#define _USE_MATH_DEFINES

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>

using namespace std;

typedef pair<long long int, long long int> P;
long long int INF = 1e18;

int main(){
	
	long long int V, E;
	cin >> V >> E;
	
	long long int cost[V][V];
	
	for(int i = 0; i < V; i++){
		for(int j = 0; j < V; j++){
			cost[i][j] = INF;
		}
	}
	
	for(int i = 0; i < E; i++){
		int u, v, c;
		cin >> u >> v >> c;
		cost[u][v] = c;
	}
	
	long long int DP[V][(1 << V)];
	
	for(int i = 0; i < V; i++){
		for(int j = 0; j < (1 << V); j++){
			DP[i][j] = INF;
		}
	}
	DP[0][0] = 0;
	
	for(int i = 0; i < (1 << V); i++){
		for(int j = 0; j < V; j++){
			if(i & (1 << j)){
				for(int k = 0; k < V; k++){
					DP[j][i] = min(DP[j][i], DP[k][i - (1 << j)] + cost[k][j]);
				}
			}
		}
	}
	
	long long int ans = DP[0][(1 << V) - 1];
	if(ans == INF){
		cout << -1 << endl;
	}else{
		cout << ans << 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
#define _USE_MATH_DEFINES

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <map>

using namespace std;

typedef pair<long long int, long long int> P;
long long int INF = 1e18;

int main(){
	
	long long int V, E;
	cin >> V >> E;
	
	long long int cost[V][V];
	
	for(int i = 0; i < V; i++){
		for(int j = 0; j < V; j++){
			cost[i][j] = INF;
		}
	}
	
	for(int i = 0; i < E; i++){
		int u, v, c;
		cin >> u >> v >> c;
		cost[u][v] = c;
	}
	
	long long int DP[V][(1 << V)];
	
	for(int i = 0; i < V; i++){
		for(int j = 0; j < (1 << V); j++){
			DP[i][j] = INF;
		}
	}
	DP[0][0] = 0;
	
	for(int i = 0; i < (1 << V); i++){
		for(int j = 0; j < V; j++){
			if(i & (1 << j)){
				for(int k = 0; k < V; k++){
					DP[j][i] = min(DP[j][i], DP[k][i - (1 << j)] + cost[k][j]);
				}
			}
		}
	}
	
	long long int ans = DP[0][(1 << V) - 1];
	if(ans == INF){
		cout << -1 << endl;
	}else{
		cout << ans << endl;
	}
	
	return 0;
}

```