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_MAX / 10;
int n;
int d[20][20];
int dp[1 << 20][20];
int rec(int S, int v) {
  if (dp[S][v] >= 0) {
    return dp[S][v];
  }
  if (S == (1 << n) - 1 && v == 0) {
    dp[S][v] = 0;
    return 0;
  }
  int res = INF;
  for (int u = 0; u < n; u++) {
    if (!(S >> u & 1)) {
      res = min(res, rec(S | 1 << u, u) + d[v][u]);
    }
  }
  dp[S][v] = res;
  return res;
}
int main() {
  memset(dp, -1, sizeof(dp));
  int V, E;
  cin >> V >> E;
  n = V;
  for (long long i = (0); i < (n); ++i)
    for (long long j = (0); j < (n); ++j) d[i][j] = INF;
  for (long long i = (0); i < (E); ++i) {
    int s, t, cost;
    cin >> s >> t >> cost;
    d[s][t] = cost;
  }
  int res = rec(0, 0);
  if (res < INF)
    cout << res << endl;
  else
    cout << -1 << endl;
  return 0;
}
