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 int dx[4] = {0, 1, 0, -1}, dy[4] = {-1, 0, 1, 0};
template <class T>
void debug(T a) {
  for (auto i : a) cout << i << endl;
}
int v, e;
int cost[20][20];
int memo[1 << 16][16][16];
int dp(const int bit, const int now, const int goal) {
  if (__builtin_popcount(bit) == v) return cost[now][goal];
  if (memo[bit][now][goal] != -1) return memo[bit][now][goal];
  int ans = ((int)(1 << 25));
  for (int i = 0; i < (int)v; i++) {
    if (bit & 1 << i || cost[now][i] < 0) continue;
    ans = min(ans, dp(bit | 1 << i, i, goal) + cost[now][i]);
  }
  return memo[bit][now][goal] = ans;
}
int main() {
  cin >> v >> e;
  for (int i = 0; i < (int)20; i++)
    for (int j = 0; j < (int)20; j++) cost[i][j] = ((int)(1 << 25));
  memset(memo, -1, sizeof memo);
  for (int i = 0; i < (int)e; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    cost[s][t] = d;
  }
  int ans = ((int)(1 << 25));
  for (int i = 0; i < (int)v; i++) {
    ans = min(ans, dp(1 << i, i, i));
  }
  if (ans <= (v + 1) * 1000)
    cout << ans << endl;
  else
    cout << -1 << endl;
}
