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;
int dp[1 << 15][15],d[15][15],a,b,c,n,p,INF=1<<30;
int rec(int s,int v){
	if(dp[s][v]!=-1)return dp[s][v];
	if(s == (1<< n) -1 && v == 0)return dp[s][v] = 0;
	int res = INF;
	for(int i = 0;i<n;i++)if(!(s>>i & 1) && d[v][i] != -1)res = min(res,rec(s|(1<<i),i)+d[v][i]);
	return dp[s][v] = res;
}
int main(){
	memset(dp,-1,sizeof(dp));
	memset(d,-1,sizeof(d));
	cin >> n >> p;
	for(int u = 0; u < p;u++)cin>>a>>b>>c,d[a][b]=c;
	cout<<(INF == (a = rec(0,0))?-1:a)<<endl;
}