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 N = 16;
const int INF = 0x3f3f3f3f;
int pd[1 << N][N][N];
int main(void) {
  int n, m;
  int adj[N][N];
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < N; j++) {
      adj[i][j] = (i == j ? 0 : INF);
    }
  }
  for (int i = 0; i < N; i++)
    for (int j = 0; j < N; j++) pd[0][i][j] = 0;
  for (int i = 1; i < 1 << N; i++) {
    for (int j = 0; j < N; j++) {
      for (int k = 0; k < N; k++) {
        pd[i][j][k] = INF;
      }
    }
  }
  scanf("%d %d", &n, &m);
  for (int i = 0; i < m; i++) {
    int a, b, c;
    scanf("%d %d %d", &a, &b, &c);
    adj[a][b] = c;
  }
  for (int i = 1; i < 1 << n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i & (1 << j)) == 0) continue;
      for (int w = 0; w < n; w++) {
        if ((i & (1 << w)) == 0) continue;
        for (int k = 0; k < n; k++) {
          if (i & (1 << k)) {
            if (i - k != 0 || k == w) {
              pd[i][j][w] =
                  min(pd[i][j][w], pd[i ^ (1 << j)][k][w] + adj[k][j]);
            }
          }
        }
      }
    }
  }
  int minn = INF;
  int idx = (1 << n) - 1;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      minn = min(minn, pd[idx][i][j] + adj[i][j]);
    }
  }
  if (minn == INF)
    puts("-1");
  else
    printf("%d\n", minn);
  return 0;
}
