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 dy[] = {0, 0, 1, -1};
int dx[] = {1, -1, 0, 0};
int dist[20][20];
int dp[1 << 20][20];
int V, E;
int s, t, d;
int rec(int S, int v) {
  if (dp[S][v] >= 0) return dp[S][v];
  if (S == (1 << V) - 1 && v == 0) return dp[S][v] = 0;
  int res = 99999999;
  for (int r = 0; r < V; r++) {
    if (!(S & 1 << r)) {
      res = min(res, rec(S | 1 << r, r) + dist[v][r]);
    }
  }
  return dp[S][v] = res;
}
int main() {
  cin >> V >> E;
  for (int i = 0; i < 20; i++)
    for (int j = 0; j < 20; j++) dist[i][j] = 99999999;
  for (int i = 0; i < E; i++) {
    cin >> s >> t >> d;
    dist[s][t] = d;
  }
  memset(dp, -1, sizeof(dp));
  int ans = rec(0, 0);
  if (ans == 99999999)
    cout << -1 << endl;
  else
    cout << ans << endl;
  return 0;
}
