#include <tuple>
// function has to live in the std namespace 
// so that it is picked up by argument-dependent name lookup (ADL).
namespace std {
    namespace
    {

        // Code from boost
        // Reciprocal of the golden ratio helps spread entropy
        //     and handles duplicates.
        // See Mike Seymour in magic-numbers-in-boosthash-combine:
        //     https://stackoverflow.com/questions/4948780

        template <class T>
        inline void hash_combine(std::size_t& seed, T const& v)
        {
            seed ^= hash<T>()(v) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
        }

        // Recursive template code derived from Matthieu M.
        template <class Tuple, size_t Index = std::tuple_size<Tuple>::value - 1>
        struct HashValueImpl
        {
            static void apply(size_t& seed, Tuple const& tuple)
            {
                HashValueImpl<Tuple, Index - 1>::apply(seed, tuple);
                hash_combine(seed, get<Index>(tuple));
            }
        };

        template <class Tuple>
        struct HashValueImpl<Tuple, 0>
        {
            static void apply(size_t& seed, Tuple const& tuple)
            {
                hash_combine(seed, get<0>(tuple));
            }
        };
    }

    template <typename ... TT>
    struct hash<std::tuple<TT...>>
    {
        size_t
            operator()(std::tuple<TT...> const& tt) const
        {
            size_t seed = 0;
            HashValueImpl<std::tuple<TT...> >::apply(seed, tt);
            return seed;
        }

    };
}