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 pair<int,int> mypair;




int main(){
int v,e;
cin>>v>>e;
vector<vector<mypair> >  g(v);
for(int i=0;i<e;i++){
int s,t,d;
cin>>s>>t>>d;
g[s].push_back(mypair(t,d));
}
/*for(int i=0;i<v;i++){
	for(int j=0;j<g[i].size();j++){
	cout<<g[i][j].first<<' ';
	}
	cout<<endl;
}*/
vector<vector<int> > dp((1<<v),vector<int> (v,(int)1e8));
dp[0][0]=0;
for(int i=0;i<(1<<v);i++){
	for(int j=0;j<v;j++){
	//	if(!((1<<j)&i)){
		if(dp[i][j]!=(int)1e8){	

			for(int k=0;k<g[j].size();k++){
				if(!(i&(1<<g[j][k].first))){
					int tmp=i|(1<<g[j][k].first);
					dp[tmp][g[j][k].first] = min(dp[tmp][g[j][k].first],dp[i][j]+g[j][k].second);
				}
			}
		}

	//	}
	}
}
int ans = dp[(1<<v)-1][0];
cout<< (ans==1e8 ? -1:ans)<<endl;
return 0;

}

