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;
long long int wt[20][20];
long long int dp[(1 << 20) + 5][20];
long long int n, m;
long long int u, v, w;
long long int p;
void initialize() {
  for (long long int i = 0; i < n; i++)
    for (long long int j = 0; j < n; j++) {
      wt[i][j] = LLONG_MAX;
    }
  for (long long int i = 0; i < (1 << n); i++)
    for (long long int j = 0; j < n; j++) dp[i][j] = -1;
  dp[1][0] = 0;
}
void floyd_warshall() {
  for (long long int k = 0; k < n; k++) {
    for (long long int i = 0; i < n; i++) {
      for (long long int j = 0; j < n; j++) {
        if (wt[i][k] != LLONG_MAX && wt[k][j] != LLONG_MAX)
          wt[i][j] = min(wt[i][j], wt[i][k] + wt[k][j]);
      }
    }
  }
}
void tsp() {
  for (long long int i = 1; i < (1 << n); i++) {
    for (long long int j = 0; j < n; j++) {
      if (dp[i][j] == -1) {
        continue;
      }
      for (long long int k = 1; k < n; k++) {
        if (((i & (1 << k)) != 0) || wt[j][k] == LLONG_MAX) {
          continue;
        }
        p = i | (1 << k);
        if (dp[p][k] == -1)
          dp[p][k] = dp[i][j] + wt[j][k];
        else
          dp[p][k] = min(dp[p][k], dp[i][j] + wt[j][k]);
      }
    }
  }
}
long long int minimum_cost() {
  long long int ans = LLONG_MAX;
  for (long long int i = 1; i < n; i++) {
    if (dp[(1 << n) - 1][i] == -1 || wt[i][0] == LLONG_MAX) continue;
    ans = min(ans, dp[(1 << n) - 1][i] + wt[i][0]);
  }
  return ans;
}
int main() {
  cin >> n;
  cin >> m;
  initialize();
  for (long long int i = 0; i < m; i++) {
    cin >> u >> v >> w;
    wt[u][v] = w;
  }
  floyd_warshall();
  tsp();
  long long int ans = minimum_cost();
  if (ans != LLONG_MAX)
    cout << ans << endl;
  else
    cout << -1 << endl;
}
