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

// macro
#define rep(i,n) for(i=0;i<n;i++)
#define ll long long
#define all(v) v.begin(), v.end()

// code starts
#define INF 1000000

int main()
{
  int v,e;cin>>v>>e;
  vector<int> s(e);
  vector<int> t(e);
  vector<int> d(e);
  int i,j,k;
  rep(i,e)cin>>s[i]>>t[i]>>d[i];
  vector<vector<int>> g(v,vector<int>(v,INF));
  rep(i,e)
  {
    g[s[i]][t[i]]=d[i];
  }
  int ans=INF;
  bool exist=false;
  vector<vector<int>> dp(1<<v,vector<int>(v,INF));
  dp[0][0]=0;
  rep(i,1<<v)
  {
    rep(j,v)
    {
      rep(k,v)
      {
        if(g[j][k]==INF)continue;
        if(i&(1<<k))continue;
        int to=(i|(1<<k));
        dp[to][k]=min(dp[to][k],dp[i][j]+g[j][k]);
      }
    }
  }
  if(dp[(1<<v)-1][0]==INF)cout<<-1<<endl;
  else cout<<dp[(1<<v)-1][0]<<endl;
}


### Prompt

In Cpp, your task is to solve 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;

// macro
#define rep(i,n) for(i=0;i<n;i++)
#define ll long long
#define all(v) v.begin(), v.end()

// code starts
#define INF 1000000

int main()
{
  int v,e;cin>>v>>e;
  vector<int> s(e);
  vector<int> t(e);
  vector<int> d(e);
  int i,j,k;
  rep(i,e)cin>>s[i]>>t[i]>>d[i];
  vector<vector<int>> g(v,vector<int>(v,INF));
  rep(i,e)
  {
    g[s[i]][t[i]]=d[i];
  }
  int ans=INF;
  bool exist=false;
  vector<vector<int>> dp(1<<v,vector<int>(v,INF));
  dp[0][0]=0;
  rep(i,1<<v)
  {
    rep(j,v)
    {
      rep(k,v)
      {
        if(g[j][k]==INF)continue;
        if(i&(1<<k))continue;
        int to=(i|(1<<k));
        dp[to][k]=min(dp[to][k],dp[i][j]+g[j][k]);
      }
    }
  }
  if(dp[(1<<v)-1][0]==INF)cout<<-1<<endl;
  else cout<<dp[(1<<v)-1][0]<<endl;
}


```