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>
int V, E, dist[15][15];
unsigned short *dist_memo;
inline int unvisited(int flag, int vertex) { return flag & (1 << vertex); }
inline int visit(int flag, int vertex) { return flag & ~(1 << vertex); }
int travel(int vertex, int unvisited_vertex) {
  int v, d, idx, min_dist = 100000;
  idx = (vertex * (1 << V)) + unvisited_vertex;
  d = dist_memo[idx];
  if (d != 0) return d;
  for (v = 0; v < V; v++) {
    if (dist[vertex][v] <= 0) {
      continue;
    }
    if (unvisited(unvisited_vertex, v)) {
      if (v == 0) {
        if (visit(unvisited_vertex, 0) == 0) {
          min_dist = dist[vertex][v];
        }
      } else {
        d = travel(v, visit(unvisited_vertex, v)) + dist[vertex][v];
        if (d < min_dist) {
          min_dist = d;
        }
      }
    }
  }
  dist_memo[idx] = min_dist;
  return min_dist;
}
int main() {
  int i, j, s, t, d, distance, unvisited_vertex;
  scanf("%d %d", &V, &E);
  for (i = 0; i < V; i++) {
    for (j = 0; j < V; j++) {
      dist[i][j] = 0;
    }
  }
  for (i = 0; i < E; i++) {
    scanf("%d %d %d", &s, &t, &d);
    dist[s][t] = d;
  }
  dist_memo = (unsigned short *)calloc(V * (1 << V), sizeof(unsigned short));
  unvisited_vertex = 0;
  for (i = 0; i < V; i++) {
    unvisited_vertex |= 1 << i;
  }
  distance = travel(0, unvisited_vertex);
  if (distance >= 100000) {
    distance = -1;
  }
  printf("%d\n", distance);
  return 0;
}
