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

#define INF 1000000000
int V, E;
int d[15][15]; //g[i][j] : i??????j??????????????¢?????????????????????-1
int dp[15][1<<15]; //dp[i][j] : i??????????????????0?????????????°??????¢(j?????¢????????£???????????±)

int tsp(int v, int b){
  //  cout<<v<<endl;
  if(dp[v][b]>0)return dp[v][b]; //?????¢????????¨????????????
  if(b==(1<<V)-1 && v==0)return dp[v][b]=0; //??¨?????????????????£?????????0????????£?????????
  int ret=INF;
  for(int i=0; i<V; i++){
    if((b>>i)&1)continue; //??¢????????£???
    if(d[v][i]==-1)continue; //????????????
    ret = min(ret, tsp(i, b|(1<<i))+d[v][i]);
  }
  return dp[v][b]=ret;
}

int main(){
  memset(d, -1, sizeof(d));
  memset(dp, -1, sizeof(dp));
  cin>>V>>E;
  for(int i=0; i<E; i++){
    int s, t, p;
    cin>>s>>t>>p;
    d[s][t]=p;
  }
  int min_d = tsp(0, 0);
  if(min_d==INF)cout<<-1<<endl;
  else cout<<min_d<<endl;
  return 0;
}
### 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
//Traveling Salesman Problem
#include<bits/stdc++.h>
using namespace std;

#define INF 1000000000
int V, E;
int d[15][15]; //g[i][j] : i??????j??????????????¢?????????????????????-1
int dp[15][1<<15]; //dp[i][j] : i??????????????????0?????????????°??????¢(j?????¢????????£???????????±)

int tsp(int v, int b){
  //  cout<<v<<endl;
  if(dp[v][b]>0)return dp[v][b]; //?????¢????????¨????????????
  if(b==(1<<V)-1 && v==0)return dp[v][b]=0; //??¨?????????????????£?????????0????????£?????????
  int ret=INF;
  for(int i=0; i<V; i++){
    if((b>>i)&1)continue; //??¢????????£???
    if(d[v][i]==-1)continue; //????????????
    ret = min(ret, tsp(i, b|(1<<i))+d[v][i]);
  }
  return dp[v][b]=ret;
}

int main(){
  memset(d, -1, sizeof(d));
  memset(dp, -1, sizeof(dp));
  cin>>V>>E;
  for(int i=0; i<E; i++){
    int s, t, p;
    cin>>s>>t>>p;
    d[s][t]=p;
  }
  int min_d = tsp(0, 0);
  if(min_d==INF)cout<<-1<<endl;
  else cout<<min_d<<endl;
  return 0;
}
```