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 dp[1 << 15][15];
int n;
int m[15][15];
int rec(int s, int v) {
  if (dp[s][v] >= 0) {
    return dp[s][v];
  }
  if (s == ((1 << n) - 1) && v == 0) {
    return dp[s][v] = 0;
  }
  int res = 1000 * 15 + 1;
  for (int u = 0; u < n; u++) {
    if ((!(s >> u & 1)) && m[v][u] >= 0) {
      res = min(res, rec(s | (1 << u), u) + m[v][u]);
    }
  }
  return dp[s][v] = res;
}
int main() {
  int v, e;
  cin >> v >> e;
  n = v;
  memset(m, -1, sizeof(m));
  int s, t, d;
  for (int i = 0; i < e; i++) {
    cin >> s >> t >> d;
    m[s][t] = d;
  }
  memset(dp, -1, sizeof(dp));
  int ans = rec(0, 0);
  if (ans == 15001) {
    printf("%d\n", -1);
  } else {
    printf("%d\n", ans);
  }
}
