template<typename _Tp, typename _Up>
	    struct is_swappable_with
	    : public __is_swappable_with_impl<_Tp, _Up>::type
	    { };
	
	  /// is_nothrow_swappable_with
	  template<typename _Tp, typename _Up>
	    struct is_nothrow_swappable_with
	    : public __is_nothrow_swappable_with_impl<_Tp, _Up>::type
	    { };
	
	#if __cplusplus >= 201402L
	  /// is_swappable_with_v
	  template<typename _Tp, typename _Up>
	    _GLIBCXX17_INLINE constexpr bool is_swappable_with_v =
	      is_swappable_with<_Tp, _Up>::value;
	
	  /// is_nothrow_swappable_with_v
	  template<typename _Tp, typename _Up>
	    _GLIBCXX17_INLINE constexpr bool is_nothrow_swappable_with_v =
	      is_nothrow_swappable_with<_Tp, _Up>::value;
	#endif // __cplusplus >= 201402L
	
	#endif// c++1z or gnu++11
	
	  // __is_invocable (std::is_invocable for C++11)
	
	  template<typename _Result, typename _Ret, typename = void>
	    struct __is_invocable_impl : false_type { };
	
	  template<typename _Result, typename _Ret>
	    struct __is_invocable_impl<_Result, _Ret, __void_t<typename _Result::type>>
	    : __or_<is_void<_Ret>, is_convertible<typename _Result::type, _Ret>>::type
	    { };
	
	  template<typename _Fn, typename... _ArgTypes>
	    struct __is_invocable
	    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>::type
	    { };
	
	  template<typename _Fn, typename _Tp, typename... _Args>
	    constexpr bool __call_is_nt(__invoke_memfun_ref)
	    {
	      using _Up = typename __inv_unwrap<_Tp>::type;
	      return noexcept((std::declval<_Up>().*std::declval<_Fn>())(
		    std::declval<_Args>()...));
	    }
	
	  template<typename _Fn, typename _Tp, typename... _Args>
	    constexpr bool __call_is_nt(__invoke_memfun_deref)
	    {
	      return noexcept(((*std::declval<_Tp>()).*std::declval<_Fn>())(
		    std::declval<_Args>()...));
	    }
	
	  template<typename _Fn, typename _Tp>
	    constexpr bool __call_is_nt(__invoke_memobj_ref)
	    {
	      using _Up = typename __inv_unwrap<_Tp>::type;
	      return noexcept(std::declval<_Up>().*std::declval<_Fn>());
	    }
	
	  template<typename _Fn, typename _Tp>
	    constexpr bool __call_is_nt(__invoke_memobj_deref)
	    {
	      return noexcept((*std::declval<_Tp>()).*std::declval<_Fn>());
	    }
	
	  template<typename _Fn, typename... _Args>
	    constexpr bool __call_is_nt(__invoke_other)
	    {
	      return noexcept(std::declval<_Fn>()(std::declval<_Args>()...));
	    }
	
	  template<typename _Result, typename _Fn, typename... _Args>
	    struct __call_is_nothrow
	    : __bool_constant<
		std::__call_is_nt<_Fn, _Args...>(typename _Result::__invoke_type{})
	      >
	    { };
	
	  template<typename _Fn, typename... _Args>
	    using __call_is_nothrow_
	      = __call_is_nothrow<__invoke_result<_Fn, _Args...>, _Fn, _Args...>;
	
	  // __is_nothrow_invocable (std::is_nothrow_invocable for C++11)
	  template<typename _Fn, typename... _Args>
	    struct __is_nothrow_invocable
	    : __and_<__is_invocable<_Fn, _Args...>,
	             __call_is_nothrow_<_Fn, _Args...>>::type
	    { };
	
	  struct __nonesuch {
	    __nonesuch() = delete;
	    ~__nonesuch() = delete;
	    __nonesuch(__nonesuch const&) = delete;
	    void operator=(__nonesuch const&) = delete;
	  };
	
	#if __cplusplus >= 201703L
	# define __cpp_lib_is_invocable 201703
	
	  /// std::invoke_result
	  template<typename _Functor, typename... _ArgTypes>
	    struct invoke_result
	    : public __invoke_result<_Functor, _ArgTypes...>
	    { };
	
	  /// std::invoke_result_t
	  template<typename _Fn, typename... _Args>
	    using invoke_result_t = typename invoke_result<_Fn, _Args...>::type;
	
	  /// std::is_invocable
	  template<typename _Fn, typename... _ArgTypes>
	    struct is_invocable
	    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>::type
	    { };
	
	  /// std::is_invocable_r
	  template<typename _Ret, typename _Fn, typename... _ArgTypes>
	    struct is_invocable_r
	    : __is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, _Ret>::type
	    { };
	
