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;
typedef struct {
  int cost, to;
} Edge;
int v, e;
vector<Edge> G[16];
int ans = -1;
int starts;
void bitdp(int bit, int cnt, int now);
int main() {
  cin >> v >> e;
  for (int i = 0, a, b, c; i < e; i++) {
    cin >> a >> b >> c;
    G[a].push_back((Edge){c, b});
  }
  for (int i = 0; i < v; i++) {
    for (int j = 0; j < G[i].size(); j++) {
      int a = 0;
      starts = i;
      bitdp(0, G[i][j].cost, G[i][j].to);
      a = 0;
    }
  }
  cout << ans << endl;
}
void bitdp(int bit, int cnt, int now) {
  int temp;
  int co = 0;
  if (bit & 1 << now) return;
  bit = bit | 1 << now;
  bitset<5> bs((long)bit);
  for (int i = 0; i < v; i++) {
    if (bit & 1 << i)
      co++;
    else
      break;
  }
  if (co == v && now == starts) {
    if (ans == -1)
      ans = cnt;
    else
      ans = min(ans, cnt);
    return;
  }
  for (int i = 0; i < G[now].size(); i++) {
    temp = bit;
    bitdp(bit, cnt + G[now][i].cost, G[now][i].to);
    bit = temp;
  }
  return;
}
