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 #ifndef BOOST_MP11_ALGORITHM_HPP_INCLUDED
 #define BOOST_MP11_ALGORITHM_HPP_INCLUDED
 
 //  Copyright 2015-2019 Peter Dimov
 //
 //  Distributed under the Boost Software License, Version 1.0.
 //
 //  See accompanying file LICENSE_1_0.txt or copy at
 //  http://www.boost.org/LICENSE_1_0.txt
 
 #include <boost/mp11/list.hpp>
 #include <boost/mp11/set.hpp>
 #include <boost/mp11/integral.hpp>
 #include <boost/mp11/utility.hpp>
 #include <boost/mp11/function.hpp>
 #include <boost/mp11/detail/mp_count.hpp>
 #include <boost/mp11/detail/mp_plus.hpp>
 #include <boost/mp11/detail/mp_map_find.hpp>
 #include <boost/mp11/detail/mp_with_index.hpp>
 #include <boost/mp11/detail/mp_fold.hpp>
 #include <boost/mp11/detail/mp_min_element.hpp>
 #include <boost/mp11/detail/mp_copy_if.hpp>
 #include <boost/mp11/detail/mp_remove_if.hpp>
 #include <boost/mp11/detail/config.hpp>
 #include <boost/mp11/integer_sequence.hpp>
 #include <type_traits>
 #include <utility>
 
 namespace boost
 {
 namespace mp11
 {
 
 // mp_transform<F, L...>
 namespace detail
 {
 
 template<template<class...> class F, class... L> struct mp_transform_impl
 {
 };
 
 template<template<class...> class F, template<class...> class L, class... T> struct mp_transform_impl<F, L<T...>>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
 
     template<class... U> struct f { using type = F<U...>; };
 
     using type = L<typename f<T>::type...>;
 
 #else
 
     using type = L<F<T>...>;
 
 #endif
 };
 
 template<template<class...> class F, template<class...> class L1, class... T1, template<class...> class L2, class... T2> struct mp_transform_impl<F, L1<T1...>, L2<T2...>>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
 
     template<class... U> struct f { using type = F<U...>; };
 
     using type = L1<typename f<T1, T2>::type...>;
 
 #else
 
     using type = L1<F<T1,T2>...>;
 
 #endif
 };
 
 template<template<class...> class F, template<class...> class L1, class... T1, template<class...> class L2, class... T2, template<class...> class L3, class... T3> struct mp_transform_impl<F, L1<T1...>, L2<T2...>, L3<T3...>>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
 
     template<class... U> struct f { using type = F<U...>; };
 
     using type = L1<typename f<T1, T2, T3>::type...>;
 
 #else
 
     using type = L1<F<T1,T2,T3>...>;
 
 #endif
 };
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, == 1900 ) || BOOST_MP11_WORKAROUND( BOOST_MP11_GCC, < 40800 )
 
 template<class... L> using mp_same_size_1 = mp_same<mp_size<L>...>;
 template<class... L> struct mp_same_size_2: mp_defer<mp_same_size_1, L...> {};
 
 #endif
 
 struct list_size_mismatch
 {
 };
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_CUDA, >= 9000000 && BOOST_MP11_CUDA < 10000000 )
 
 template<template<class...> class F, class... L> struct mp_transform_cuda_workaround
 {
     using type = mp_if<mp_same<mp_size<L>...>, detail::mp_transform_impl<F, L...>, detail::list_size_mismatch>;
 };
 
 #endif
 
 } // namespace detail
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, == 1900 ) || BOOST_MP11_WORKAROUND( BOOST_MP11_GCC, < 40800 )
 
 template<template<class...> class F, class... L> using mp_transform = typename mp_if<typename detail::mp_same_size_2<L...>::type, detail::mp_transform_impl<F, L...>, detail::list_size_mismatch>::type;
 
 #else
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_CUDA, >= 9000000 && BOOST_MP11_CUDA < 10000000 )
 
 template<template<class...> class F, class... L> using mp_transform = typename detail::mp_transform_cuda_workaround< F, L...>::type::type;
 
 #else
 
 template<template<class...> class F, class... L> using mp_transform = typename mp_if<mp_same<mp_size<L>...>, detail::mp_transform_impl<F, L...>, detail::list_size_mismatch>::type;
 
 #endif
 
 #endif
 
 template<class Q, class... L> using mp_transform_q = mp_transform<Q::template fn, L...>;
 
 namespace detail
 {
 
 template<template<class...> class F, template<class...> class L1, class... T1, template<class...> class L2, class... T2, template<class...> class L3, class... T3, template<class...> class L4, class... T4, class... L> struct mp_transform_impl<F, L1<T1...>, L2<T2...>, L3<T3...>, L4<T4...>, L...>
 {
     using A1 = L1<mp_list<T1, T2, T3, T4>...>;
 
     template<class V, class T> using _f = mp_transform<mp_push_back, V, T>;
 
     using A2 = mp_fold<mp_list<L...>, A1, _f>;
 
     template<class T> using _g = mp_apply<F, T>;
 
     using type = mp_transform<_g, A2>;
 };
 
 } // namespace detail
 
 // mp_transform_if<P, F, L...>
 namespace detail
 {
 
 template<template<class...> class P, template<class...> class F, class... L> struct mp_transform_if_impl
 {
     // the stupid quote-unquote dance avoids "pack expansion used as argument for non-pack parameter of alias template"
 
     using Qp = mp_quote<P>;
     using Qf = mp_quote<F>;
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
 
     template<class... U> struct _f_ { using type = mp_eval_if_q<mp_not<mp_invoke_q<Qp, U...>>, mp_first<mp_list<U...>>, Qf, U...>; };
     template<class... U> using _f = typename _f_<U...>::type;
 
