#include <iostream>
#include <algorithm>
using namespace std;

int dp[1<<15][15];
int path[15][15];

int main(){
	
	for(int i=0;i<(1<<15)*15;i++)dp[i/15][i%15]=114514;
	for(int i=0;i<15*15;i++)path[i/15][i%15]=114514;
	
	int v,e;
	cin>>v>>e;
	for(int i=0;i<e;i++){
		int s,t,d;
		cin>>s>>t>>d;
		path[s][t]=d;
	}
	
	//?????????
	dp[0][0]=0;
	
	for(int i=0;i<(1<<v);i++){
		for(int j=0;j<v;j++){
			if(dp[i][j]==114514)continue;
			
			for(int k=0;k<v;k++){
				if(i & (1<<k))continue;
				dp[i+(1<<k)][k]=min(dp[i+(1<<k)][k],dp[i][j]+path[j][k]);
			}
		}
	}
	cout<<(dp[(1<<v)-1][0]==114514?-1:dp[(1<<v)-1][0])<<endl;
	
	
	return 0;
}

### Prompt

Please formulate a CPP solution 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>
using namespace std;

int dp[1<<15][15];
int path[15][15];

int main(){
	
	for(int i=0;i<(1<<15)*15;i++)dp[i/15][i%15]=114514;
	for(int i=0;i<15*15;i++)path[i/15][i%15]=114514;
	
	int v,e;
	cin>>v>>e;
	for(int i=0;i<e;i++){
		int s,t,d;
		cin>>s>>t>>d;
		path[s][t]=d;
	}
	
	//?????????
	dp[0][0]=0;
	
	for(int i=0;i<(1<<v);i++){
		for(int j=0;j<v;j++){
			if(dp[i][j]==114514)continue;
			
			for(int k=0;k<v;k++){
				if(i & (1<<k))continue;
				dp[i+(1<<k)][k]=min(dp[i+(1<<k)][k],dp[i][j]+path[j][k]);
			}
		}
	}
	cout<<(dp[(1<<v)-1][0]==114514?-1:dp[(1<<v)-1][0])<<endl;
	
	
	return 0;
}

```