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 v, e;
vector<pair<int, int> > Edge[15];
int solve(int bit, int now);
int main() {
  int s, t, d;
  cin >> v >> e;
  for (int i = 0; i < e; i++) {
    cin >> s >> t >> d;
    Edge[s].push_back(pair<int, int>(t, d));
  }
  int ans = solve(0, 0);
  if (ans == (1 << 30))
    cout << "-1" << endl;
  else
    cout << ans << endl;
}
int solve(int bit, int now) {
  int cost = 1 << 30;
  if (bit == (1 << v) - 1) return 0;
  for (int i = 0; i < Edge[now].size(); i++) {
    if ((bit & 1 << Edge[now][i].first) == 0) {
      cost =
          min(cost, solve(bit | 1 << Edge[now][i].first, Edge[now][i].first) +
                        Edge[now][i].second);
    }
  }
  return cost;
}
