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 dp[1 << 15][15], d[15][15], a, b, c, n, p, INF = 1 << 30;
int rec(int s, int v) {
  if (dp[s][v] != -1) return dp[s][v];
  if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;
  int res = INF;
  for (int i = 0; i < n; i++)
    if (!(s >> i & 1) && d[v][i] != 0)
      res = min(res, rec(s | (1 << i), i) + d[v][i]);
  return dp[s][v] = res;
}
int main() {
  memset(dp, -1, sizeof(dp));
  cin >> n >> p;
  for (int u = 0; u < p; u++) cin >> a >> b >> c, d[a][b] = c;
  cout << (INF == (a = rec(0, 0)) ? -1 : a) << endl;
}
