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 N, M, a, b, c, x[18][18];
int dp[18][1 << 18];
int main() {
  for (int i = 0; i < 18; i++) {
    for (int j = 0; j < 18; j++) {
      x[i][j] = 1000000000;
    }
    for (int j = 0; j < (1 << 18); j++) {
      dp[i][j] = 1000000000;
    }
  }
  cin >> N >> M;
  for (int i = 0; i < M; i++) {
    cin >> a >> b >> c;
    x[a][b] = c;
    x[b][a] = c;
  }
  dp[0][1] = 0;
  for (int i = 0; i < (1 << N); i++) {
    for (int j = 0; j < N; j++) {
      if (dp[j][i] < 1000000000) {
        for (int k = 0; k < N; k++) {
          if ((i / (1 << k)) % 2 == 0) {
            int dist1 = dp[j][i] + x[j][k];
            int pos = i + (1 << k);
            if (dp[k][pos] > dist1) {
              dp[k][pos] = dist1;
            }
          }
        }
      }
    }
  }
  int maxn = 1000000000;
  for (int i = 0; i < N; i++) {
    maxn = min(dp[i][(1 << N) - 1] + x[0][i], maxn);
  }
  if (maxn == 1000000000) {
    maxn = -1;
  }
  cout << maxn << endl;
  return 0;
}
