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 getbit(int mask, int num) { return (mask >> num) & 1; }
int main() {
  int n, m, a, b, c, l = 1;
  cin >> n >> m;
  for (int i = 0; i < n; i++) l *= 2;
  l--;
  int rebra[n][n];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) rebra[i][j] = -1;
  for (int i = 0; i < m; i++) {
    cin >> a >> b >> c;
    rebra[a][b] = c;
  }
  long long dp[l + 1][n];
  for (int i = 0; i <= l; i++)
    for (int j = 0; j < n; j++) dp[i][j] = -1;
  dp[1][0] = 0;
  long long f = 1;
  for (long long mask = 1; mask <= l; mask++)
    for (int j = 0; j < n; j++)
      if ((getbit(mask, j) == 1) && (dp[mask][j] != -1))
        for (int q = 0; q < n; q++)
          if ((rebra[j][q] != -1) && (getbit(mask, q) == 0)) {
            f = 1;
            for (int y = 0; y < q; y++) f *= 2;
            f += mask;
            if ((dp[f][q] == -1) || (dp[mask][j] + rebra[j][q] < dp[f][q])) {
              dp[f][q] = dp[mask][j] + rebra[j][q];
              f = 0;
            }
          }
  int mm = -1;
  for (int i = 1; i < n; i++)
    if ((dp[l][i] != -1) && (rebra[i][0] != -1))
      if (mm == -1) {
        mm = dp[l][i] + rebra[i][0];
      } else {
        if ((mm == -1) || (dp[l][i] + rebra[i][0] < mm))
          mm = dp[l][i] + rebra[i][0];
      }
  if (mm == -1)
    cout << "No solution";
  else
    cout << mm;
}
