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;
long long int INF = 1e18;
int main() {
  long long int V, E;
  cin >> V >> E;
  long long int cost[V][V];
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) {
      cost[i][j] = INF;
    }
  }
  for (int i = 0; i < E; i++) {
    int u, v, c;
    cin >> u >> v >> c;
    cost[u][v] = c;
  }
  long long int DP[V][(1 << V)];
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < (1 << V); j++) {
      DP[i][j] = INF;
    }
  }
  DP[0][0] = 0;
  for (int i = 0; i < (1 << V); i++) {
    for (int j = 0; j < V; j++) {
      if (i & (1 << j)) {
        for (int k = 0; k < V; k++) {
          DP[j][i] = min(DP[j][i], DP[k][i - (1 << j)] + cost[k][j]);
        }
      }
    }
  }
  int ans = DP[0][(1 << V) - 1];
  if (ans == INF) {
    cout << -1 << endl;
  } else {
    cout << ans << endl;
  }
  return 0;
}
