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 glaf[15][15];
int V, E;
int salesman(int count, int cost, int s, bool check[]) {
  int ans = -1;
  if (count != 0) check[s] = true;
  for (int i = 0; i < V; i++) {
    if (!check[i])
      break;
    else if (i == V - 1)
      return cost;
  }
  for (int i = 0; i < V; i++) {
    if (glaf[s][i] != -1 && !check[i]) {
      int goal_cost = salesman(count + 1, cost + glaf[s][i], i, check);
      if (ans == -1 || (goal_cost != -1 && goal_cost < ans)) ans = goal_cost;
    }
  }
  check[s] = false;
  return ans;
}
int main() {
  cin >> V >> E;
  for (int i = 0; i < 15; i++)
    for (int j = 0; j < 15; j++) glaf[i][j] = -1;
  bool check[V];
  for (int i = 1; i < V; i++) check[i] = false;
  int s, t, d;
  for (int i = 0; i < E; i++) {
    cin >> s >> t >> d;
    glaf[s][t] = d;
  }
  int ans = salesman(0, 0, 0, check);
  cout << ans << endl;
}
