#include<iostream>
#include<algorithm>
#include<cstring>

using namespace std;

const int INF=1<<25;

int n;
int m[15][15];
int dp[15][1<<15];

int rec(int s,int v)
{
	if(dp[v][s]>=0)return dp[v][s];
	else if(s==(1<<n)-1&&v==0)return dp[v][s]=0;
	
	int res=INF;
	for(int u=0;u<n;u++)
	{
		if(!(s>>u&1)&&m[v][u]!=INF)res=min(res,rec(s|1<<u,u)+m[v][u]);
	}
	return dp[v][s]=res;
}

int main()
{
	int e,s,t,d;cin>>n>>e;
	for(int i=0;i<n;i++)for(int j=0;j<n;j++)m[i][j]=INF;
	for(int i=0;i<e;i++)
	{
		cin>>s>>t>>d;
		m[s][t]=d;
	}
	
	memset(dp,-1,sizeof(dp));
	int ans=rec(0,0);
	if(ans!=INF)cout<<rec(0,0)<<endl;
	else cout<<-1<<endl;
	return 0;
}
### Prompt

Please create a solution in Cpp to 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<algorithm>
#include<cstring>

using namespace std;

const int INF=1<<25;

int n;
int m[15][15];
int dp[15][1<<15];

int rec(int s,int v)
{
	if(dp[v][s]>=0)return dp[v][s];
	else if(s==(1<<n)-1&&v==0)return dp[v][s]=0;
	
	int res=INF;
	for(int u=0;u<n;u++)
	{
		if(!(s>>u&1)&&m[v][u]!=INF)res=min(res,rec(s|1<<u,u)+m[v][u]);
	}
	return dp[v][s]=res;
}

int main()
{
	int e,s,t,d;cin>>n>>e;
	for(int i=0;i<n;i++)for(int j=0;j<n;j++)m[i][j]=INF;
	for(int i=0;i<e;i++)
	{
		cin>>s>>t>>d;
		m[s][t]=d;
	}
	
	memset(dp,-1,sizeof(dp));
	int ans=rec(0,0);
	if(ans!=INF)cout<<rec(0,0)<<endl;
	else cout<<-1<<endl;
	return 0;
}
```