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;
using ll = long long int;
using P = pair<int, int>;
using T = tuple<int, int, int>;
using edge = struct { int to, cost; };
const int MOD = 1e9 + 7;
const int iINF = 1e9;
const long long int llINF = 1e18;
const double PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
vector<edge> graph[16];
int dp[16][1 << 16];
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int V, E;
  cin >> V >> E;
  for (int i = 0; i < (E); i++) {
    int s, t, d;
    cin >> s >> t >> d;
    graph[s].push_back(edge{t, d});
  }
  for (int i = 0; i < (V); i++) {
    for (int j = 0; j < (1 << V); j++) {
      dp[i][j] = iINF;
    }
  }
  for (int i = 0; i < (V); i++) {
    dp[i][0] = 0;
  }
  for (int S = 0; S < (1 << V); S++) {
    for (int i = 0; i < (V); i++) {
      if (dp[i][S] == iINF) continue;
      for (auto e : graph[i]) {
        if ((S >> e.to) & 1) continue;
        dp[e.to][S | 1 << e.to] =
            min(dp[e.to][S | 1 << e.to], dp[i][S] + e.cost);
      }
    }
  }
  cout << (dp[0][(1 << V) - 1] == iINF ? -1 : dp[0][(1 << V) - 1]) << endl;
  return 0;
}
