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;
struct Edge {
  int to;
  int value;
};
struct Node {
  int value;
  vector<Edge> edge;
};
int v, e;
int s, t, d;
Node node[15];
int solve(int pos, int stat) {
  if (stat == (1 << v) - 1) return 0;
  int cost = 1 << 24;
  for (int i = 0; i < node[pos].edge.size(); ++i) {
    if (!(stat & 1 << node[pos].edge[i].to)) {
      cost = min(cost,
                 solve(node[pos].edge[i].to, stat | 1 << node[pos].edge[i].to) +
                     node[pos].edge[i].value);
    }
  }
  return cost;
}
int main() {
  cin >> v >> e;
  for (int i = 0; i < e; ++i) {
    cin >> s >> t >> d;
    node[s].edge.push_back((Edge){t, d});
  }
  int dst = solve(0, 0);
  if (dst == 1 << 24) {
    cout << -1 << endl;
  } else {
    cout << dst << endl;
  }
}