 #else
 
     template<class... U> using _f = mp_eval_if_q<mp_not<mp_invoke_q<Qp, U...>>, mp_first<mp_list<U...>>, Qf, U...>;
 
 #endif
 
     using type = mp_transform<_f, L...>;
 };
 
 } // namespace detail
 
 template<template<class...> class P, template<class...> class F, class... L> using mp_transform_if = typename detail::mp_transform_if_impl<P, F, L...>::type;
 template<class Qp, class Qf, class... L> using mp_transform_if_q = typename detail::mp_transform_if_impl<Qp::template fn, Qf::template fn, L...>::type;
 
 // mp_filter<P, L...>
 namespace detail
 {
 
 template<template<class...> class P, class L1, class... L> struct mp_filter_impl
 {
     using Qp = mp_quote<P>;
 
     template<class T1, class... T> using _f = mp_if< mp_invoke_q<Qp, T1, T...>, mp_list<T1>, mp_list<> >;
 
     using _t1 = mp_transform<_f, L1, L...>;
     using _t2 = mp_apply<mp_append, _t1>;
 
     using type = mp_assign<L1, _t2>;
 };
 
 } // namespace detail
 
 template<template<class...> class P, class... L> using mp_filter = typename detail::mp_filter_impl<P, L...>::type;
 template<class Q, class... L> using mp_filter_q = typename detail::mp_filter_impl<Q::template fn, L...>::type;
 
 // mp_fill<L, V>
 namespace detail
 {
 
 template<class L, class V> struct mp_fill_impl
 {
 // An error "no type named 'type'" here means that the L argument of mp_fill is not a list
 };
 
 template<template<class...> class L, class... T, class V> struct mp_fill_impl<L<T...>, V>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1900 )
 
     template<class...> struct _f { using type = V; };
     using type = L<typename _f<T>::type...>;
 
 #else
 
     template<class...> using _f = V;
     using type = L<_f<T>...>;
 
 #endif
 };
 
 #if defined(BOOST_MP11_HAS_TEMPLATE_AUTO)
 
 template<template<auto...> class L, auto... A, class V> struct mp_fill_impl<L<A...>, V>
 {
     using type = L<((void)A, V::value)...>;
 };
 
 #endif
 
 } // namespace detail
 
 template<class L, class V> using mp_fill = typename detail::mp_fill_impl<L, V>::type;
 
 // mp_contains<L, V>
 template<class L, class V> using mp_contains = mp_to_bool<mp_count<L, V>>;
 
 // mp_repeat(_c)<L, N>
 namespace detail
 {
 
 template<class L, std::size_t N> struct mp_repeat_c_impl
 {
     using _l1 = typename mp_repeat_c_impl<L, N/2>::type;
     using _l2 = typename mp_repeat_c_impl<L, N%2>::type;
 
     using type = mp_append<_l1, _l1, _l2>;
 };
 
 template<class L> struct mp_repeat_c_impl<L, 0>
 {
     using type = mp_clear<L>;
 };
 
 template<class L> struct mp_repeat_c_impl<L, 1>
 {
     using type = L;
 };
 
 } // namespace detail
 
 template<class L, std::size_t N> using mp_repeat_c = typename detail::mp_repeat_c_impl<L, N>::type;
 template<class L, class N> using mp_repeat = typename detail::mp_repeat_c_impl<L, std::size_t{ N::value }>::type;
 
 // mp_product<F, L...>
 namespace detail
 {
 
 template<template<class...> class F, class P, class... L> struct mp_product_impl_2
 {
 };
 
 template<template<class...> class F, class P> struct mp_product_impl_2<F, P>
 {
     using type = mp_list<mp_rename<P, F>>;
 };
 
 template<template<class...> class F, class P, template<class...> class L1, class... T1, class... L> struct mp_product_impl_2<F, P, L1<T1...>, L...>
 {
     using type = mp_append<typename mp_product_impl_2<F, mp_push_back<P, T1>, L...>::type...>;
 };
 
 template<template<class...> class F, class... L> struct mp_product_impl
 {
 };
 
 template<template<class...> class F> struct mp_product_impl<F>
 {
     using type = mp_list< F<> >;
 };
 
 template<template<class...> class F, class L1, class... L> struct mp_product_impl<F, L1, L...>
 {
     using type = mp_assign<L1, typename mp_product_impl_2<F, mp_list<>, L1, L...>::type>;
 };
 
 } // namespace detail
 
 template<template<class...> class F, class... L> using mp_product = typename detail::mp_product_impl<F, L...>::type;
 template<class Q, class... L> using mp_product_q = typename detail::mp_product_impl<Q::template fn, L...>::type;
 
 // mp_drop(_c)<L, N>
 namespace detail
 {
 
 template<class L, class L2, class En> struct mp_drop_impl;
 
 template<template<class...> class L, class... T, template<class...> class L2, class... U> struct mp_drop_impl<L<T...>, L2<U...>, mp_true>
 {
     template<class... W> static mp_identity<L<W...>> f( U*..., mp_identity<W>*... );
 
     using R = decltype( f( static_cast<mp_identity<T>*>(0) ... ) );
 
     using type = typename R::type;
 };
 
 } // namespace detail
 
 template<class L, std::size_t N> using mp_drop_c = mp_assign<L, typename detail::mp_drop_impl<mp_rename<L, mp_list>, mp_repeat_c<mp_list<void>, N>, mp_bool<N <= mp_size<L>::value>>::type>;
 
 template<class L, class N> using mp_drop = mp_drop_c<L, std::size_t{ N::value }>;
 
