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.

Constraints

* 2 ≤ |V| ≤ 15
* 0 ≤ di ≤ 1,000
* There are no multiedge

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.

Examples

Input

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


Output

16


Input

3 3
0 1 1
1 2 1
0 2 1


Output

-1
#include <bits/stdc++.h>
using namespace std;
struct edge {
  long long u;
  long long v;
  long long cost;
  edge() {}
  edge(long long u, long long v, long long c) : u(u), v(v), cost(c) {}
};
int main(void) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long V, E;
  cin >> V >> E;
  vector<vector<edge>> G(V);
  for (int i = 0; i < E; i++) {
    long long s, t, d;
    cin >> s >> t >> d;
    G[s].emplace_back(edge(s, t, d));
  }
  vector<vector<long long>> dp(1 << V, vector<long long>(V, 1 << 30));
  dp[0][0] = 0;
  for (int j = 0; j < V; j++) {
    for (int i = 0; i < (1 << V); i++) {
      for (auto e : G[j]) {
        if (!((i >> e.v) & 1)) {
          dp[i | (1 << e.v)][e.v] =
              min(dp[i | (1 << e.v)][e.v], dp[i][e.u] + e.cost);
        }
      }
    }
  }
  long long ret = dp[(1 << V) - 1][0];
  if (ret == 1 << 30) ret = -1;
  cout << ret << endl;
  return 0;
}
