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();
}
template <class T>
inline T sqr(T x) {
  return x * x;
}
const double EPS = 1e-10;
const double PI = acos(-1.0);
const int INF = (int)1000000007;
const long long MOD = (long long)1000000007;
const long long INF2 = (long long)100000000000000000;
int main() {
  int V, E;
  cin >> V >> E;
  vector<vector<int>> adj(V, vector<int>(V));
  for (int e = 0; e < E; e++) {
    int s, t, d;
    cin >> s >> t >> d;
    adj[s][t] = d;
  }
  vector<vector<int>> dp(1 << V, vector<int>(V));
  for (int i = 0; i < (1 << V); i++) {
    for (int j = 0; j < V; j++) {
      dp[i][j] = INF;
    }
  }
  dp[1][0] = 0;
  for (int s = 0; s < (1 << V); s++) {
    for (int v = 0; v < V; v++) {
      if (dp[s][v] == INF) continue;
      for (int k = 0; k < V; k++) {
        if (s >> k & 1) continue;
        int nexts = s | (1 << k);
        if (adj[v][k] != 0) {
          dp[nexts][k] = min(dp[nexts][k], dp[s][v] + adj[v][k]);
        }
      }
    }
  }
  int all = (1 << V) - 1;
  int ans = INF;
  for (int v = 0; v < V; v++) {
    if (dp[all][v] == INF) continue;
    if (adj[v][0] == 0) continue;
    ans = min(ans, dp[all][v] + adj[v][0]);
  }
  if (ans == INF) {
    cout << -1 << endl;
  } else {
    cout << ans << endl;
  }
  return 0;
}
