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 INF = 1000000007;
int n, m;
bool canMove[15][15] = {false};
int ecost[15][15];
int dp[1 << 15][15];
int main() {
  int i, j, k;
  cin >> n >> m;
  for (i = 0; i < m; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    ecost[s][t] = d;
    canMove[s][t] = true;
  }
  for (i = 0; i < (1 << n); i++)
    for (j = 0; j < n; j++) dp[i][j] = INF;
  dp[1][0] = 0;
  for (i = 1; i < (1 << n) - 1; i++) {
    for (j = 0; j < n; j++) {
      for (k = 0; k < n; k++) {
        if (!canMove[j][k]) continue;
        dp[i | (1 << k)][k] = min(dp[i | (1 << k)][k], dp[i][j] + ecost[j][k]);
      }
    }
  }
  int ans = INF;
  for (j = 0; j < n; j++) {
    if (dp[(1 << n) - 1][j] < INF && canMove[j][0]) {
      ans = min(ans, dp[(1 << n) - 1][j] + ecost[j][0]);
    }
  }
  if (ans >= INF)
    cout << -1 << endl;
  else
    cout << ans << endl;
  return 0;
}
