#include<bits/stdc++.h>
using namespace std;
#define INF 1000000000

int main()
{
    int V,E;cin >> V>> E;
    vector<vector<int>> graph(V,vector<int> (V,-1));
    int u,v;
    for (int i=0;i<E;i++)
    {
        cin >> u >> v;
        cin >> graph[u][v];
    }
    vector<vector<int>> dp(1<<(V-1),vector<int> (V,INF)); //dp[s][v] sは今まで訪れた点集合、vは今いる点
    dp[0][0]=0;
    for (int i=0;i<1<<(V-1);i++) //iだけ1indexed
    {
        for (int u=0;u<V;u++)
        {
            for (int v=1;v<V;v++)
            {
                if (((i>>(v-1))&1)==0)
                {
                    if (graph[u][v]>=0)
                    {
                        //cout << (1<<(v-1)) << endl;
                        //cout << "i"<<i<< endl;
                        dp[i+(1<<(v-1))][v]=min(dp[i+(1<<(v-1))][v],dp[i][u]+graph[u][v]);
                    }
                }
            }
        }
    }
    int ans=INF;
    for (int i=1;i<V;i++)
    {
        if (graph[i][0]>=0) ans=min(ans,dp[(1<<(V-1))-1][i]+graph[i][0]);
    }
    if (ans==INF) cout << -1 << endl;
    else cout << ans << endl;
    return 0;
}

### Prompt

Create a solution in Cpp for 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;
#define INF 1000000000

int main()
{
    int V,E;cin >> V>> E;
    vector<vector<int>> graph(V,vector<int> (V,-1));
    int u,v;
    for (int i=0;i<E;i++)
    {
        cin >> u >> v;
        cin >> graph[u][v];
    }
    vector<vector<int>> dp(1<<(V-1),vector<int> (V,INF)); //dp[s][v] sは今まで訪れた点集合、vは今いる点
    dp[0][0]=0;
    for (int i=0;i<1<<(V-1);i++) //iだけ1indexed
    {
        for (int u=0;u<V;u++)
        {
            for (int v=1;v<V;v++)
            {
                if (((i>>(v-1))&1)==0)
                {
                    if (graph[u][v]>=0)
                    {
                        //cout << (1<<(v-1)) << endl;
                        //cout << "i"<<i<< endl;
                        dp[i+(1<<(v-1))][v]=min(dp[i+(1<<(v-1))][v],dp[i][u]+graph[u][v]);
                    }
                }
            }
        }
    }
    int ans=INF;
    for (int i=1;i<V;i++)
    {
        if (graph[i][0]>=0) ans=min(ans,dp[(1<<(V-1))-1][i]+graph[i][0]);
    }
    if (ans==INF) cout << -1 << endl;
    else cout << ans << endl;
    return 0;
}

```