 // mp_from_sequence<S, F>
 namespace detail
 {
 
 template<class S, class F> struct mp_from_sequence_impl;
 
 template<template<class T, T... I> class S, class U, U... J, class F> struct mp_from_sequence_impl<S<U, J...>, F>
 {
     using type = mp_list_c<U, (F::value + J)...>;
 };
 
 } // namespace detail
 
 template<class S, class F = mp_int<0>> using mp_from_sequence = typename detail::mp_from_sequence_impl<S, F>::type;
 
 // mp_iota(_c)<N, F>
 template<std::size_t N, std::size_t F = 0> using mp_iota_c = mp_from_sequence<make_index_sequence<N>, mp_size_t<F>>;
 template<class N, class F = mp_int<0>> using mp_iota = mp_from_sequence<make_integer_sequence<typename std::remove_const<decltype(N::value)>::type, N::value>, F>;
 
 // mp_at(_c)<L, I>
 namespace detail
 {
 
 template<class L, std::size_t I> struct mp_at_c_impl;
 
 #if defined(BOOST_MP11_HAS_TYPE_PACK_ELEMENT)
 
 template<template<class...> class L, class... T, std::size_t I> struct mp_at_c_impl<L<T...>, I>
 {
     using type = __type_pack_element<I, T...>;
 };
 
 #if defined(BOOST_MP11_HAS_TEMPLATE_AUTO)
 
 template<template<auto...> class L, auto... A, std::size_t I> struct mp_at_c_impl<L<A...>, I>
 {
     using type = __type_pack_element<I, mp_value<A>...>;
 };
 
 #endif
 
 #else
 
 template<class L, std::size_t I> struct mp_at_c_impl
 {
     using _map = mp_transform<mp_list, mp_iota<mp_size<L> >, mp_rename<L, mp_list>>;
     using type = mp_second<mp_map_find<_map, mp_size_t<I> > >;
 };
 
 #endif
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_CUDA, >= 9000000 && BOOST_MP11_CUDA < 10000000 )
 
 template<class L, std::size_t I> struct mp_at_c_cuda_workaround
 {
     using type = mp_if_c<(I < mp_size<L>::value), detail::mp_at_c_impl<L, I>, void>;
 };
 
 #endif
 
 } // namespace detail
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_CUDA, >= 9000000 && BOOST_MP11_CUDA < 10000000 )
 
 template<class L, std::size_t I> using mp_at_c = typename detail::mp_at_c_cuda_workaround< L, I >::type::type;
 
 #else
 
 template<class L, std::size_t I> using mp_at_c = typename mp_if_c<(I < mp_size<L>::value), detail::mp_at_c_impl<L, I>, void>::type;
 
 #endif
 
 template<class L, class I> using mp_at = mp_at_c<L, std::size_t{ I::value }>;
 
 // mp_take(_c)<L, N>
 namespace detail
 {
 
 template<std::size_t N, class L, class E = void> struct mp_take_c_impl
 {
 };
 
 template<template<class...> class L, class... T>
 struct mp_take_c_impl<0, L<T...>>
 {
     using type = L<>;
 };
 
 template<template<class...> class L, class T1, class... T>
 struct mp_take_c_impl<1, L<T1, T...>>
 {
     using type = L<T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class... T>
 struct mp_take_c_impl<2, L<T1, T2, T...>>
 {
     using type = L<T1, T2>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class... T>
 struct mp_take_c_impl<3, L<T1, T2, T3, T...>>
 {
     using type = L<T1, T2, T3>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class... T>
 struct mp_take_c_impl<4, L<T1, T2, T3, T4, T...>>
 {
     using type = L<T1, T2, T3, T4>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class... T>
 struct mp_take_c_impl<5, L<T1, T2, T3, T4, T5, T...>>
 {
     using type = L<T1, T2, T3, T4, T5>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class... T>
 struct mp_take_c_impl<6, L<T1, T2, T3, T4, T5, T6, T...>>
 {
     using type = L<T1, T2, T3, T4, T5, T6>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class... T>
 struct mp_take_c_impl<7, L<T1, T2, T3, T4, T5, T6, T7, T...>>
 {
     using type = L<T1, T2, T3, T4, T5, T6, T7>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class... T>
 struct mp_take_c_impl<8, L<T1, T2, T3, T4, T5, T6, T7, T8, T...>>
 {
     using type = L<T1, T2, T3, T4, T5, T6, T7, T8>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class... T>
 struct mp_take_c_impl<9, L<T1, T2, T3, T4, T5, T6, T7, T8, T9, T...>>
 {
     using type = L<T1, T2, T3, T4, T5, T6, T7, T8, T9>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class T10, class... T, std::size_t N>
 struct mp_take_c_impl<N, L<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T...>, typename std::enable_if<N >= 10>::type>
 {
     using type = mp_append<L<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10>, typename mp_take_c_impl<N-10, L<T...>>::type>;
 };
 
 } // namespace detail
 
 template<class L, std::size_t N> using mp_take_c = mp_assign<L, typename detail::mp_take_c_impl<N, mp_rename<L, mp_list>>::type>;
 template<class L, class N> using mp_take = mp_take_c<L, std::size_t{ N::value }>;
 
 // mp_back<L>
 template<class L> using mp_back = mp_at_c<L, mp_size<L>::value - 1>;
 
 // mp_pop_back<L>
 template<class L> using mp_pop_back = mp_take_c<L, mp_size<L>::value - 1>;
 
