#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
#include <queue>
#include <algorithm>
#define shosu(x) fixed<<setprecision(x)
using namespace std;
typedef pair<int,int> P;
const int inf=1<<30;
const double pi=acos(-1);

int V,E;
vector<vector<int> > G,dp;

int func(int S,int v){
	if(dp[S][v]!=inf) return dp[S][v];
	if(S==(1<<V)-1&&v==0) return dp[S][v]=0;
	int tmp=inf-1;
	for(int i=0;i<V;i++){
		if(G[v][i]==inf) continue;
		if(!(S>>i&1)) tmp=min(tmp,func(S|1<<i,i)+G[v][i]);
	}
	return dp[S][v]=tmp;
}

int main(){
	cin>>V>>E;
	G=vector<vector<int> >(V,vector<int>(V,inf));
	for(int i=0;i<E;i++){
		int s,t,d;
		cin>>s>>t>>d;
		G[s][t]=d;
	}
	dp=vector<vector<int> >(1<<V,vector<int>(V,inf));
	int ans=func(0,0);
	if(ans==inf-1) cout<<-1<<endl;
	else cout<<ans<<endl;
}
### Prompt

Create a solution in Cpp for the following problem:

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

### Response

```cpp
#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
#include <queue>
#include <algorithm>
#define shosu(x) fixed<<setprecision(x)
using namespace std;
typedef pair<int,int> P;
const int inf=1<<30;
const double pi=acos(-1);

int V,E;
vector<vector<int> > G,dp;

int func(int S,int v){
	if(dp[S][v]!=inf) return dp[S][v];
	if(S==(1<<V)-1&&v==0) return dp[S][v]=0;
	int tmp=inf-1;
	for(int i=0;i<V;i++){
		if(G[v][i]==inf) continue;
		if(!(S>>i&1)) tmp=min(tmp,func(S|1<<i,i)+G[v][i]);
	}
	return dp[S][v]=tmp;
}

int main(){
	cin>>V>>E;
	G=vector<vector<int> >(V,vector<int>(V,inf));
	for(int i=0;i<E;i++){
		int s,t,d;
		cin>>s>>t>>d;
		G[s][t]=d;
	}
	dp=vector<vector<int> >(1<<V,vector<int>(V,inf));
	int ans=func(0,0);
	if(ans==inf-1) cout<<-1<<endl;
	else cout<<ans<<endl;
}
```