#include<iostream>
#include<string>
#include<algorithm>
#include<cmath>
#include<vector>
#include<stack>
#include<climits>
#include<cstring>
using namespace std;
const int INF=INT_MAX/2;

struct edge { int to, weight;};
typedef vector<edge> Edges;
typedef vector<Edges> Graph;

int  DP[1 << 15][15];

int rec(int S, int v, int V, Graph &G){
	if(DP[S][v]>=0){
		return DP[S][v];
	}
	if (S==(1 << V)-1 && v==0) 
	{
		return DP[S][v]=0;
	}

	int r = INF;
	for(int i=0;i<G[v].size();i++){
		edge f = G[v][i];
		if((S >> f.to)%2==0){
			r=min(r,rec((S | (1 << f.to)) ,f.to,V,G)+f.weight);
		}
	}
	return DP[S][v]=r;
}

int main(){
	int V,E,d,s;
	edge e;
	cin >> V >> E ;

	Graph G(V);
	for (int i=0;i<E;i++){
		cin >> s >> e.to >> e.weight;
		G[s].push_back(e);
	}

	memset(DP,-1,sizeof(DP));
	int result =rec(0,0,V,G) ;
	if(result>=INF){
		cout << -1<< endl;
	}else{
		cout << result <<endl;
	}

	return 0 ;
}
### Prompt

Develop a solution in cpp to the problem described below:

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<string>
#include<algorithm>
#include<cmath>
#include<vector>
#include<stack>
#include<climits>
#include<cstring>
using namespace std;
const int INF=INT_MAX/2;

struct edge { int to, weight;};
typedef vector<edge> Edges;
typedef vector<Edges> Graph;

int  DP[1 << 15][15];

int rec(int S, int v, int V, Graph &G){
	if(DP[S][v]>=0){
		return DP[S][v];
	}
	if (S==(1 << V)-1 && v==0) 
	{
		return DP[S][v]=0;
	}

	int r = INF;
	for(int i=0;i<G[v].size();i++){
		edge f = G[v][i];
		if((S >> f.to)%2==0){
			r=min(r,rec((S | (1 << f.to)) ,f.to,V,G)+f.weight);
		}
	}
	return DP[S][v]=r;
}

int main(){
	int V,E,d,s;
	edge e;
	cin >> V >> E ;

	Graph G(V);
	for (int i=0;i<E;i++){
		cin >> s >> e.to >> e.weight;
		G[s].push_back(e);
	}

	memset(DP,-1,sizeof(DP));
	int result =rec(0,0,V,G) ;
	if(result>=INF){
		cout << -1<< endl;
	}else{
		cout << result <<endl;
	}

	return 0 ;
}
```