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 MAX_N = 15;
int n, m;
long long dp[1 << MAX_N][MAX_N];
long long d[MAX_N][MAX_N];
int s[MAX_N];
int t[MAX_N];
int D[MAX_N];
long long solve() {
  for (int S = 0; S < 1 << n; S++) {
    fill(dp[S], dp[S] + n, 999999999);
  }
  dp[(1 << n) - 1][0] = 0;
  for (int S = (1 << n) - 2; S >= 0; S--) {
    for (int v = 0; v < n; v++) {
      for (int u = 0; u < n; u++) {
        if (!(S >> u & 1)) {
          dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + d[v][u]);
        }
      }
    }
  }
  return dp[0][0];
}
int main() {
  long long ans = 999999999 - 1;
  cin >> n >> m;
  for (int i = 0; i < m; i++) {
    cin >> s[i] >> t[i] >> D[i];
  }
  for (int i = 0; i < n; i++) {
    fill(d[0], d[n], 999999999);
    for (int j = 0; j < m; j++) {
      d[(s[j] + n - i) % n][(t[j] + n - i) % n] = D[j];
    }
    ans = min(ans, solve());
  }
  if (ans > 16000) {
    cout << "-1\n";
  } else {
    cout << ans << "\n";
  }
}
