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 edge[15][15], v, e, dp[15][1 << 15];
  cin >> v >> e;
  memset(edge, -1, sizeof(edge));
  memset(dp, -1, sizeof(dp));
  for (int i = 0; i < v; i++) {
    dp[i][0] = 0;
  }
  for (int i = 0; i < e; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    edge[s][t] = d;
  }
  for (int i = 0; i < (1 << v); i++) {
    for (int j = 0; j < v; j++) {
      if (dp[j][i] != -1) {
        for (int k = 0; k < v; k++) {
          if ((i >> k & 1) == 0 && edge[j][k] != -1 &&
              (dp[k][i | (1 << k)] == -1 ||
               dp[k][i | (1 << k)] < dp[j][i] + edge[j][k])) {
            dp[k][i | (1 << k)] = dp[j][i] + edge[j][k];
          }
        }
      }
    }
  }
  int ans = -1;
  for (int i = 1; i < v; i++) {
    if (ans == -1 || dp[i][(1 << v) - 1] < ans) {
      ans = dp[i][(1 << v) - 1];
    }
  }
  cout << ans << endl;
  return 0;
}
