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 dp[(1 << 15)][15];
int d[15][15];
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i < (int)(n); ++i) {
    for (int j = 0; j < (int)(n); ++j) {
      d[i][j] = 1000000005;
    }
  }
  for (int i = 0; i < (int)(m); ++i) {
    int a, b, c;
    cin >> a >> b >> c;
    d[a][b] = c;
  }
  for (int i = 0; i < (int)((1 << n)); ++i) {
    for (int j = 0; j < (int)(n); ++j) {
      dp[i][j] = 1000000005;
    }
  }
  for (int i = 0; i < (int)(n); ++i) {
    dp[0][i] = 0;
  }
  for (int i = 0; i < (int)(1 << n); ++i) {
    for (int j = 0; j < (int)(n); ++j) {
      for (int k = 0; k < (int)(n); ++k) {
        if (!(i & (1 << k))) {
          dp[i | (1 << k)][j] = min(dp[i | (1 << k)][j], dp[i][k] + d[k][j]);
        }
      }
    }
  }
  int ans = 1000000005;
  for (int i = 0; i < (int)(n); ++i) {
    ans = min(ans, dp[(1 << n) - 1][i]);
  }
  if (ans == 1000000005) {
    cout << "-1\n";
  } else {
    cout << ans << endl;
  }
}
