#include<iostream>
#include<algorithm>
#include<vector>
#include<numeric>
#include<string>
#include<cmath>
#include<set>
#include<queue>
#include<bitset>
using namespace std;

const int inf = 1001001000;

int TSP(int bit,int v, vector<vector<int>> &dist, vector<vector<int>> &dp){
	if (dp[bit][v] >= 0) return dp[bit][v];
	if (bit == ((1 << dist.size()) - 1) && v == 0) {
		dp[bit][v] = 0;
		return dp[bit][v];
	}
	int res = inf;

	for (int u = 0; u < dist.size(); u++){
		if ((bit>>u&1) == 0) {
			res = min(res,TSP((bit|(1<<u)),u,dist,dp) + dist[v][u]);
		}
	}
	dp[bit][v] = res;
	return dp[bit][v];
}
int main(){
	int v, e; cin >> v >> e;
	vector<vector<int>> dist(v,vector<int>(v,inf));
	vector<vector<int>> dp((1 << v),vector<int>(v,-1));
	for (int i = 0; i < e; i++){
		int s, t, d; cin >> s >> t >> d;
		dist[s][t] = d;
	}

	int ans = TSP(0,0,dist,dp);
	
	if (ans == inf) cout << -1 << endl;
	else cout << ans << 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<algorithm>
#include<vector>
#include<numeric>
#include<string>
#include<cmath>
#include<set>
#include<queue>
#include<bitset>
using namespace std;

const int inf = 1001001000;

int TSP(int bit,int v, vector<vector<int>> &dist, vector<vector<int>> &dp){
	if (dp[bit][v] >= 0) return dp[bit][v];
	if (bit == ((1 << dist.size()) - 1) && v == 0) {
		dp[bit][v] = 0;
		return dp[bit][v];
	}
	int res = inf;

	for (int u = 0; u < dist.size(); u++){
		if ((bit>>u&1) == 0) {
			res = min(res,TSP((bit|(1<<u)),u,dist,dp) + dist[v][u]);
		}
	}
	dp[bit][v] = res;
	return dp[bit][v];
}
int main(){
	int v, e; cin >> v >> e;
	vector<vector<int>> dist(v,vector<int>(v,inf));
	vector<vector<int>> dp((1 << v),vector<int>(v,-1));
	for (int i = 0; i < e; i++){
		int s, t, d; cin >> s >> t >> d;
		dist[s][t] = d;
	}

	int ans = TSP(0,0,dist,dp);
	
	if (ans == inf) cout << -1 << endl;
	else cout << ans << endl;


	return 0;
}



```