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 V, E, o;
int dis[16][16], dp[16][1 << 16];
int solve(int s, int state) {
  if (~dp[s][state]) {
    return dp[s][state];
  }
  if (state == (1 << V) - 1) {
    return dp[s][state] = dis[s][o];
  }
  int res = INT_MAX;
  for (int i = 0; i < V; i++) {
    if (state >> i & 1 || dis[s][i] == 1000000) continue;
    res = min(res, solve(i, state | 1 << i) + dis[s][i]);
  }
  return dp[s][state] = res;
}
int main() {
  cin >> V >> E;
  while (E--) {
    int s, t, w;
    cin >> s >> t >> w;
    dis[s][t] = w;
  }
  for (int s = 0; s < V; s++) {
    for (int t = 0; t < V; t++) {
      if (!dis[s][t]) {
        dis[s][t] = 1000000;
      }
    }
  }
  int ans = INT_MAX;
  for (int s = 0; s < V; s++) {
    o = s;
    memset(dp, -1, sizeof(dp));
    ans = min(ans, solve(s, 1 << s));
  }
  if (ans > 1000000) {
    ans = -1;
  }
  cout << ans << endl;
  return 0;
}
