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;
const int MAX_V = 15;
const int INF = 1 << 28;
int G[MAX_V][MAX_V];
int V, E;
int memo[MAX_V][1 << MAX_V];
void init() { memset(memo, -1, sizeof(memo)); }
int dfs(int v, int used) {
  if (used == (1 << V) - 1) return G[v][0];
  if (memo[v][used] >= 0) return memo[v][used];
  int ret = INF;
  for (int u = 0; u < V; u++) {
    if (v == u || (used & (1 << u))) continue;
    ret = min(ret, dfs(u, used | (1 << u)) + G[v][u]);
  }
  return memo[v][used] = ret;
}
int TSP() {
  int ret = INF;
  init();
  for (int i = 0; i < V; i++) {
    ret = min(ret, dfs(i, (1 << i)) + G[0][i]);
  }
  return ret;
}
int main() {
  cin >> V >> E;
  for (int i = 0; i < V; i++) {
    for (int j = 0; j < V; j++) G[i][j] = INF;
    G[i][i] = 0;
  }
  for (int i = 0; i < E; i++) {
    int s, t, d;
    cin >> s >> t >> d;
    G[s][t] = d;
  }
  int Ans = TSP();
  cout << (Ans == INF ? -1 : Ans) << endl;
  return 0;
}
