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 / 100;
int TSP(vector<vector<int>> &graph, int src) {
  int v = graph.size(), n = 1 << v;
  vector<vector<int>> dp(v, vector<int>(n, inf));
  for (int i = (0); i < (v); ++i) {
    dp[i][1 << i] = graph[src][i];
  }
  for (int s = (1); s < (n); ++s) {
    for (int i = (0); i < (v); ++i) {
      if (!(s & (1 << i))) continue;
      for (int j = (0); j < (v); ++j) {
        if (s & (1 << j)) continue;
        if (graph[i][j] != -1)
          dp[j][s | (1 << j)] =
              min(dp[j][s | (1 << j)], dp[i][s] + graph[i][j]);
      }
    }
  }
  return dp[src][n - 1];
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int v, e;
  cin >> v >> e;
  vector<vector<int>> graph(v, vector<int>(v, -1));
  for (int i = (0); i < (e); ++i) {
    int s, t, d;
    cin >> s >> t >> d;
    graph[s][t] = d;
  }
  int ans = TSP(graph, 0);
  cout << (ans >= inf ? -1 : ans) << endl;
  return 0;
}
