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 d[15][15];
int tsp(int start, int visited_flag, int city_num) {
  int rtn = 100000000;
  if (visited_flag == (1 << city_num) - 1) {
    if (d[start][0] == -1) {
      return rtn;
    } else {
      return d[start][0];
    }
  }
  for (int i = 0; i < city_num; i++) {
    if (!(visited_flag & (1 << i)) && d[start][i] != -1) {
      rtn = min(rtn, d[start][i] + tsp(i, visited_flag | (1 << i), city_num));
    }
  }
  return rtn;
}
int main() {
  int V, E, frm, to, cost, ans;
  cin >> V >> E;
  memset(d, -1, sizeof(d));
  for (int i = 0; i < E; i++) {
    cin >> frm >> to >> cost;
    d[frm][to] = cost;
  }
  ans = tsp(0, 1, V);
  if (ans >= 100000000) {
    cout << -1 << endl;
  } else {
    cout << ans << endl;
  }
  return 0;
}
