#include <bits/stdc++.h>
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
//#define SIZE 200005
//#define INF 1000000005LL
#define SIZE 1<<16
#define INF 1e18
//#define INF 1e18
#define MOD 1000000007

using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

int V,E;
ll d[17][17];
ll dp[SIZE][17];

void bitDP_init(){
  fill(d[0],d[17],INF);
}

ll bitDP(){
  fill(dp[0],dp[SIZE],INF);
  dp[0][0] = 0;
  for(int S=0;S<1<<V;S++){
    rep(v,0,V) rep(u,0,V){ //Sを通り次にvに進む
      if(S>>u & 1){
        dp[S][v] = min(dp[S][v],dp[S-(1<<u)][u]+d[u][v]);
      }
    }
  }
  return dp[(1<<V)-1][0];
}

int main(){

  cin >> V >> E;
  bitDP_init();
  rep(i,0,E){
    int s,t;
    ll D;
    cin >> s >> t >> D;
    d[s][t] = D;
  }

  ll ans = bitDP();
  if(ans >= INF) ans = -1;

  cout << ans << endl;

  return 0;
}


### Prompt

Please formulate 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 <bits/stdc++.h>
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
//#define SIZE 200005
//#define INF 1000000005LL
#define SIZE 1<<16
#define INF 1e18
//#define INF 1e18
#define MOD 1000000007

using namespace std;
typedef long long int ll;
typedef pair <int,int> P;

int V,E;
ll d[17][17];
ll dp[SIZE][17];

void bitDP_init(){
  fill(d[0],d[17],INF);
}

ll bitDP(){
  fill(dp[0],dp[SIZE],INF);
  dp[0][0] = 0;
  for(int S=0;S<1<<V;S++){
    rep(v,0,V) rep(u,0,V){ //Sを通り次にvに進む
      if(S>>u & 1){
        dp[S][v] = min(dp[S][v],dp[S-(1<<u)][u]+d[u][v]);
      }
    }
  }
  return dp[(1<<V)-1][0];
}

int main(){

  cin >> V >> E;
  bitDP_init();
  rep(i,0,E){
    int s,t;
    ll D;
    cin >> s >> t >> D;
    d[s][t] = D;
  }

  ll ans = bitDP();
  if(ans >= INF) ans = -1;

  cout << ans << endl;

  return 0;
}


```