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;
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T>
inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
bool checked(int chouten, int i) {
  if (((1 << i) | chouten) == chouten) {
    return true;
  } else
    return false;
}
int pluscheck(int chouten, int i) { return (chouten | (1 << i)); }
bool ren() {}
int graph[16][16];
int dynamic[((1 << 16) - 1)][16];
int V, E;
int roop(int chouten, int genzai, int len) {
  if (dynamic[chouten][genzai] != -1) return dynamic[chouten][genzai];
  if (len >= 10000000) {
    return 10000000;
    ;
  }
  if (chouten == (1 << (V)) - 1) {
    if (genzai == 0)
      return len;
    else
      return 10000000;
    ;
  } else {
    int newlen, out;
    out = 10000000;
    ;
    for (int i = 0; i < 16; i++) {
      if (checked(chouten, i)) continue;
      if (graph[genzai][i]) {
        newlen = len + graph[genzai][i];
        out = min(out, roop(pluscheck(chouten, i), i, newlen));
      }
    }
    return out;
  }
}
int main() {
  cin >> V >> E;
  int s, t, d;
  for (int i = 0; i < 16; i++) {
    for (int j = 0; j < 16; j++) {
      graph[i][j] = 0;
    }
  }
  for (int i = 0; i < E; i++) {
    cin >> s >> t >> d;
    graph[s][t] = d;
  }
  for (int i = 0; i < ((1 << 16) - 1); i++) {
    for (int j = 0; j < 16; j++) {
      dynamic[i][j] = -1;
    }
  }
  int rinzi = roop(0, 0, 0);
  if (rinzi < 10000000)
    cout << rinzi << endl;
  else
    cout << -1 << endl;
  return 0;
}
