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 V_MAX = 15;
const int INF = 10000000;
int n, e;
int g[V_MAX][V_MAX];
int dp[1 << V_MAX][V_MAX];
int tsp(int visited, int v) {
  if (dp[visited][v] != -1) return dp[visited][v];
  if (visited == (1 << n) - 1 && v == 0) return 0;
  int res = INF;
  for (int u = 0; u < n; ++u) {
    if (!(visited & (1 << u))) {
      res = min(res, tsp(visited | (1 << u), u) + g[v][u]);
    }
  }
  return res;
}
int main() {
  scanf("%d %d", &n, &e);
  fill(&g[0][0], &g[n][0], INF);
  for (int i = 0; i < e; ++i) {
    int s, t, d;
    scanf("%d %d %d", &s, &t, &d);
    g[s][t] = d;
  }
  fill(&dp[0][0], &dp[1 << V_MAX][0], -1);
  int d = tsp(0, 0);
  if (d == INF)
    printf("-1\n");
  else
    printf("%d\n", d);
  return 0;
}
