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;
struct TSP {
  int n, d[16][16], dp[(1 << 16)][16];
  TSP(int sz) : n(sz) {
    for (int i = 0; i < 16; i++)
      for (int j = 0; j < 16; j++) d[i][j] = 1e8;
  }
  void add(int a, int b, int c) { d[a][b] = c; }
  int solve() {
    for (int i = 0; i < (1 << n); i++)
      for (int j = 0; j < n; j++) dp[i][j] = 1e8;
    dp[0][0] = 0;
    for (int i = 0; i < (1 << n); i++) {
      for (int j = 0; j < n; j++) {
        if (!((1 << j) & i)) {
          for (int k = 0; k < n; k++) {
            dp[i | (1 << j)][j] = min(dp[i | (1 << j)][j], dp[i][k] + d[k][j]);
          }
        }
      }
    }
    if (dp[(1 << n) - 1][0] = 1e8) return -1;
    return dp[(1 << n) - 1][0];
  }
};
int main() {
  int n, m;
  cin >> n >> m;
  TSP T(n);
  for (int i = 0; i < m; i++) {
    int x, y, z;
    cin >> x >> y >> z;
    T.add(x, y, z);
  }
  cout << T.solve() << endl;
}
