#include<bits/stdc++.h>
using namespace std;
struct TSP{
  int n,d[16][16],dp[(1<<16)][16];
  TSP(int sz):n(sz){
    for(int i=0;i<16;i++)
      for(int j=0;j<16;j++) d[i][j]=1e8;
  }
  void add(int a,int b,int c){
    d[a][b] = c;
    //d[b][a] = c;
  }
  int solve(){
    for(int i=0;i<(1<<n);i++)
      for(int j=0;j<n;j++) dp[i][j]=1e8;
    dp[0][0]=0;
    for(int i=0;i<(1<<n);i++){
      for(int j=0;j<n;j++){
        if(!((1<<j)&i)){
          for(int k=0;k<n;k++){
            dp[i|(1<<j)][j]=min(dp[i|(1<<j)][j],dp[i][k]+d[k][j]);
          }
        }
      }
    }
    if(dp[(1<<n)-1][0]==1e8)return -1;
    return dp[(1<<n)-1][0];
  }
};
int main(){
  int n,m;
  cin>>n>>m;
  TSP T(n);
  for(int i=0;i<m;i++){
    int x,y,z;
    cin>>x>>y>>z;
    T.add(x,y,z);
  }
  cout<<T.solve()<<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;
struct TSP{
  int n,d[16][16],dp[(1<<16)][16];
  TSP(int sz):n(sz){
    for(int i=0;i<16;i++)
      for(int j=0;j<16;j++) d[i][j]=1e8;
  }
  void add(int a,int b,int c){
    d[a][b] = c;
    //d[b][a] = c;
  }
  int solve(){
    for(int i=0;i<(1<<n);i++)
      for(int j=0;j<n;j++) dp[i][j]=1e8;
    dp[0][0]=0;
    for(int i=0;i<(1<<n);i++){
      for(int j=0;j<n;j++){
        if(!((1<<j)&i)){
          for(int k=0;k<n;k++){
            dp[i|(1<<j)][j]=min(dp[i|(1<<j)][j],dp[i][k]+d[k][j]);
          }
        }
      }
    }
    if(dp[(1<<n)-1][0]==1e8)return -1;
    return dp[(1<<n)-1][0];
  }
};
int main(){
  int n,m;
  cin>>n>>m;
  TSP T(n);
  for(int i=0;i<m;i++){
    int x,y,z;
    cin>>x>>y>>z;
    T.add(x,y,z);
  }
  cout<<T.solve()<<endl;
}

```