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 = 10000000;
int solve(vector<vector<int>> &dists) {
  const int v = dists.size();
  vector<vector<int>> dp(1 << v, vector<int>(v, INF));
  dp[1][0] = 0;
  const int all = (1 << v) - 1;
  for (int S = 1; S <= all; S++) {
    int tS = S;
    while (tS > 0) {
      int bs = tS - (tS & ~(tS - 1));
      int s = __builtin_ctzll(bs);
      for (int e = 0; e < v; e++) {
        if (dists[s][e] != INF && (~S & (1 << e)) != 0) {
          const int nS = S | (1 << e);
          if (nS == all) {
            dp[nS][e] = min(dp[nS][e], dp[S][s] + dists[s][e] + dists[e][0]);
          } else {
            dp[nS][e] = min(dp[nS][e], dp[S][s] + dists[s][e]);
          }
        }
      }
      tS -= bs;
    }
  }
  int ans = INF;
  for (int i = 0; i < v; i++) {
    ans = min(ans, dp[all][i]);
  }
  return ans == INF ? -1 : ans;
}
int main() {
  int v, e;
  cin >> v >> e;
  vector<vector<int>> dists(v, vector<int>(v, INF));
  for (int i = 0; i < e; i++) {
    int s, e, d;
    cin >> s >> e >> d;
    dists[s][e] = d;
  }
  cout << solve(dists) << endl;
  return 0;
}
