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 long long int INF = 1e15;
const long long int MOD = 1e9 + 7;
signed main() {
  long long int v, e;
  cin >> v >> e;
  vector<vector<long long int>> edge(v, vector<long long int>(v, INF));
  for (long long int i = 0; i < (e); ++i) {
    long long int s, t, d;
    cin >> s >> t >> d;
    edge[s][t] = d;
  }
  vector<vector<long long int>> cost(1 << v, vector<long long int>(v, INF));
  vector<vector<long long int>> path(1 << v, vector<long long int>(v));
  for (long long int i = 0; i < (v); ++i) {
    cost[1 << i][i] = 0;
  }
  for (long long int s = 1; s < (1 << v); s++) {
    for (long long int i = 0; i < (v); ++i) {
      if ((s >> i) % 2 == 0) {
        continue;
      }
      for (long long int j = 0; j < (v); ++j) {
        if ((s >> j) % 2 == 1 || edge[i][j] == INF) {
          continue;
        }
        if (cost[s | (1 << j)][j] > cost[s][i] + edge[i][j]) {
          cost[s | (1 << j)][j] = cost[s][i] + edge[i][j];
          path[s | (1 << j)][j] = i;
        }
      }
    }
  }
  long long int ans = INF;
  for (long long int i = 0; i < (v); ++i) {
    long long int last;
    if (ans > cost[(1 << v) - 1][i] && cost[(1 << v) - 1][i] != INF) {
      last = i;
    }
    if (cost[(1 << v) - 1][i] == INF) {
      continue;
    }
    long long int s = (1 << v) - 1;
    long long int first = i;
    for (long long int j = 0; j < v - 1; j++) {
      long long int from = path[s][first];
      s ^= 1 << first;
      first = from;
    }
    if (ans > cost[(1 << v) - 1][i] + edge[last][first]) {
      ans = cost[(1 << v) - 1][i] + edge[last][first];
    }
  }
  if (ans == INF) {
    cout << -1 << endl;
  } else {
    cout << ans << endl;
  }
  return 0;
}
