#include<bits/stdc++.h>
using namespace std;

int V, E, mat[15][15]={0}, m[1<<15][15]={0};
int INF =1e8 ;

int TSP(int x, int y){
	int i;
	if(m[x][y]>=0){
		return (m[x][y]);
	}
	if(x==(1<<V) -1 && y==0){
		return (m[x][y]= 0);
	}
	int min_path=INF;

	for(i=0; i<V; i++){
		if(!(x>>i & 1)){
			min_path=min(min_path, TSP(x | 1<<i, i) + mat[y][i]);
		}
	}


	return (m[x][y]=min_path);
}

int main(){
	int s, t, d, i, j;
	int out;

	cin>>V>>E; //getchar();
	for(i=0; i<V;i++){
		for(j=0; j<V; j++){
			mat[i][j]=INF;
		}
	}
	for(i=0; i<E; i++){
		cin>>s>>t>>d; //getchar();
		mat[s][t]=d;
	}

	memset(m, -1, sizeof(m));

	out=TSP(0,0);
	if(out == INF){
		cout<< -1 ;
	}else{
		cout<< out;
	}
    cout<<endl;
    //getchar();
    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<bits/stdc++.h>
using namespace std;

int V, E, mat[15][15]={0}, m[1<<15][15]={0};
int INF =1e8 ;

int TSP(int x, int y){
	int i;
	if(m[x][y]>=0){
		return (m[x][y]);
	}
	if(x==(1<<V) -1 && y==0){
		return (m[x][y]= 0);
	}
	int min_path=INF;

	for(i=0; i<V; i++){
		if(!(x>>i & 1)){
			min_path=min(min_path, TSP(x | 1<<i, i) + mat[y][i]);
		}
	}


	return (m[x][y]=min_path);
}

int main(){
	int s, t, d, i, j;
	int out;

	cin>>V>>E; //getchar();
	for(i=0; i<V;i++){
		for(j=0; j<V; j++){
			mat[i][j]=INF;
		}
	}
	for(i=0; i<E; i++){
		cin>>s>>t>>d; //getchar();
		mat[s][t]=d;
	}

	memset(m, -1, sizeof(m));

	out=TSP(0,0);
	if(out == INF){
		cout<< -1 ;
	}else{
		cout<< out;
	}
    cout<<endl;
    //getchar();
    return 0;
}

```