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;
const int INF = 1 << 29;
const double EPS = 1e-9;
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};
int dp[1 << 16][20];
int d[20][20];
int main() {
  int V, E;
  cin >> V >> E;
  for (int i = 0; i < (1 << 20); i++) {
    for (int j = 0; j < V; j++) {
      dp[i][j] = INF;
    }
  }
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) {
      d[i][j] = INF;
    }
  }
  for (int i = 0; i < E; i++) {
    int x, y, c;
    cin >> x >> y >> c;
    d[x][y] = c;
  }
  dp[1][0] = 0;
  for (int i = 0; i < (1 << V); i++) {
    for (int j = 0; j < V; j++) {
      if ((i >> j & 1) == 0) continue;
      for (int k = 0; k < V; k++) {
        if ((i >> k & 1) == 1) continue;
        dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + d[j][k]);
      }
    }
  }
  int ans = INF;
  for (int i = 0; i < V; i++) {
    ans = min(ans, dp[(1 << V) - 1][i] + d[i][0]);
  }
  if (ans >= INF) {
    cout << -1 << endl;
  } else {
    cout << ans << endl;
  }
  return 0;
}
