#include <iostream>
#include <numeric>
#include <queue>
#include <cstring>
#include <stdio.h>
#include <string>
#include <vector>
#include <algorithm>
#include <limits.h>
using namespace std;
typedef vector<int> vi;
typedef long long ll;
typedef long long ll;
typedef vector<ll> vll;
typedef pair<int,int> P;
typedef pair<int,pair<int,int> > PP;
int dp[1<<16][16];
int dis[20][20];
int V,E;
const int inf=1e9+5;

int rec(int S,int v)
{
  if(dp[S][v]>=0)
    {
      return dp[S][v];
    }
  if(S==(1<<V)-1 && v==0)
    {
      return dp[S][v]=0;
    }
  int res=inf;
  for(int u=0;u<V;u++)
    {
      if(!(S>>u & 1))
	{
	  res=min(res,rec(S | (1<<u),u)+dis[v][u]);
	}
    }
  return dp[S][v]=res;
}

int main(int argc,char const* argv[])
{
  memset(dp,-1,sizeof(dp));
  memset(dis,inf,sizeof(dis));
  cin >> V >> E;
  for(int i=0;i<E;i++)
    {
      int s,t,d;
      cin >> s >> t >> d;
      dis[s][t]=d;
    }
  int ans=rec(0,0);
  if(ans>150000)
    {
      cout << -1 << endl;
    }
  else
    {
      cout << ans << endl;
    }
  return 0;
}


### Prompt

Your challenge is to write a cpp solution to 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 <iostream>
#include <numeric>
#include <queue>
#include <cstring>
#include <stdio.h>
#include <string>
#include <vector>
#include <algorithm>
#include <limits.h>
using namespace std;
typedef vector<int> vi;
typedef long long ll;
typedef long long ll;
typedef vector<ll> vll;
typedef pair<int,int> P;
typedef pair<int,pair<int,int> > PP;
int dp[1<<16][16];
int dis[20][20];
int V,E;
const int inf=1e9+5;

int rec(int S,int v)
{
  if(dp[S][v]>=0)
    {
      return dp[S][v];
    }
  if(S==(1<<V)-1 && v==0)
    {
      return dp[S][v]=0;
    }
  int res=inf;
  for(int u=0;u<V;u++)
    {
      if(!(S>>u & 1))
	{
	  res=min(res,rec(S | (1<<u),u)+dis[v][u]);
	}
    }
  return dp[S][v]=res;
}

int main(int argc,char const* argv[])
{
  memset(dp,-1,sizeof(dp));
  memset(dis,inf,sizeof(dis));
  cin >> V >> E;
  for(int i=0;i<E;i++)
    {
      int s,t,d;
      cin >> s >> t >> d;
      dis[s][t]=d;
    }
  int ans=rec(0,0);
  if(ans>150000)
    {
      cout << -1 << endl;
    }
  else
    {
      cout << ans << endl;
    }
  return 0;
}


```