Problem:
Traveling Salesman Problem

For a given weighted directed graph G(V, E), find the distance of the shortest route that meets the following criteria:

It is a closed cycle where it ends at the same point it starts.

It visits each vertex exactly once.

Input

|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in the graph. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the distance between si and ti (the i-th edge).

Output

Print the shortest distance in a line. If there is no solution, print -1.

Constraints

2 ≤ |V| ≤ 15

0 ≤ di ≤ 1,000

There are no multiedge

Sample Input 1

4 6
0 1 2
1 2 3
1 3 9
2 0 1
2 3 6
3 2 4

Sample Output 1

16

Sample Input 2

3 3
0 1 1
1 2 1
0 2 1

Sample Output 2

-1

Solution in C++14 (judge verdict: Accepted)

#define STOPIT
#include <bits/stdc++.h>
#define loop(n) for (lint ngtkana_is_a_genius = 0; ngtkana_is_a_genius < lint(n); ngtkana_is_a_genius++)
#define rep(i, begin, end) for (lint i = lint(begin); (i) < lint(end); i++)
#define all(v) v.begin(), v.end()
#define rand(l, r) std::uniform_int_distribution<>(l, r)(mt)
using lint = long long;
auto mt = std::mt19937_64(std::random_device{}());
auto cmn = [](auto& a, auto b){ if (a > b) {a = b; return true;} return false; };
auto cmx = [](auto& a, auto b){ if (a < b) {a = b; return true;} return false; };
void debug_impl() { std::cerr << std::endl; }
template <typename Head, typename... Tail>
void debug_impl(Head head, Tail... tail) { std::cerr << " " << head; debug_impl(tail...); }
#ifndef STOPIT
#define debug(...)\
  do {\
    std::cerr << std::boolalpha << "[" << #__VA_ARGS__ << "]:";\
    debug_impl(__VA_ARGS__);\
    std::cerr << std::noboolalpha;\
  } while (false)
#else
#define debug(...) {}
#endif

template < typename Container, typename Value = typename Container::value_type, std::enable_if_t<!std::is_same< Container, std::string >::value, std::nullptr_t> = nullptr>
std::istream& operator>> (std::istream& is, Container& v)
  { for (auto & x : v) { is >> x; } return is; }

template < typename Container, typename Value = typename Container::value_type, std::enable_if_t<!std::is_same< Container, std::string >::value, std::nullptr_t> = nullptr >
std::ostream& operator<< (std::ostream& os, Container const& v) {
 os << "{";
  for (auto it = v.begin(); it != v.end(); it++)
    {os << (it != v.begin() ? "," : "") << *it;}
  return os << "}";
}

template <typename T>
auto make_vector_impl(size_t sz, T t) {return std::vector<T>(sz, t);}

template <size_t N, typename T, typename U, std::enable_if_t<N == 1, std::nullptr_t> = nullptr>
auto make_vector(size_t sz, U u) {return make_vector_impl(sz, T(u));}

template <size_t N, typename T, std::enable_if_t<N == 1, std::nullptr_t> = nullptr>
auto make_vector(size_t sz) {return std::vector<T>(sz);}

template <size_t N, typename T, typename... Args, std::enable_if_t<N != 1, std::nullptr_t> = nullptr>
auto make_vector(size_t a, Args... args) {return make_vector_impl(a, make_vector<N - 1, T>(args...));}

template <typename T, typename Size_t>
auto& at(T& t, Size_t i) {return t.at(i);}

template <typename T, typename Size_t, typename... Args>
auto& at(T& t, Size_t i, Args... args) {return at(t.at(i), args...);}

// require gcc >= 7.1.0
template < class ... Keys >
class fmt_t {
    using storage_t = std::tuple< Keys ... >;
    storage_t storage;
    static constexpr std::size_t N = sizeof ... (Keys);

    // is_exact_match_impl
    template < std::size_t I, class Value >
      auto is_exact_match_impl(long, Value) const
        { return false; }

    template < std::size_t I, class Value,
      std::enable_if_t<
        std::is_same< std::decay_t< Value > , char >::value
        == std::is_same< std::tuple_element_t< I, storage_t >, char >::value,
      std::nullptr_t > = nullptr,
      class = decltype(std::declval< Value >() == std::get< I >(std::declval< storage_t >())) >
      auto is_exact_match_impl(int, Value x) const
        { return x == std::get< I >(storage); }

    template < class Value, std::size_t ... Is >
      auto find_exact_match_impl(Value x, std::integer_sequence< std::size_t, Is ... >) const {
        auto ret = false;
        (void)std::initializer_list< std::nullptr_t >
          { (ret |= is_exact_match_impl< Is >(int{}, x), nullptr) ...  };
        return ret;
      }

    template < class Value >
      auto exists_exact_match(Value x) const
      {  return find_exact_match_impl(x, std::make_index_sequence< N >()); }

