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;
struct ed {
  int t;
  int pos;
  vector<int> exp;
};
int main() {
  int V, E;
  bool flag = false, tflag = false;
  queue<struct ed> st;
  vector<int> ex;
  cin >> V >> E;
  vector<vector<int> > v(V, vector<int>(V));
  vector<int> temp(V);
  fill(temp.begin(), temp.end(), -1);
  fill(v.begin(), v.end(), temp);
  int s, t;
  for (int i = 0; i < E; i++) {
    cin >> s >> t;
    cin >> v[s][t];
  }
  struct ed e;
  for (int i = 0; i < V; i++) {
    e.exp.push_back(0);
  }
  int pre, res = 1 << 29;
  e.t = 0;
  e.pos = 0;
  st.push(e);
  while (!st.empty()) {
    tflag = false;
    e = st.front();
    st.pop();
    for (int i = 0; i < V; i++) {
      if (v[e.pos][i] != -1 && e.exp[i] == 0) {
        e.t += v[e.pos][i];
        e.exp[i] = 1;
        pre = e.pos;
        e.pos = i;
        if (i == 0) {
          tflag = true;
          for (int j = 0; j < V; j++) {
            if (e.exp[j] == 0) {
              tflag = false;
            }
          }
        }
        if (tflag) {
          res = min(res, e.t);
          flag = true;
        } else {
          st.push(e);
        }
        e.pos = pre;
        e.exp[i] = 0;
        e.t -= v[e.pos][i];
      }
    }
  }
  if (!flag) res = -1;
  cout << res << endl;
  return 0;
}
