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;
int main() {
  int V, E, s, t, d;
  cin >> V >> E;
  vector<vector<int> > M(V, vector<int>(V, 1 << 27));
  for (int i = 0; i < E; i++) {
    cin >> s >> t >> d;
    M[s][t] = d;
  }
  vector<vector<int> > dp(V, vector<int>(1 << V, 1 << 27));
  dp[0][0] = 0;
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) {
      for (int k = 0; k < (1 << V); k++) {
        for (int l = 0; l < V; l++) {
          if ((k / (1 << j)) % 2 == 1) {
            dp[j][k] = min(dp[j][k], dp[l][k - (1 << j)] + M[l][j]);
          }
        }
      }
    }
  }
  cout << dp[0][(1 << V) - 1] << endl;
  return 0;
}
