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 = 0;
int E = 0;
vector<pair<int, int> > graph[20];
int dp[1 << 15][15] = {0};
int DP(int bit, int v) {
  if (dp[bit][v] != (pow(10, 9))) return dp[bit][v];
  if (bit == (1 << V) - 1 && v == 0) return dp[bit][v] = 0;
  if (bit == (1 << V)) return dp[bit][v] = (pow(10, 9));
  int res = (pow(10, 9)) - 1;
  for (int i = 0; i < graph[v].size(); i++) {
    pair<int, int> cmp = graph[v][i];
    if (!((bit >> cmp.first) & 1)) {
      res = min(res, DP(bit | (1 << cmp.first), cmp.first) + cmp.second);
    }
  }
  return dp[bit][v] = res;
}
int solve() {
  for (int i = 0; i < (1 << V); i++) {
    for (int j = 0; j < V; j++) {
      dp[i][j] = (pow(10, 9));
    }
  }
  return DP(0, 0);
}
int main() {
  cin >> V >> E;
  for (int i = 0; i < E; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    graph[s].push_back(pair<int, int>(t, d));
  }
  if (solve() != (pow(10, 9)))
    printf("%d\n", solve());
  else
    puts("-1");
  return 0;
}
