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

struct edge{
  int to,c;
};

int V,E,ST;
vector<edge> G[20];
int dp[(1<<15)][16];
int solve(int st,int id){
  if( dp[st][id] != -1 ) return dp[st][id];
  if( st == (1<<V)-1 && id == ST ) return dp[st][id] = 0;
  int ret = (1<<29);
  for(int i=0;i<(int)G[id].size();i++){
    edge e = G[id][i];
    if( (st & (1<<e.to) ) ) continue;
    ret = min( ret, solve(st|(1<<e.to),e.to) + e.c );
  }
  return dp[st][id] = ret;
}

int main(){
  cin >> V >> E;
  for(int i=0;i<E;i++){
    int s,t,d;
    cin >> s >> t >> d;
    G[s].push_back((edge){t,d});
  }
  int res = (1<<29);
  for(int i=0;i<V;i++){
    memset(dp,-1,sizeof(dp));
    res = min ( res, solve(0,i) );
    ST++;
  }
  cout << (res==(1<<29)?-1:res) << endl;


}
### Prompt

Develop a solution in cpp 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
#include<bits/stdc++.h>
using namespace std;

struct edge{
  int to,c;
};

int V,E,ST;
vector<edge> G[20];
int dp[(1<<15)][16];
int solve(int st,int id){
  if( dp[st][id] != -1 ) return dp[st][id];
  if( st == (1<<V)-1 && id == ST ) return dp[st][id] = 0;
  int ret = (1<<29);
  for(int i=0;i<(int)G[id].size();i++){
    edge e = G[id][i];
    if( (st & (1<<e.to) ) ) continue;
    ret = min( ret, solve(st|(1<<e.to),e.to) + e.c );
  }
  return dp[st][id] = ret;
}

int main(){
  cin >> V >> E;
  for(int i=0;i<E;i++){
    int s,t,d;
    cin >> s >> t >> d;
    G[s].push_back((edge){t,d});
  }
  int res = (1<<29);
  for(int i=0;i<V;i++){
    memset(dp,-1,sizeof(dp));
    res = min ( res, solve(0,i) );
    ST++;
  }
  cout << (res==(1<<29)?-1:res) << endl;


}
```