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

struct edge{int to,dist;};
using Graph  = vector<vector<edge>>;
#define INF 1e9

int main(){
    int V,E;
    cin >> V >> E;  

    Graph G(V);
    for(int i = 0;i < E;i++){
        int s,t,d;
        cin >> s >> t >> d;
        G[s].push_back({t,d});
    }

    vector<vector<int>> dp(1 << V, vector<int>(V,INF));
    dp[0][0] = 0;

    for(int bit = 0;bit < (1 << V);bit++){
        for(int nowV = 0; nowV < V;nowV++){
            if(dp[bit][nowV] == INF) continue;
            for(auto e : G[nowV]){
                if((bit >> e.to) & 1) continue;
                int nbit = bit | (1 << e.to);
                dp[nbit][e.to] = min(dp[nbit][e.to], dp[bit][nowV] + e.dist);
            }
        }
    }
    cout << (dp[(1 << V) -1][0] == INF ? -1 : dp[(1 << V) -1][0]) << endl;
}


### Prompt

Please provide a cpp coded solution 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
#include<bits/stdc++.h>
using namespace std;

struct edge{int to,dist;};
using Graph  = vector<vector<edge>>;
#define INF 1e9

int main(){
    int V,E;
    cin >> V >> E;  

    Graph G(V);
    for(int i = 0;i < E;i++){
        int s,t,d;
        cin >> s >> t >> d;
        G[s].push_back({t,d});
    }

    vector<vector<int>> dp(1 << V, vector<int>(V,INF));
    dp[0][0] = 0;

    for(int bit = 0;bit < (1 << V);bit++){
        for(int nowV = 0; nowV < V;nowV++){
            if(dp[bit][nowV] == INF) continue;
            for(auto e : G[nowV]){
                if((bit >> e.to) & 1) continue;
                int nbit = bit | (1 << e.to);
                dp[nbit][e.to] = min(dp[nbit][e.to], dp[bit][nowV] + e.dist);
            }
        }
    }
    cout << (dp[(1 << V) -1][0] == INF ? -1 : dp[(1 << V) -1][0]) << endl;
}


```