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

const int INF=1e9;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int V,E; cin >> V >> E;
    struct edge{int to,cost;};
    vector<vector<edge>> G(V);
    for (int i=0;i<E;++i){
        int s,t,d; cin >> s >> t >> d;
        G[s].emplace_back(edge{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 i=0;i<V;++i){
            for (auto e:G[i]){
                int j=e.to;
                if (!(bit&1<<j)){
                    dp[bit|1<<j][j]=min(dp[bit|1<<j][j],dp[bit][i]+e.cost);
                }
            }
        }
    }
    cout << (dp[(1<<V)-1][0]==INF?-1:dp[(1<<V)-1][0]) << endl;
}

### Prompt

Please formulate 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;

const int INF=1e9;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int V,E; cin >> V >> E;
    struct edge{int to,cost;};
    vector<vector<edge>> G(V);
    for (int i=0;i<E;++i){
        int s,t,d; cin >> s >> t >> d;
        G[s].emplace_back(edge{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 i=0;i<V;++i){
            for (auto e:G[i]){
                int j=e.to;
                if (!(bit&1<<j)){
                    dp[bit|1<<j][j]=min(dp[bit|1<<j][j],dp[bit][i]+e.cost);
                }
            }
        }
    }
    cout << (dp[(1<<V)-1][0]==INF?-1:dp[(1<<V)-1][0]) << endl;
}

```