 // mp_replace<L, V, W>
 namespace detail
 {
 
 template<class L, class V, class W> struct mp_replace_impl;
 
 template<template<class...> class L, class... T, class V, class W> struct mp_replace_impl<L<T...>, V, W>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
     template<class A> struct _f { using type = mp_if<std::is_same<A, V>, W, A>; };
     using type = L<typename _f<T>::type...>;
 #else
     template<class A> using _f = mp_if<std::is_same<A, V>, W, A>;
     using type = L<_f<T>...>;
 #endif
 };
 
 } // namespace detail
 
 template<class L, class V, class W> using mp_replace = typename detail::mp_replace_impl<L, V, W>::type;
 
 // mp_replace_if<L, P, W>
 namespace detail
 {
 
 template<class L, template<class...> class P, class W> struct mp_replace_if_impl;
 
 template<template<class...> class L, class... T, template<class...> class P, class W> struct mp_replace_if_impl<L<T...>, P, W>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
     template<class U> struct _f { using type = mp_if<P<U>, W, U>; };
     using type = L<typename _f<T>::type...>;
 #else
     template<class U> using _f = mp_if<P<U>, W, U>;
     using type = L<_f<T>...>;
 #endif
 };
 
 } // namespace detail
 
 template<class L, template<class...> class P, class W> using mp_replace_if = typename detail::mp_replace_if_impl<L, P, W>::type;
 template<class L, class Q, class W> using mp_replace_if_q = mp_replace_if<L, Q::template fn, W>;
 
 // mp_copy_if<L, P>
 //   in detail/mp_copy_if.hpp
 
 // mp_remove<L, V>
 namespace detail
 {
 
 template<class L, class V> struct mp_remove_impl;
 
 template<template<class...> class L, class... T, class V> struct mp_remove_impl<L<T...>, V>
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, < 1920 )
     template<class U> struct _f { using type = mp_if<std::is_same<U, V>, mp_list<>, mp_list<U>>; };
     using type = mp_append<L<>, typename _f<T>::type...>;
 #else
     template<class U> using _f = mp_if<std::is_same<U, V>, mp_list<>, mp_list<U>>;
     using type = mp_append<L<>, _f<T>...>;
 #endif
 };
 
 } // namespace detail
 
 template<class L, class V> using mp_remove = typename detail::mp_remove_impl<L, V>::type;
 
 // mp_remove_if<L, P>
 //   in detail/mp_remove_if.hpp
 
 // mp_flatten<L, L2 = mp_clear<L>>
 namespace detail
 {
 
 template<class L2> struct mp_flatten_impl
 {
     template<class T> using fn = mp_if<mp_similar<L2, T>, T, mp_list<T>>;
 };
 
 } // namespace detail
 
 template<class L, class L2 = mp_clear<L>> using mp_flatten = mp_apply<mp_append, mp_push_front<mp_transform_q<detail::mp_flatten_impl<L2>, L>, mp_clear<L>>>;
 
 // mp_partition<L, P>
 namespace detail
 {
 
 template<class L, template<class...> class P> struct mp_partition_impl;
 
 template<template<class...> class L, class... T, template<class...> class P> struct mp_partition_impl<L<T...>, P>
 {
     using type = L<mp_copy_if<L<T...>, P>, mp_remove_if<L<T...>, P>>;
 };
 
 } // namespace detail
 
 template<class L, template<class...> class P> using mp_partition = typename detail::mp_partition_impl<L, P>::type;
 template<class L, class Q> using mp_partition_q = mp_partition<L, Q::template fn>;
 
 // mp_sort<L, P>
 namespace detail
 {
 
 template<class L, template<class...> class P> struct mp_sort_impl;
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T, template<class...> class P> struct mp_sort_impl<L<T...>, P>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = L<>;
 };
 
 #else
 
 template<template<class...> class L, template<class...> class P> struct mp_sort_impl<L<>, P>
 {
     using type = L<>;
 };
 
 #endif
 
 template<template<class...> class L, class T1, template<class...> class P> struct mp_sort_impl<L<T1>, P>
 {
     using type = L<T1>;
 };
 
 template<template<class...> class L, class T1, class... T, template<class...> class P> struct mp_sort_impl<L<T1, T...>, P>
 {
     template<class U> using F = P<U, T1>;
 
     using part = mp_partition<L<T...>, F>;
 
     using S1 = typename mp_sort_impl<mp_first<part>, P>::type;
     using S2 = typename mp_sort_impl<mp_second<part>, P>::type;
 
     using type = mp_append<mp_push_back<S1, T1>, S2>;
 };
 
 } // namespace detail
 
 template<class L, template<class...> class P> using mp_sort = typename detail::mp_sort_impl<L, P>::type;
 template<class L, class Q> using mp_sort_q = mp_sort<L, Q::template fn>;
 
 // mp_nth_element(_c)<L, I, P>
 namespace detail
 {
 
 template<class L, std::size_t I, template<class...> class P> struct mp_nth_element_impl;
 
 template<template<class...> class L, class T1, std::size_t I, template<class...> class P> struct mp_nth_element_impl<L<T1>, I, P>
 {
     static_assert( I == 0, "mp_nth_element index out of range" );
     using type = T1;
 };
 
 template<template<class...> class L, class T1, class... T, std::size_t I, template<class...> class P> struct mp_nth_element_impl<L<T1, T...>, I, P>
 {
     static_assert( I < 1 + sizeof...(T), "mp_nth_element index out of range" );
 
     template<class U> using F = P<U, T1>;
 
     using part = mp_partition<L<T...>, F>;
 
     using L1 = mp_first<part>;
     static std::size_t const N1 = mp_size<L1>::value;
 
     using L2 = mp_second<part>;
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_CUDA, >= 9000000 && BOOST_MP11_CUDA < 10000000 )
 
     struct detail
     {
         struct mp_nth_element_impl_cuda_workaround
         {
             using type = mp_cond<
 
                 mp_bool<(I < N1)>, mp_nth_element_impl<L1, I, P>,
                 mp_bool<(I == N1)>, mp_identity<T1>,
                 mp_true, mp_nth_element_impl<L2, I - N1 - 1, P>
 
