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>
const int MAX_V = 15, INF = std::numeric_limits<int>::max() >> 2;
int V, E;
std::vector<std::vector<int> > d(MAX_V, std::vector<int>(MAX_V, INF));
int dp[1 << MAX_V + 1][MAX_V];
int sv;
int rec(int S, int v) {
  if (S == (1 << V) - 1 && v == sv) return dp[S][v] = 0;
  if (~dp[S][v]) return dp[S][v];
  int ret = INF;
  for (int u = 0; u < (V); ++u)
    if (!(S >> u & 1)) ret = std::min(ret, rec(S | 1 << u, u) + d[v][u]);
  return dp[S][v] = ret;
}
int main() {
  scanf("%d%d", &V, &E);
  for (int i = 0; i < (E); ++i) {
    int s, t;
    scanf("%d%d", &s, &t);
    scanf("%d", &d[s][t]);
  }
  int ans = INF;
  for (int v = 0; v < (V); ++v) {
    memset((dp), (-1), sizeof(dp));
    sv = v;
    ans = std::min(ans, rec(0, v));
  }
  printf("%d\n", ans == INF ? -1 : ans);
  return 0;
}
