#include<iostream>
#include<algorithm>
#include<vector>
#include<cstdio>

using namespace std;

int V,E;
int map[15][15];
int dp[1<<15][15];

int saiki(int vis,int pos){

    int r = 1<<28;
    if(dp[vis][pos] != -1) return dp[vis][pos];
    if(pos == 0 && vis == (1<<V)-1){
       	return 0;
    }
    for(int i=0;i<V;i++){
	if(map[pos][i] != -1 && !(vis & (1<<i)) ){
	    r = min(r,saiki( vis | (1<<i) ,i) + map[pos][i]);
	
	}
    }

    return dp[vis][pos] = r;
}
int main(){

    int s,t;
    cin >> V >> E;
    fill(&map[0][0],&map[15][0],-1);
    for(int i=0;i<E;i++){
	cin >> s >> t;
	cin >> map[s][t];
    }
    fill(&dp[0][0],&dp[1<<15][0],-1);

    int res = saiki(0,0);

    if(res >= 1<<28) res = -1;
    cout << res << endl;

    return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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<cstdio>

using namespace std;

int V,E;
int map[15][15];
int dp[1<<15][15];

int saiki(int vis,int pos){

    int r = 1<<28;
    if(dp[vis][pos] != -1) return dp[vis][pos];
    if(pos == 0 && vis == (1<<V)-1){
       	return 0;
    }
    for(int i=0;i<V;i++){
	if(map[pos][i] != -1 && !(vis & (1<<i)) ){
	    r = min(r,saiki( vis | (1<<i) ,i) + map[pos][i]);
	
	}
    }

    return dp[vis][pos] = r;
}
int main(){

    int s,t;
    cin >> V >> E;
    fill(&map[0][0],&map[15][0],-1);
    for(int i=0;i<E;i++){
	cin >> s >> t;
	cin >> map[s][t];
    }
    fill(&dp[0][0],&dp[1<<15][0],-1);

    int res = saiki(0,0);

    if(res >= 1<<28) res = -1;
    cout << res << endl;

    return 0;
}
```