	  /// std::is_nothrow_invocable
	  template<typename _Fn, typename... _ArgTypes>
	    struct is_nothrow_invocable
	    : __and_<__is_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, void>,
	             __call_is_nothrow_<_Fn, _ArgTypes...>>::type
	    { };
	
	  template<typename _Result, typename _Ret, typename = void>
	    struct __is_nt_invocable_impl : false_type { };
	
	  template<typename _Result, typename _Ret>
	    struct __is_nt_invocable_impl<_Result, _Ret,
					  __void_t<typename _Result::type>>
	    : __or_<is_void<_Ret>,
		    __and_<is_convertible<typename _Result::type, _Ret>,
			   is_nothrow_constructible<_Ret, typename _Result::type>>>
	    { };
	
	  /// std::is_nothrow_invocable_r
	  template<typename _Ret, typename _Fn, typename... _ArgTypes>
	    struct is_nothrow_invocable_r
	    : __and_<__is_nt_invocable_impl<__invoke_result<_Fn, _ArgTypes...>, _Ret>,
	             __call_is_nothrow_<_Fn, _ArgTypes...>>::type
	    { };
	
	  /// std::is_invocable_v
	  template<typename _Fn, typename... _Args>
	    inline constexpr bool is_invocable_v = is_invocable<_Fn, _Args...>::value;
	
	  /// std::is_nothrow_invocable_v
	  template<typename _Fn, typename... _Args>
	    inline constexpr bool is_nothrow_invocable_v
	      = is_nothrow_invocable<_Fn, _Args...>::value;
	
	  /// std::is_invocable_r_v
	  template<typename _Fn, typename... _Args>
	    inline constexpr bool is_invocable_r_v
	      = is_invocable_r<_Fn, _Args...>::value;
	
	  /// std::is_nothrow_invocable_r_v
	  template<typename _Fn, typename... _Args>
	    inline constexpr bool is_nothrow_invocable_r_v
	      = is_nothrow_invocable_r<_Fn, _Args...>::value;
	#endif // C++17
	
	#if __cplusplus >= 201703L
	# define __cpp_lib_type_trait_variable_templates 201510L
	template <typename _Tp>
	  inline constexpr bool is_void_v = is_void<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_null_pointer_v = is_null_pointer<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_integral_v = is_integral<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_floating_point_v = is_floating_point<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_array_v = is_array<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_pointer_v = is_pointer<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_lvalue_reference_v =
	    is_lvalue_reference<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_rvalue_reference_v =
	    is_rvalue_reference<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_member_object_pointer_v =
	    is_member_object_pointer<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_member_function_pointer_v =
	    is_member_function_pointer<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_enum_v = is_enum<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_union_v = is_union<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_class_v = is_class<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_function_v = is_function<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_reference_v = is_reference<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_arithmetic_v = is_arithmetic<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_fundamental_v = is_fundamental<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_object_v = is_object<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_scalar_v = is_scalar<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_compound_v = is_compound<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_member_pointer_v = is_member_pointer<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_const_v = is_const<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_volatile_v = is_volatile<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivial_v = is_trivial<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_copyable_v =
	    is_trivially_copyable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_standard_layout_v = is_standard_layout<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_pod_v = is_pod<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_literal_type_v = is_literal_type<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_empty_v = is_empty<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_polymorphic_v = is_polymorphic<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_abstract_v = is_abstract<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_final_v = is_final<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_signed_v = is_signed<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_unsigned_v = is_unsigned<_Tp>::value;
	template <typename _Tp, typename... _Args>
	  inline constexpr bool is_constructible_v =
	    is_constructible<_Tp, _Args...>::value;
	template <typename _Tp>
	  inline constexpr bool is_default_constructible_v =
	    is_default_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_copy_constructible_v =
	    is_copy_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_move_constructible_v =
	    is_move_constructible<_Tp>::value;
	template <typename _Tp, typename _Up>
	  inline constexpr bool is_assignable_v = is_assignable<_Tp, _Up>::value;
	template <typename _Tp>
	  inline constexpr bool is_copy_assignable_v = is_copy_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_move_assignable_v = is_move_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_destructible_v = is_destructible<_Tp>::value;
	template <typename _Tp, typename... _Args>
	  inline constexpr bool is_trivially_constructible_v =
	    is_trivially_constructible<_Tp, _Args...>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_default_constructible_v =
	    is_trivially_default_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_copy_constructible_v =
	    is_trivially_copy_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_move_constructible_v =
	    is_trivially_move_constructible<_Tp>::value;
	template <typename _Tp, typename _Up>
	  inline constexpr bool is_trivially_assignable_v =
	    is_trivially_assignable<_Tp, _Up>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_copy_assignable_v =
	    is_trivially_copy_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_move_assignable_v =
	    is_trivially_move_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_trivially_destructible_v =
	    is_trivially_destructible<_Tp>::value;
	template <typename _Tp, typename... _Args>
	  inline constexpr bool is_nothrow_constructible_v =
	    is_nothrow_constructible<_Tp, _Args...>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_default_constructible_v =
	    is_nothrow_default_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_copy_constructible_v =
	    is_nothrow_copy_constructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_move_constructible_v =
	    is_nothrow_move_constructible<_Tp>::value;
	template <typename _Tp, typename _Up>
	  inline constexpr bool is_nothrow_assignable_v =
	    is_nothrow_assignable<_Tp, _Up>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_copy_assignable_v =
	    is_nothrow_copy_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_move_assignable_v =
	    is_nothrow_move_assignable<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool is_nothrow_destructible_v =
	    is_nothrow_destructible<_Tp>::value;
	template <typename _Tp>
	  inline constexpr bool has_virtual_destructor_v =
	    has_virtual_destructor<_Tp>::value;
	template <typename _Tp>
	  inline constexpr size_t alignment_of_v = alignment_of<_Tp>::value;
	template <typename _Tp>
	  inline constexpr size_t rank_v = rank<_Tp>::value;
	template <typename _Tp, unsigned _Idx = 0>
	  inline constexpr size_t extent_v = extent<_Tp, _Idx>::value;
	template <typename _Tp, typename _Up>
	  inline constexpr bool is_same_v = is_same<_Tp, _Up>::value;
	template <typename _Base, typename _Derived>
	  inline constexpr bool is_base_of_v = is_base_of<_Base, _Derived>::value;
	template <typename _From, typename _To>
	  inline constexpr bool is_convertible_v = is_convertible<_From, _To>::value;
	
