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

typedef long long ll;
typedef vector<vector<ll> > Adj_Mat;


bool contain(int mask, int pos){
	  return ( mask & (1<<pos) ) != 0;
}

int main(){

	  // Input Graph
	  int V,E;
	  cin >> V >> E;
	  Adj_Mat G(V,vector<ll>(V,INT_MAX));
	  for(int i=0; i<E; i++){
			int s,t,d; cin >> s >> t >> d;
			G[s][t] = d;
	  }

	  ll ans = INT_MAX;
	  // Dynamic Programming for TSP
	  for(int st=0; st<V; st++){

			ll dp[ (1<<V) ][ V ];
			for(int i=0; i<(1<<V); i++) for(int j=0; j<V; j++) dp[i][j] = INT_MAX;
			dp[ 0 ][ st ] = 0;

			for(int S=1; S<(1<<V); S++)
				  for(int v=0; v<V; v++)
						if( contain(S,v) )
							  for(int j=0; j<V; j++)
									dp[S][v] = min(dp[S][v], dp[S-(1<<v)][j] + G[j][v]);
			ans = min(ans,dp[(1<<V)-1][st]);
	  }
	  if( ans >= 1e+9 ) ans = -1;
	  cout << ans << endl;
}
### 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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<vector<ll> > Adj_Mat;


bool contain(int mask, int pos){
	  return ( mask & (1<<pos) ) != 0;
}

int main(){

	  // Input Graph
	  int V,E;
	  cin >> V >> E;
	  Adj_Mat G(V,vector<ll>(V,INT_MAX));
	  for(int i=0; i<E; i++){
			int s,t,d; cin >> s >> t >> d;
			G[s][t] = d;
	  }

	  ll ans = INT_MAX;
	  // Dynamic Programming for TSP
	  for(int st=0; st<V; st++){

			ll dp[ (1<<V) ][ V ];
			for(int i=0; i<(1<<V); i++) for(int j=0; j<V; j++) dp[i][j] = INT_MAX;
			dp[ 0 ][ st ] = 0;

			for(int S=1; S<(1<<V); S++)
				  for(int v=0; v<V; v++)
						if( contain(S,v) )
							  for(int j=0; j<V; j++)
									dp[S][v] = min(dp[S][v], dp[S-(1<<v)][j] + G[j][v]);
			ans = min(ans,dp[(1<<V)-1][st]);
	  }
	  if( ans >= 1e+9 ) ans = -1;
	  cout << ans << endl;
}
```