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;
string alph("abcdefghijklmnopqrstuvwxyz");
struct edge {
  long long from, to, cost;
};
vector<edge> G;
double pi = 3.141592653589793;
pair<long long, long long> sg[10];
long long a[55], b[55];
long long n, m;
long long d[16][16];
long long dp[1 << 16][16];
long long solve(long long s, long long v) {
  if (dp[s][v] >= 0) return dp[s][v];
  if (s == (1 << n) - 1 && v == 0) return dp[s][v] = 0;
  long long res = 1000000007;
  for (long long u = 0; u < n; ++u) {
    if (!(s >> u & 1)) {
      res = min(res, solve(s | 1 << u, u) + d[v][u]);
    }
  }
  return dp[s][v] = res;
}
signed main() {
  cin >> n >> m;
  for (long long i = 0; i < n; ++i)
    for (long long j = 0; j < n; ++j) d[i][j] = 1000000007;
  for (long long i = 0; i < m; ++i) {
    long long a, b, c;
    cin >> a >> b >> c;
    d[a][b] = c;
  }
  memset(dp, -1, sizeof(dp));
  cout << solve(0, 0) << endl;
  return 0;
}
