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, edge[15][15], dp[15][1 << 15];
int rec(int S, int s, int n) {
  if (dp[s][S] != -1) {
    return dp[s][S];
  }
  if (S == ((1 << v) - 1) && edge[n][s] != -1) {
    return dp[s][S] = edge[n][s];
  }
  int res = 0x3fffffff;
  for (int i = 0; i < v; i++) {
    if (((S >> i) & 1) == 0 && edge[n][i] != -1) {
      res = min(rec(S | (1 << i), s, i) + edge[n][i], res);
    }
  }
  return dp[s][S] = res;
}
int main() {
  cin >> v >> e;
  memset(edge, -1, sizeof(edge));
  memset(dp, -1, sizeof(dp));
  for (int i = 0; i < e; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    edge[s][t] = d;
  }
  for (int i = 0; i < v; i++) {
    rec(1 << i, i, i);
  }
  int ans = dp[1][2];
  for (int i = 1; i < v; i++) {
    ans = dp[i][1 << i];
  }
  if (ans == 0x3fffffff) {
    ans = -1;
  }
  cout << ans << endl;
  return 0;
}
