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_V = 17;
const int INF = 1e9;
int traveling_salesman(int V, int G[MAX_V][MAX_V]) {
  int dp[(1 << V)][V];
  for (int i = 0; i < (int)((1 << V)); ++i)
    for (int j = 0; j < (int)(V); ++j) dp[i][j] = INF;
  dp[0][0] = 0;
  for (int i = 0; i < (int)((1 << V)); ++i) {
    for (int j = 0; j < (int)(V); ++j) {
      for (int k = 0; k < (int)(V); ++k) {
        int mask = (1 << k), cost = G[j][k];
        if ((i & mask) || cost < 0) continue;
        dp[(i | mask)][k] = min(dp[(i | mask)][k], dp[i][j] + cost);
      }
    }
  }
  int ans = INF;
  for (int i = 0; i < (int)(V); ++i) ans = min(ans, dp[(1 << V) - 1][i]);
  return ans;
}
int main() {
  int G[MAX_V][MAX_V];
  int V, E;
  cin >> V >> E;
  memset(G, -1, sizeof(G));
  for (int i = 0; i < (int)(E); ++i) {
    int f, t, c;
    cin >> f >> t >> c;
    G[f][t] = c;
  }
  int ans = traveling_salesman(V, G);
  cout << (ans == INF ? -1 : ans) << endl;
  return 0;
}
