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;
const int INF = INT_MAX / 2;
struct edge {
  int to, weight;
};
int DP[1 << 15][15];
int rec(int S, int v, int V, vector<vector<edge> > &G) {
  if (DP[S][v] >= 0) {
    return DP[S][v];
  }
  if (S == (1 << V) - 1 && v == 0) {
    return DP[S][v] = 0;
  }
  int r = INF;
  for (int i = 0; i < G[v].size(); i++) {
    edge f = G[v][i];
    if ((S >> f.to) % 2 == 0) {
      r = min(r, rec((S | (1 << f.to)), f.to, V, G) + f.weight);
    }
  }
  return DP[S][v] = r;
}
int main() {
  int V, E, d, s;
  edge e;
  cin >> V >> E;
  vector<vector<edge> > G(V);
  for (int i = 0; i < E; i++) {
    cin >> s >> e.to >> e.weight;
    G[s].push_back(e);
  }
  memset(DP, -1, sizeof(DP));
  cout << rec(0, 0, V, G) << endl;
  return 0;
}