             >;
         };
     };
 
     using type = typename detail::mp_nth_element_impl_cuda_workaround::type::type;
 
 #else
 
     using type = typename mp_cond<
 
         mp_bool<(I < N1)>, mp_nth_element_impl<L1, I, P>,
         mp_bool<(I == N1)>, mp_identity<T1>,
         mp_true, mp_nth_element_impl<L2, I - N1 - 1, P>
 
     >::type;
 
 #endif
 };
 
 } // namespace detail
 
 template<class L, std::size_t I, template<class...> class P> using mp_nth_element_c = typename detail::mp_nth_element_impl<L, I, P>::type;
 template<class L, class I, template<class...> class P> using mp_nth_element = typename detail::mp_nth_element_impl<L, std::size_t{ I::value }, P>::type;
 template<class L, class I, class Q> using mp_nth_element_q = mp_nth_element<L, I, Q::template fn>;
 
 // mp_find<L, V>
 namespace detail
 {
 
 template<class L, class V> struct mp_find_impl;
 
 #if BOOST_MP11_CLANG && defined( BOOST_MP11_HAS_FOLD_EXPRESSIONS )
 
 struct mp_index_holder
 {
     std::size_t i_;
     bool f_;
 };
 
 constexpr inline mp_index_holder operator+( mp_index_holder const & v, bool f )
 {
     if( v.f_ )
     {
         return v;
     }
     else if( f )
     {
         return { v.i_, true };
     }
     else
     {
         return { v.i_ + 1, false };
     }
 }
 
 template<template<class...> class L, class... T, class V> struct mp_find_impl<L<T...>, V>
 {
     static constexpr mp_index_holder _v{ 0, false };
     using type = mp_size_t< (_v + ... + std::is_same<T, V>::value).i_ >;
 };
 
 #elif !defined( BOOST_MP11_NO_CONSTEXPR )
 
 template<template<class...> class L, class V> struct mp_find_impl<L<>, V>
 {
     using type = mp_size_t<0>;
 };
 
 #if defined( BOOST_MP11_HAS_CXX14_CONSTEXPR )
 
 constexpr std::size_t cx_find_index( bool const * first, bool const * last )
 {
     std::size_t m = 0;
 
     while( first != last && !*first )
     {
         ++m;
         ++first;
     }
 
     return m;
 }
 
 #else
 
 constexpr std::size_t cx_find_index( bool const * first, bool const * last )
 {
     return first == last || *first? 0: 1 + cx_find_index( first + 1, last );
 }
 
 #endif
 
 template<template<class...> class L, class... T, class V> struct mp_find_impl<L<T...>, V>
 {
     static constexpr bool _v[] = { std::is_same<T, V>::value... };
     using type = mp_size_t< cx_find_index( _v, _v + sizeof...(T) ) >;
 };
 
 #else
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T, class V> struct mp_find_impl<L<T...>, V>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = mp_size_t<0>;
 };
 
 #else
 
 template<template<class...> class L, class V> struct mp_find_impl<L<>, V>
 {
     using type = mp_size_t<0>;
 };
 
 #endif
 
 template<template<class...> class L, class... T, class V> struct mp_find_impl<L<V, T...>, V>
 {
     using type = mp_size_t<0>;
 };
 
 template<template<class...> class L, class T1, class... T, class V> struct mp_find_impl<L<T1, T...>, V>
 {
     using _r = typename mp_find_impl<mp_list<T...>, V>::type;
     using type = mp_size_t<1 + _r::value>;
 };
 
 #endif
 
 } // namespace detail
 
 template<class L, class V> using mp_find = typename detail::mp_find_impl<L, V>::type;
 
 // mp_find_if<L, P>
 namespace detail
 {
 
 template<class L, template<class...> class P> struct mp_find_if_impl;
 
 #if BOOST_MP11_CLANG && defined( BOOST_MP11_HAS_FOLD_EXPRESSIONS )
 
 template<template<class...> class L, class... T, template<class...> class P> struct mp_find_if_impl<L<T...>, P>
 {
     static constexpr mp_index_holder _v{ 0, false };
     using type = mp_size_t< (_v + ... + P<T>::value).i_ >;
 };
 
 #elif !defined( BOOST_MP11_NO_CONSTEXPR )
 
 template<template<class...> class L, template<class...> class P> struct mp_find_if_impl<L<>, P>
 {
     using type = mp_size_t<0>;
 };
 
 template<template<class...> class L, class... T, template<class...> class P> struct mp_find_if_impl<L<T...>, P>
 {
     static constexpr bool _v[] = { P<T>::value... };
     using type = mp_size_t< cx_find_index( _v, _v + sizeof...(T) ) >;
 };
 
 #else
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T, template<class...> class P> struct mp_find_if_impl<L<T...>, P>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = mp_size_t<0>;
 };
 
 #else
 
 template<template<class...> class L, template<class...> class P> struct mp_find_if_impl<L<>, P>
 {
     using type = mp_size_t<0>;
 };
 
