#include<iostream>
using namespace std;
#define REP(i,n) for(int i=0;i<(int)(n);i++)
const int VMAX = 16, INF = VMAX * 1000;
int dist[VMAX][VMAX];

int dp[1 << VMAX][VMAX];

void init(int V) {
  REP(i, V) {
    REP(j, V) {
      dist[i][j] = INF;
    }
  }
  REP(i, 1 << V) {
    REP(j, V) {
      dp[i][j] = INF;
    }
  }
}

void solve(int V) {
  dp[(1 << V) - 1][0] = 0;
  for (int S = (1 << V) - 1; S >= 0; S--) {
    for (int v = 0; v < V; v++) {
      for (int u = 0; u < V; u++) {
        if (!((S >> u) & 1)) {
          dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + dist[u][v]);
        }
      }
    }
  }
}

int main() {
  int V, E;
  cin >> V >> E;
  init(V);
  REP(i, E) {
    int s, t, d;
    cin >> s >> t >> d;
    dist[s][t] = d;
  }

  solve(V);

  cout << (dp[0][0] == INF ? -1 : dp[0][0]) << endl;
}
### Prompt

Generate 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>
using namespace std;
#define REP(i,n) for(int i=0;i<(int)(n);i++)
const int VMAX = 16, INF = VMAX * 1000;
int dist[VMAX][VMAX];

int dp[1 << VMAX][VMAX];

void init(int V) {
  REP(i, V) {
    REP(j, V) {
      dist[i][j] = INF;
    }
  }
  REP(i, 1 << V) {
    REP(j, V) {
      dp[i][j] = INF;
    }
  }
}

void solve(int V) {
  dp[(1 << V) - 1][0] = 0;
  for (int S = (1 << V) - 1; S >= 0; S--) {
    for (int v = 0; v < V; v++) {
      for (int u = 0; u < V; u++) {
        if (!((S >> u) & 1)) {
          dp[S][v] = min(dp[S][v], dp[S | 1 << u][u] + dist[u][v]);
        }
      }
    }
  }
}

int main() {
  int V, E;
  cin >> V >> E;
  init(V);
  REP(i, E) {
    int s, t, d;
    cin >> s >> t >> d;
    dist[s][t] = d;
  }

  solve(V);

  cout << (dp[0][0] == INF ? -1 : dp[0][0]) << endl;
}
```