    // tuple_format_impl
    template < class Tuple,  std::size_t ... Is >
    std::string tuple_format_impl(const Tuple& tuple, std::integer_sequence< std::size_t, Is ... >) const {
      std::string ret = "(";
      (void)std::initializer_list< std::nullptr_t >
        { (ret = ret + (Is == 0 ? "" : ",") + format(std::get< Is >(tuple)), nullptr) ... };
      return ret + ")";
    }

    // usual_format
    template < class Value >
    std::string usual_format(long, Value x) const
      { return std::to_string(x); }

    template < class Value, std::enable_if_t< std::is_same< std::decay_t< Value >, char >::value, std::nullptr_t > = nullptr >
    std::string usual_format(int, Value c) const
      { return std::string{'\''} + std::string{c} + std::string{'\''}; }

    std::string usual_format(int, char const* s) const
      { return "\"" + std::string(s) + "\""; }

    std::string usual_format(int, std::string const s) const
      { return "\"" + s + "\""; }

    template < class Container, class = typename Container::value_type >
    std::string usual_format(int, Container const & v) const {
      return "{" + std::accumulate(v.begin(), v .end(), std::string{},
        [this](auto const& s, auto const x) { return s + (s.empty() ? "" : ",") + this->format(x); })
        + "}";
    }

    template < class Tuple, std::size_t N = std::tuple_size< Tuple >::value >
    std::string usual_format(int, Tuple const& tuple) const
      { return tuple_format_impl(tuple, std::make_index_sequence< N >()); }

    // format
    template < class Value > std::string format(Value&& x) const
      { return exists_exact_match(x) ? std::string{'_'} : usual_format(int{}, x); }

  public:
    fmt_t()=default;
    template < Keys ... > fmt_t(Keys&& ... keys ) : storage(keys ... ){}

    template < class Value > std::string operator()(Value&& x) const
      { return format(x); }
};
template < class ... Keys > auto fmt(Keys&& ... keys)
  { return fmt_t< Keys ... >(std::forward< Keys >(keys) ... ); }

template < class Value >
bool bat(Value x, std::size_t pos) { return (x >> pos) & Value{1}; }

/*
0からスタートします。訪問済みの頂点集合と、そのうち現在いる頂点を管理します。
配る DP で、その頂点から出ている辺の数だけ更新していきます。
dp{bs | 1<<j][j] <- dp[bs][i] + adj[i][j], where i->j
すると、dp[N-1][i] + adj[i][0] for i = 1,2,... の min が答えです。
*/

int main() {
  std::cin.tie(0); std::cin.sync_with_stdio(false);
  int n; std::cin >> n;
  int inf = std::numeric_limits<int>::max();
  auto adj = make_vector<2,int>(n,n,inf);
  int q; std::cin >> q;
  loop(q) {
    int u, v, d;
    std::cin >> u >> v >> d;
    at(adj,u,v) = d;
  }
  debug(fmt(inf)(adj));

  int s = 0;
  int N = 1 << n;
  auto dp = make_vector<2,int>(N,n,inf);
  at(dp,1<<s,s) = 0;
  rep(bs,0,N) {
    rep(i,0,n) {
      if (!bat(bs,i)) continue;
      int crr = at(dp,bs,i);
      if (crr == inf) continue;
      rep(j,0,n) {
        if (bat(bs,j)) continue;
        int d = at(adj,i,j);
        if (d == inf) continue;
        cmn(at(dp, bs | 1<<j, j), crr + d);
      }
    }
  }
  rep(bs,0,N) {
    auto x = std::bitset<16>(bs);
    auto y = fmt(inf)(dp.at(bs));
    debug(x,y);
  }

  int ans = inf;
  rep(i,1,n) {
    int x = at(dp,N-1,i);
    int y = at(adj,i,0);
    if (x==inf || y==inf) continue;
    cmn(ans,x+y);
  }
  if (ans == inf) ans = -1;
  std::cout << ans << std::endl;
  return 0;
}