 #endif
 
 template<class L, template<class...> class P> struct mp_find_if_impl_2
 {
     using _r = typename mp_find_if_impl<L, P>::type;
     using type = mp_size_t<1 + _r::value>;
 };
 
 template<template<class...> class L, class T1, class... T, template<class...> class P> struct mp_find_if_impl<L<T1, T...>, P>
 {
     using type = typename mp_if<P<T1>, mp_identity<mp_size_t<0>>, mp_find_if_impl_2<mp_list<T...>, P>>::type;
 };
 
 #endif
 
 } // namespace detail
 
 template<class L, template<class...> class P> using mp_find_if = typename detail::mp_find_if_impl<L, P>::type;
 template<class L, class Q> using mp_find_if_q = mp_find_if<L, Q::template fn>;
 
 // mp_reverse<L>
 namespace detail
 {
 
 template<class L> struct mp_reverse_impl;
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T> struct mp_reverse_impl<L<T...>>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = L<>;
 };
 
 #else
 
 template<template<class...> class L> struct mp_reverse_impl<L<>>
 {
     using type = L<>;
 };
 
 #endif
 
 template<template<class...> class L, class T1> struct mp_reverse_impl<L<T1>>
 {
     using type = L<T1>;
 };
 
 template<template<class...> class L, class T1, class T2> struct mp_reverse_impl<L<T1, T2>>
 {
     using type = L<T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3> struct mp_reverse_impl<L<T1, T2, T3>>
 {
     using type = L<T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4> struct mp_reverse_impl<L<T1, T2, T3, T4>>
 {
     using type = L<T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5> struct mp_reverse_impl<L<T1, T2, T3, T4, T5>>
 {
     using type = L<T5, T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6> struct mp_reverse_impl<L<T1, T2, T3, T4, T5, T6>>
 {
     using type = L<T6, T5, T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7> struct mp_reverse_impl<L<T1, T2, T3, T4, T5, T6, T7>>
 {
     using type = L<T7, T6, T5, T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8> struct mp_reverse_impl<L<T1, T2, T3, T4, T5, T6, T7, T8>>
 {
     using type = L<T8, T7, T6, T5, T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9> struct mp_reverse_impl<L<T1, T2, T3, T4, T5, T6, T7, T8, T9>>
 {
     using type = L<T9, T8, T7, T6, T5, T4, T3, T2, T1>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class T10, class... T> struct mp_reverse_impl<L<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T...>>
 {
     using type = mp_push_back<typename mp_reverse_impl<L<T...>>::type, T10, T9, T8, T7, T6, T5, T4, T3, T2, T1>;
 };
 
 } // namespace detail
 
 template<class L> using mp_reverse = typename detail::mp_reverse_impl<L>::type;
 
 // mp_fold<L, V, F>
 //   in detail/mp_fold.hpp
 
 // mp_reverse_fold<L, V, F>
 namespace detail
 {
 
 template<class L, class V, template<class...> class F> struct mp_reverse_fold_impl;
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T, class V, template<class...> class F> struct mp_reverse_fold_impl<L<T...>, V, F>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = V;
 };
 
 #else
 
 template<template<class...> class L, class V, template<class...> class F> struct mp_reverse_fold_impl<L<>, V, F>
 {
     using type = V;
 };
 
 #endif
 
 template<template<class...> class L, class T1, class... T, class V, template<class...> class F> struct mp_reverse_fold_impl<L<T1, T...>, V, F>
 {
     using rest = typename mp_reverse_fold_impl<L<T...>, V, F>::type;
     using type = F<T1, rest>;
 };
 
 template<template<class...> class L, class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8, class T9, class T10, class... T, class V, template<class...> class F> struct mp_reverse_fold_impl<L<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T...>, V, F>
 {
     using rest = typename mp_reverse_fold_impl<L<T...>, V, F>::type;
     using type = F<T1, F<T2, F<T3, F<T4, F<T5, F<T6, F<T7, F<T8, F<T9, F<T10, rest> > > > > > > > > >;
 };
 
 } // namespace detail
 
 template<class L, class V, template<class...> class F> using mp_reverse_fold = typename detail::mp_reverse_fold_impl<L, V, F>::type;
 template<class L, class V, class Q> using mp_reverse_fold_q = mp_reverse_fold<L, V, Q::template fn>;
 
 // mp_unique<L>
 namespace detail
 {
 
 template<class L> struct mp_unique_impl;
 
 template<template<class...> class L, class... T> struct mp_unique_impl<L<T...>>
 {
     using type = mp_set_push_back<L<>, T...>;
 };
 
 } // namespace detail
 
 template<class L> using mp_unique = typename detail::mp_unique_impl<L>::type;
 
 // mp_unique_if<L, P>
 namespace detail
 {
 
 template<template<class...> class P> struct mp_unique_if_push_back
 {
     template<class...> struct impl
     {
     };
 
     template<template<class...> class L, class... Ts, class T>
     struct impl<L<Ts...>, T>
     {
         using type = mp_if<mp_any<P<Ts, T>...>, L<Ts...>, L<Ts..., T>>;
     };
 
     template<class... T> using fn = typename impl<T...>::type;
 };
 
 } // namespace detail
 
 template<class L, template<class...> class P>
 using mp_unique_if = mp_fold_q<L, mp_clear<L>, detail::mp_unique_if_push_back<P>>;
 
 template<class L, class Q> using mp_unique_if_q = mp_unique_if<L, Q::template fn>;
 
 // mp_all_of<L, P>
 template<class L, template<class...> class P> using mp_all_of = mp_bool< mp_count_if<L, P>::value == mp_size<L>::value >;
 template<class L, class Q> using mp_all_of_q = mp_all_of<L, Q::template fn>;
 
 // mp_none_of<L, P>
 template<class L, template<class...> class P> using mp_none_of = mp_bool< mp_count_if<L, P>::value == 0 >;
 template<class L, class Q> using mp_none_of_q = mp_none_of<L, Q::template fn>;
 