	#ifdef _GLIBCXX_HAVE_BUILTIN_HAS_UNIQ_OBJ_REP
	# define __cpp_lib_has_unique_object_representations 201606
	  /// has_unique_object_representations
	  template<typename _Tp>
	    struct has_unique_object_representations
	    : bool_constant<__has_unique_object_representations(
	      remove_cv_t<remove_all_extents_t<_Tp>>
	      )>
	    { };
	
	  template<typename _Tp>
	    inline constexpr bool has_unique_object_representations_v
	      = has_unique_object_representations<_Tp>::value;
	#endif
	
	#ifdef _GLIBCXX_HAVE_BUILTIN_IS_AGGREGATE
	# define __cpp_lib_is_aggregate 201703
	  /// is_aggregate
	  template<typename _Tp>
	    struct is_aggregate
	    : bool_constant<__is_aggregate(remove_cv_t<_Tp>)> { };
	
	  /// is_aggregate_v
	  template<typename _Tp>
	    inline constexpr bool is_aggregate_v = is_aggregate<_Tp>::value;
	#endif
	#endif // C++17
	
	#if __cplusplus > 201703L
	  /// Remove references and cv-qualifiers.
	  template<typename _Tp>
	    struct remove_cvref
	    {
	      using type = __remove_cvref_t<_Tp>;
	    };
	
	  template<typename _Tp>
	    using remove_cvref_t = __remove_cvref_t<_Tp>;
	
	  /// Identity metafunction.
	  template<typename _Tp>
	    struct type_identity { using type = _Tp; };
	
	  template<typename _Tp>
	    using type_identity_t = typename type_identity<_Tp>::type;
	
	  /// Unwrap a reference_wrapper
	  template<typename _Tp>
	    struct unwrap_reference { using type = _Tp; };
	
	  template<typename _Tp>
	    struct unwrap_reference<reference_wrapper<_Tp>> { using type = _Tp&; };
	
	  template<typename _Tp>
	    using unwrap_reference_t = typename unwrap_reference<_Tp>::type;
	
	  /// Decay type and if it's a reference_wrapper, unwrap it
	  template<typename _Tp>
	    struct unwrap_ref_decay { using type = unwrap_reference_t<decay_t<_Tp>>; };
	
	  template<typename _Tp>
	    using unwrap_ref_decay_t = typename unwrap_ref_decay<_Tp>::type;
	
	#define __cpp_lib_bounded_array_traits 201902L
	
	  /// True for a type that is an array of known bound.
	  template<typename _Tp>
	    struct is_bounded_array
	    : public __is_array_known_bounds<_Tp>
	    { };
	
	  /// True for a type that is an array of unknown bound.
	  template<typename _Tp>
	    struct is_unbounded_array
	    : public __is_array_unknown_bounds<_Tp>
	    { };
	
	  template<typename _Tp>
	    inline constexpr bool is_bounded_array_v
	      = is_bounded_array<_Tp>::value;
	
	  template<typename _Tp>
	    inline constexpr bool is_unbounded_array_v
	      = is_unbounded_array<_Tp>::value;
	
	#ifdef _GLIBCXX_HAVE_BUILTIN_IS_CONSTANT_EVALUATED
	
	#define __cpp_lib_is_constant_evaluated 201811L
	
	  constexpr inline bool
	  is_constant_evaluated() noexcept
	  { return __builtin_is_constant_evaluated(); }
	#endif
	
	#endif // C++2a
	
	_GLIBCXX_END_NAMESPACE_VERSION
	} // namespace std
	
	#endif  // C++11
	
	#endif  // _GLIBCXX_TYPE_TRAITS