#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
static const int INF = 1 << 20;

int main(){
	int V, E;
	cin >> V >> E;
	vector<vector<int> > adj(V, vector<int>(V, INF));
	for(int i = 0; i < E; i++){
		int s, t, d;
		cin >> s >> t >> d;
		adj[s][t] = min(adj[s][t], d);
	}
	vector<vector<int> > memo(1 << V, vector<int>(V, INF));
	int res = INF;
	for(int i = 1; i < (1 << V); i++){
		for(int j = 0; j < V; j++){
			if(i == 1){
				if(j == 0) memo[i][j] = 0;
				continue;
			}
			if(!(i & (1 << j))) continue;
			for(int k = 0; k < V; k++){
				if(k == j) continue;
				if(!(i & (1 << k))) continue;
				memo[i][j] = min(memo[i][j], memo[i - (1 << j)][k] + adj[k][j]);
			}
			if(i == (1 << V) - 1){
				if(adj[j][0] == INF) continue;
				res = min(res, memo[i][j] + adj[j][0]);
			}
		}
	}
	cout << (res == INF ? -1 : res) << endl;
	return 0;
}


### Prompt

Your challenge is to write 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<vector>
#include<algorithm>
using namespace std;
static const int INF = 1 << 20;

int main(){
	int V, E;
	cin >> V >> E;
	vector<vector<int> > adj(V, vector<int>(V, INF));
	for(int i = 0; i < E; i++){
		int s, t, d;
		cin >> s >> t >> d;
		adj[s][t] = min(adj[s][t], d);
	}
	vector<vector<int> > memo(1 << V, vector<int>(V, INF));
	int res = INF;
	for(int i = 1; i < (1 << V); i++){
		for(int j = 0; j < V; j++){
			if(i == 1){
				if(j == 0) memo[i][j] = 0;
				continue;
			}
			if(!(i & (1 << j))) continue;
			for(int k = 0; k < V; k++){
				if(k == j) continue;
				if(!(i & (1 << k))) continue;
				memo[i][j] = min(memo[i][j], memo[i - (1 << j)][k] + adj[k][j]);
			}
			if(i == (1 << V) - 1){
				if(adj[j][0] == INF) continue;
				res = min(res, memo[i][j] + adj[j][0]);
			}
		}
	}
	cout << (res == INF ? -1 : res) << endl;
	return 0;
}


```