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 V, E, G[15][15], dp[1 << 15][15];
const int INF = 1000000;
int solve() {
  for (int s = (1 << V) - 1; s >= 0; --s) {
    for (int t = 0; t < V; ++t) {
      if (s == (1 << V) - 1) {
        dp[s][t] = 0;
      } else {
        dp[s][t] = INF;
      }
    }
  }
  for (int s = (1 << V) - 2; s >= 0; --s) {
    for (int t = 0; t < V; ++t) {
      for (int u = 0; u < V; ++u) {
        if (!(s >> u & 1)) {
          dp[s][t] = min(dp[s][t], dp[s | (1 << u)][u] + G[t][u]);
        }
      }
    }
  }
  return (dp[0][0] != INF) ? dp[0][0] : -1;
}
int main() {
  for (int i = 0; i < 15; ++i) {
    for (int j = 0; j < 15; ++j) {
      G[i][j] = INF;
    }
  }
  cin >> V >> E;
  for (int i = 0; i < E; ++i) {
    int s, t, d;
    cin >> s >> t >> d;
    G[s][t] = d;
  }
  cout << solve() << endl;
  return 0;
}