 // mp_any_of<L, P>
 template<class L, template<class...> class P> using mp_any_of = mp_bool< mp_count_if<L, P>::value != 0 >;
 template<class L, class Q> using mp_any_of_q = mp_any_of<L, Q::template fn>;
 
 // mp_replace_at_c<L, I, W>
 namespace detail
 {
 
 template<class L, class I, class W> struct mp_replace_at_impl
 {
     static_assert( I::value >= 0, "mp_replace_at<L, I, W>: I must not be negative" );
 
     template<class T1, class T2> using _p = std::is_same<T2, mp_size_t<I::value>>;
     template<class T1, class T2> using _f = W;
 
     using type = mp_transform_if<_p, _f, L, mp_iota<mp_size<L> > >;
 };
 
 } // namespace detail
 
 template<class L, class I, class W> using mp_replace_at = typename detail::mp_replace_at_impl<L, I, W>::type;
 template<class L, std::size_t I, class W> using mp_replace_at_c = typename detail::mp_replace_at_impl<L, mp_size_t<I>, W>::type;
 
 //mp_for_each<L>(f)
 namespace detail
 {
 
 template<class... T, class F> BOOST_MP11_CONSTEXPR F mp_for_each_impl( mp_list<T...>, F && f )
 {
     using A = int[sizeof...(T)];
     return (void)A{ ((void)f(T()), 0)... }, std::forward<F>(f);
 }
 
 template<class F> BOOST_MP11_CONSTEXPR F mp_for_each_impl( mp_list<>, F && f )
 {
     return std::forward<F>(f);
 }
 
 } // namespace detail
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, >= 1900 )
 
 // msvc has a limit of 1024
 
 template<class L, class F> BOOST_MP11_CONSTEXPR mp_if_c<mp_size<L>::value <= 1024, F> mp_for_each( F && f )
 {
     return detail::mp_for_each_impl( mp_rename<L, mp_list>(), std::forward<F>(f) );
 }
 
 template<class L, class F> BOOST_MP11_CONSTEXPR mp_if_c<mp_size<L>::value >= 1025, F> mp_for_each( F && f )
 {
     using L2 = mp_rename<L, mp_list>;
 
     using L3 = mp_take_c<L2, 1024>;
     using L4 = mp_drop_c<L2, 1024>;
 
     return mp_for_each<L4>( mp_for_each<L3>( std::forward<F>(f) ) );
 }
 
 #else
 
 template<class L, class F> BOOST_MP11_CONSTEXPR F mp_for_each( F && f )
 {
     return detail::mp_for_each_impl( mp_rename<L, mp_list>(), std::forward<F>(f) );
 }
 
 #endif
 
 // mp_insert<L, I, T...>
 template<class L, class I, class... T> using mp_insert = mp_append<mp_take<L, I>, mp_push_front<mp_drop<L, I>, T...>>;
 
 // mp_insert_c<L, I, T...>
 template<class L, std::size_t I, class... T> using mp_insert_c = mp_append<mp_take_c<L, I>, mp_push_front<mp_drop_c<L, I>, T...>>;
 
 // mp_erase<L, I, J>
 template<class L, class I, class J> using mp_erase = mp_append<mp_take<L, I>, mp_drop<L, J>>;
 
 // mp_erase_c<L, I, J>
 template<class L, std::size_t I, std::size_t J> using mp_erase_c = mp_append<mp_take_c<L, I>, mp_drop_c<L, J>>;
 
 // mp_starts_with<L1, L2>
 // contributed by Glen Joseph Fernandes (glenjofe@gmail.com)
 namespace detail {
 
 template<class L1, class L2>
 struct mp_starts_with_impl { };
 
 template<template<class...> class L1, class... T1, template<class...> class L2,
     class... T2>
 struct mp_starts_with_impl<L1<T1...>, L2<T2...> > {
     template<class L>
     static mp_false check(L);
 
     template<class... T>
     static mp_true check(mp_list<T2..., T...>);
 
     using type = decltype(check(mp_list<T1...>()));
 };
 
 } // namespace detail
 
 template<class L1, class L2>
 using mp_starts_with = typename detail::mp_starts_with_impl<L1, L2>::type;
 
 // mp_rotate_left(_c)<L, N>
 namespace detail
 {
 
 // limit divisor to 1 to avoid division by 0 and give a rotation of 0 for lists containing 0 or 1 elements
 template<std::size_t Ln, std::size_t N> using canonical_left_rotation = mp_size_t<N % (Ln == 0? 1: Ln)>;
 
 // perform right rotation as a left rotation by inverting the number of elements to rotate
 template<std::size_t Ln, std::size_t N> using canonical_right_rotation = mp_size_t<Ln - N % (Ln == 0? 1: Ln)>;
 
 // avoid errors when rotating fixed-sized lists by using mp_list for the transformation
 template<class L, class N, class L2 = mp_rename<L, mp_list>> using mp_rotate_impl = mp_assign<L, mp_append< mp_drop<L2, N>, mp_take<L2, N> >>;
 
 } // namespace detail
 
 template<class L, std::size_t N> using mp_rotate_left_c = detail::mp_rotate_impl<L, detail::canonical_left_rotation<mp_size<L>::value, N>>;
 template<class L, class N> using mp_rotate_left = mp_rotate_left_c<L, std::size_t{ N::value }>;
 
 // mp_rotate_right(_c)<L, N>
 template<class L, std::size_t N> using mp_rotate_right_c = mp_rotate_left<L, detail::canonical_right_rotation<mp_size<L>::value, N>>;
 template<class L, class N> using mp_rotate_right = mp_rotate_right_c<L, std::size_t{ N::value }>;
 
