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 n, m;
  int s, t, d;
  int e[15][15];
  int dp[1 << 15][15];
  scanf("%d %d", &n, &m);
  for (int i = 0; i < 15; i++) fill_n(e[i], 15, 1 << 15);
  for (int i = 0; i < m; i++) {
    scanf("%d %d %d", &s, &t, &d);
    e[s][t] = d;
  }
  for (int i = 0; i < (1 << n); i++) fill_n(dp[i], n, 1 << 15);
  dp[(1 << n) - 1][0] = 0;
  for (int i = (1 << n) - 2; i >= 0; i--) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        if (!(i >> k & 1))
          dp[i][j] = min(dp[i][j], dp[i | 1 << k][k] + e[j][k]);
        printf("dp[%d][%d]=%d\n", i, j, dp[i][j]);
      }
    }
  }
  printf("%d\n", (dp[0][0] == 1 << 15 ? -1 : dp[0][0]));
}
