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 n;
int d[15][15];
int dp[1 << 15][15];
int main(void) {
  fill((int*)dp, (int*)(dp + 15), 1 << 20);
  dp[(1 << n) - 1][0] = 0;
  for (int S = (1 << n) - 2; S >= 0; S--) {
    for (int v = 0; v < n; v++) {
      for (int u = 0; u < n; u++) {
        if (!(S >> u & 1)) {
          dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + dp[v][u]);
        }
      }
    }
  }
  cout << dp[0][0] << endl;
}
