#include <iostream>

using namespace std;

int V,E,G[15][15],dp[1<<15][15];
const int INF = 1000000;

int solve() {
  for (int s=(1<<V)-1;s>=0;--s) {
    for (int t=0;t<V;++t) {
      dp[s][t] = INF;
    }
  }
  dp[(1<<V)-1][0] = 0;
  for (int s=(1<<V)-2;s>=0;--s) {
    for (int t=0;t<V;++t) {
      for (int u=0;u<V;++u) {
        if (!(s>>u&1)) {
          dp[s][t] = min(dp[s][t],dp[s|(1<<u)][u]+G[t][u]);
        }
      }
    }
  }
  return (dp[0][0] != INF)?dp[0][0]:-1;
}

int main() {
  for (int i=0;i<15;++i) {
    for (int j=0;j<15;++j) {
      G[i][j] = INF;
    }
  }
  cin>>V>>E;
  for (int i=0;i<E;++i) {
    int s,t,d;
    cin>>s>>t>>d;
    G[s][t] = d;
  }
  cout<<solve()<<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
#include <iostream>

using namespace std;

int V,E,G[15][15],dp[1<<15][15];
const int INF = 1000000;

int solve() {
  for (int s=(1<<V)-1;s>=0;--s) {
    for (int t=0;t<V;++t) {
      dp[s][t] = INF;
    }
  }
  dp[(1<<V)-1][0] = 0;
  for (int s=(1<<V)-2;s>=0;--s) {
    for (int t=0;t<V;++t) {
      for (int u=0;u<V;++u) {
        if (!(s>>u&1)) {
          dp[s][t] = min(dp[s][t],dp[s|(1<<u)][u]+G[t][u]);
        }
      }
    }
  }
  return (dp[0][0] != INF)?dp[0][0]:-1;
}

int main() {
  for (int i=0;i<15;++i) {
    for (int j=0;j<15;++j) {
      G[i][j] = INF;
    }
  }
  cin>>V>>E;
  for (int i=0;i<E;++i) {
    int s,t,d;
    cin>>s>>t>>d;
    G[s][t] = d;
  }
  cout<<solve()<<endl;
  return 0;
}

```