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;
bool contain(int mask, int pos) { return (mask & (1 << pos)) != 0; }
int main() {
  int V, E;
  cin >> V >> E;
  vector<vector<long long> > G(V, vector<long long>(V, INT_MAX));
  for (int i = 0; i < E; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    G[s][t] = d;
  }
  long long ans = INT_MAX;
  for (int st = 0; st < V; st++) {
    long long dp[(1 << V)][V];
    for (int i = 0; i < (1 << V); i++)
      for (int j = 0; j < V; j++) dp[i][j] = INT_MAX;
    dp[0][st] = 0;
    for (int S = 1; S < (1 << V); S++)
      for (int v = 0; v < V; v++)
        if (contain(S, v))
          for (int j = 0; j < V; j++)
            dp[S][v] = min(dp[S][v], dp[S - (1 << v)][j] + G[j][v]);
  }
  if (ans >= 1e+9) ans = -1;
  cout << ans << endl;
}
