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;
const int INF = 2e9;
int rec(int S, int v, vector<vector<int>> dp, vector<vector<int>> dist, int n) {
  if (dp[S][v] >= 0) return dp[S][v];
  if (S == (1 << n) - 1 && v == 0) return dp[S][v] = 0;
  int res = INF;
  for (int(i) = 0; (i) < (n); (i)++) {
    if (!(S >> i & 1) && dist[v][i]) {
      res = min(res, rec(S | 1 << i, i, dp, dist, n) + dist[v][i]);
    }
  }
  return dp[S][v] = res;
}
int main() {
  int V, E;
  cin >> V >> E;
  vector<vector<int>> dist(V, vector<int>(V, 0));
  for (int(i) = 0; (i) < (E); (i)++) {
    int s, t, d;
    cin >> s >> t >> d;
    dist[s][t] = d;
  }
  vector<vector<int>> dp(1 << V, vector<int>(V + 1, -1));
  int ans = rec(0, 0, dp, dist, V);
  if (ans == INF)
    cout << -1 << endl;
  else
    cout << ans << endl;
  return 0;
}