 // mp_min_element<L, P>
 // mp_max_element<L, P>
 //   in detail/mp_min_element.hpp
 
 // mp_power_set<L>
 namespace detail
 {
 
 template<class L> struct mp_power_set_impl;
 
 } // namespace detail
 
 template<class L> using mp_power_set = typename detail::mp_power_set_impl<L>::type;
 
 namespace detail
 {
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T> struct mp_power_set_impl< L<T...> >
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = L< L<> >;
 };
 
 #else
 
 template<template<class...> class L> struct mp_power_set_impl< L<> >
 {
     using type = L< L<> >;
 };
 
 #endif
 
 template<template<class...> class L, class T1, class... T> struct mp_power_set_impl< L<T1, T...> >
 {
     using S1 = mp_power_set< L<T...> >;
 
     template<class L2> using _f = mp_push_front<L2, T1>;
 
     using S2 = mp_transform<_f, S1>;
 
     using type = mp_append< S1, S2 >;
 };
 
 } // namespace detail
 
 // mp_partial_sum<L, V, F>
 namespace detail
 {
 
 template<template<class...> class F> struct mp_partial_sum_impl_f
 {
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1900 )
 
     template<class V, class T> using fn = mp_list<F<mp_first<V>, T>, mp_push_back<mp_second<V>, F<mp_first<V>, T>> >;
 
 #else
 
     template<class V, class T, class N = F<mp_first<V>, T>> using fn = mp_list<N, mp_push_back<mp_second<V>, N>>;
 
 #endif
 };
 
 } // namespace detail
 
 template<class L, class V, template<class...> class F> using mp_partial_sum = mp_second<mp_fold_q<L, mp_list<V, mp_clear<L>>, detail::mp_partial_sum_impl_f<F>> >;
 template<class L, class V, class Q> using mp_partial_sum_q = mp_partial_sum<L, V, Q::template fn>;
 
 // mp_iterate<V, F, R>
 namespace detail
 {
 
 template<class V, template<class...> class F, template<class...> class R, class N> struct mp_iterate_impl;
 
 } // namespace detail
 
 template<class V, template<class...> class F, template<class...> class R> using mp_iterate = typename detail::mp_iterate_impl<V, F, R, mp_valid<R, V>>::type;
 
 namespace detail
 {
 
 template<class V, template<class...> class F, template<class...> class R> struct mp_iterate_impl<V, F, R, mp_false>
 {
     template<class X> using _f = mp_list<F<X>>;
     using type = mp_eval_or<mp_list<>, _f, V>;
 };
 
 template<class V, template<class...> class F, template<class...> class R> struct mp_iterate_impl<V, F, R, mp_true>
 {
     using type = mp_push_front<mp_iterate<R<V>, F, R>, F<V>>;
 };
 
 } // namespace detail
 
 template<class V, class Qf, class Qr> using mp_iterate_q = mp_iterate<V, Qf::template fn, Qr::template fn>;
 
 // mp_pairwise_fold<L, F>
 namespace detail
 {
 
 template<class L, class Q> using mp_pairwise_fold_impl = mp_transform_q<Q, mp_pop_back<L>, mp_pop_front<L>>;
 
 } // namespace detail
 
 template<class L, class Q> using mp_pairwise_fold_q = mp_eval_if<mp_empty<L>, mp_clear<L>, detail::mp_pairwise_fold_impl, L, Q>;
 template<class L, template<class...> class F> using mp_pairwise_fold = mp_pairwise_fold_q<L, mp_quote<F>>;
 
 // mp_intersperse<L, S>
 namespace detail
 {
 
 template<class L, class S> struct mp_intersperse_impl
 {
 };
 
 #if BOOST_MP11_WORKAROUND( BOOST_MP11_MSVC, <= 1800 )
 
 template<template<class...> class L, class... T, class S> struct mp_intersperse_impl<L<T...>, S>
 {
     static_assert( sizeof...(T) == 0, "T... must be empty" );
     using type = L<>;
 };
 
 #else
 
 template<template<class...> class L, class S> struct mp_intersperse_impl<L<>, S>
 {
     using type = L<>;
 };
 
 #endif
 
 template<template<class...> class L, class T1, class... T, class S> struct mp_intersperse_impl<L<T1, T...>, S>
 {
     using type = mp_append<L<T1>, L<S, T>...>;
 };
 
 } // namespace detail
 
 template<class L, class S> using mp_intersperse = typename detail::mp_intersperse_impl<L, S>::type;
 
 // mp_split<L, S>
 namespace detail
 {
 
 template<class L, class S, class J> struct mp_split_impl;
 
 } // namespace detail
 
 template<class L, class S> using mp_split = typename detail::mp_split_impl<L, S, mp_find<L, S>>::type;
 
 namespace detail
 {
 
 template<class L, class S, class J> using mp_split_impl_ = mp_push_front<mp_split<mp_drop_c<L, J::value + 1>, S>, mp_take<L, J>>;
 
 template<class L, class S, class J> struct mp_split_impl
 {
     using type = mp_eval_if_c<mp_size<L>::value == J::value, mp_push_back<mp_clear<L>, L>, mp_split_impl_, L, S, J>;
 };
 
 } // namespace detail
 
 // mp_join<L, S>
 
 template<class L, class S> using mp_join = mp_apply<mp_append, mp_intersperse<L, mp_list<S>>>;
 
 } // namespace mp11
 } // namespace boost
 
 #endif // #ifndef BOOST_MP11_ALGORITHM_HPP_INCLUDED

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