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;
int V, E;
int d[15][15];
int memo[1 << 15][15];
int recur(int s, int v) {
  if (memo[s][v] < (15 * 1000 + 1)) return memo[s][v];
  if (s == (1 << V) - 1 and v == 0) return memo[s][v] = 0;
  int result = (15 * 1000 + 1);
  for (int i = 0; i < (V); ++i)
    if (not(s & 1 << i)) {
      result = min(result, d[v][i] + recur(s | 1 << i, i));
    }
  return memo[s][v] = result;
}
int main() {
  cin >> V >> E;
  for (int i = 0; i < (V); ++i)
    for (int j = 0; j < (V); ++j) d[i][j] = (15 * 1000 + 1);
  for (int i = 0; i < (E); ++i) {
    int a, b;
    cin >> a >> b;
    cin >> d[a][b];
  }
  for (int i = 0; i < (1 << V); ++i)
    for (int j = 0; j < (V); ++j) memo[i][j] = (15 * 1000 + 1);
  cout << (recur(0, 0) < (15 * 1000 + 1) ? recur(0, 0) : -1) << endl;
  return 0;
}
