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;
long long int K;
int d[15][15];
int dp[1 << 15][15];
int color[15];
void solve() {
  for (int S = 0; S < 1 << V; S++) {
    fill(dp[S], dp[S] + V, 10000005);
  }
  dp[(1 << V) - 1][0] = 0;
  for (int S = (1 << V) - 2; S >= 0; S--) {
    for (int v = 0; v < V; v++) {
      for (int u = 0; u < V; u++) {
        if (!(S >> u & 1)) {
          dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + d[v][u]);
        }
      }
    }
  }
  if (dp[0][0] >= 10000005)
    printf("-1\n");
  else
    printf("%d\n", dp[0][0]);
}
int dfs(int v, int a) {
  color[v] = 1;
  a++;
  for (int i = 0; i < V; i++) {
    if (d[v][i] != 10000005 && color[i] == 0) {
      a = dfs(i, a);
    }
  }
  return a;
}
int main() {
  int s, t, dd;
  scanf("%d %d", &V, &E);
  if (E == 0) {
    printf("-1\n");
    return 0;
  }
  for (int i = 0; i <= V; i++) {
    fill(d[i], d[i] + V + 1, 10000005);
  }
  for (int i = 0; i < E; i++) {
    scanf("%d%d%d", &s, &t, &dd);
    d[s][t] = dd;
  }
  solve();
  return 0;
}
