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>
int V, E;
int G[15][15];
int dp[1 << 15][15];
int min(int a, int b) {
  if (a < b)
    return a;
  else
    return b;
}
void print() {
  int i, j;
  for (i = 0; i < V; i++) {
    for (j = 0; j < V; j++) {
      printf("%d ", dp[i][j]);
    }
    printf("\n");
  }
  printf("\n");
}
int rec(int S, int v) {
  if (dp[S][v] >= 0) return dp[S][v];
  if (S == (1 << V) - 1 && v == 0) return dp[S][v] = 0;
  int u, res = 100000;
  for (u = 0; u < V; u++) {
    if (!(S >> u & 1)) {
      res = min(res, rec(S | 1 << u, u) + G[v][u]);
    }
  }
  return dp[S][v] = res;
}
int main() {
  int i, j;
  int s, t, d;
  int min = 100000;
  int ans;
  scanf("%d %d", &V, &E);
  memset(dp, -1, sizeof(dp));
  for (i = 0; i < 1 << V; i++) {
    for (j = 0; j < V; j++) {
      G[i][j] = 100000;
    }
  }
  for (i = 0; i < E; i++) {
    scanf("%d %d %d", &s, &t, &d);
    G[s][t] = d;
  }
  for (i = 0; i < V; i++) {
    ans = rec(0, i);
    if (min > ans) min = ans;
  }
  if (min == 100000) min = -1;
  printf("%d\n", min);
  return 0;
}
