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 INF = 1 << 30;
int DP[1 << 15][15];
int G[15][15];
int V, E;
int rec(int S, int now) {
  if (DP[S][now] >= 0) return DP[S][now];
  if (S == (1 << V) - 1 and now == 0) return DP[S][now] = 0;
  int ret = INF;
  for (long long(v) = 0; (v) < (V); (v)++) {
    if (S & (1 << v)) continue;
    if (G[now][v] == INF) continue;
    ret = min(ret, rec(S | (1 << v), v)) + G[now][v];
  }
  return DP[S][now] = ret;
}
int main() {
  cin >> V >> E;
  for (long long(i) = 0; (i) < (V); (i)++)
    for (long long(j) = 0; (j) < (V); (j)++) G[i][j] = INF;
  for (long long(i) = 0; (i) < (1 << V); (i)++)
    for (long long(j) = 0; (j) < (V); (j)++) DP[i][j] = -1;
  for (long long(i) = 0; (i) < (E); (i)++) {
    int s, t, d;
    cin >> s >> t >> d;
    G[s][t] = d;
  }
  int ans = rec(0, 0);
  cout << (ans >= INF ? -1 : ans) << endl;
  return 0;
}
