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>
const int inf = INT_MAX / 3;
const int max_v = 15;
int d[max_v][max_v];
int dp[(1 << max_v) - 1][max_v];
using namespace std;
int main() {
  int V, E;
  cin >> V >> E;
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) {
      d[i][j] = (i == j) ? 0 : inf;
    }
  }
  for (int i = 0; i < E; i++) {
    int ts, tt, td;
    cin >> ts >> tt >> td;
    d[ts][tt] = td;
  }
  for (int s = (1 << V) - 1; s >= 0; s--) {
    for (int v = 0; v < V; v++) {
      dp[s][v] = inf;
    }
  }
  dp[(1 << V) - 1][0] = 0;
  for (int s = (1 << V) - 1; s >= 0; s--) {
    for (int v = 0; v < V; v++) {
      for (int u = 0; u < V; u++) {
        cout << "s:" << s << " v:" << v << " u:" << u << endl;
        if (!((s >> u) & 1)) {
          dp[s][v] = min(dp[s][v], dp[s | 1 << u][u] + d[u][v]);
          cout << " dp:" << dp[s][v] << endl;
        }
      }
    }
  }
  if (dp[0][0] >= inf) {
    cout << -1 << endl;
  } else {
    cout << dp[0][0] << endl;
  }
  return 0;
}
