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 INF = (1ll << 60);
struct Edge {
  long long s, t, d;
};
int main() {
  long long V, E;
  cin >> V >> E;
  vector<vector<Edge>> G(V);
  for (long long i = 0; i < E; i++) {
    Edge e;
    cin >> e.s >> e.t >> e.d;
    G[e.t].push_back(e);
  }
  vector<vector<long long>> dist((1ll << V), vector<long long>(V, INF));
  dist[1][0] = 0;
  for (long long i = 2; i < (1ll << V); i++)
    for (long long j = 0; j < V; j++) {
      if ((1ll << j) & i)
        for (Edge e : G[j])
          dist[i][j] = min(dist[i][j], dist[(1ll << j) ^ i][e.s] + e.d);
    }
  long long ans = INF;
  for (Edge e : G[0]) ans = min(ans, dist[(1ll << V) - 1][e.s] + e.d);
  if (ans == INF) ans = -1;
  cout << ans << endl;
}
