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;
inline int get_bit(int mask, int num) { return (mask >> num) & 1; }
inline int add_bit(int mask, int num) { return (mask + (1 << num)); }
int main() {
  int n = 0, m = 0;
  int i = 0, j = 0;
  cin >> n >> m;
  vector<vector<pair<int, int> > > graph(n);
  for (i = 0; i < m; i++) {
    int source, destiny, len;
    cin >> source >> destiny >> len;
    graph[source].push_back(make_pair(destiny, len));
  }
  int max_mask = pow(2, n);
  vector<vector<int> > dp(max_mask, vector<int>(n, -1));
  dp[1][0] = 0;
  for (int mask = 1; mask < max_mask; mask++) {
    for (int vertex = 0; vertex < n; vertex++) {
      for (i = 0; i < graph[vertex].size(); i++) {
        int next = graph[vertex][i].first;
        if (!get_bit(mask, next)) {
          if ((dp[add_bit(mask, next)][next] < dp[mask][vertex]) ||
              (-1 == dp[add_bit(mask, next)][next])) {
            dp[add_bit(mask, next)][next] =
                dp[mask][vertex] + graph[vertex][i].second;
          }
        }
      }
    }
  }
  int result = -1;
  for (i = 1; i < n; i++) {
    for (j = 0; j < graph[i].size(); j++) {
      if (0 == graph[i][j].first) {
        if ((result > dp[max_mask - 1][i] + graph[i][j].second) ||
            (result = -1)) {
          result = dp[max_mask - 1][i] + graph[i][j].second;
        }
      }
    }
  }
  cout << result;
  return 0;
}
