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;
struct Edge {
  int len;
  int to;
};
int n;
int m;
int state;
int ans;
int dp[1 << 16][15];
int adj[15][15];
void calc(int s) {
  int state = 1 << n;
  int start = 1 << s;
  for (int i = 0; i < state; i++) {
    for (int j = 0; j < n; j++) {
      dp[i][j] = 0x33433433;
    }
  }
  dp[start][s] = 0;
  for (int i = start + 1; i < state; i++) {
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        bool s1 = ((i >> j) & 1);
        bool s2 = ((i >> k) & 1);
        if (j == k) continue;
        if (adj[k][j] == -1) continue;
        if (s1 && s2) {
          dp[i][j] = min(dp[i][j], dp[i & ~(1 << j)][k] + adj[k][j]);
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    if (adj[i][s] == -1) continue;
    ans = min(ans, dp[state - 1][i] + adj[i][s]);
  }
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      adj[i][j] = -1;
    }
  }
  for (int i = 0; i < m; i++) {
    int s, t, l;
    scanf("%d%d%d", &s, &t, &l);
    adj[s][t] = l;
    adj[t][s] = l;
  }
  ans = 0x33433433;
  for (int i = 0; i < n; i++) {
    calc(i);
  }
  printf("%d\n", ans);
}
