#include<iostream>
#include<algorithm>
#include<math.h>

using namespace std;

#define INF 1000000007
#define MAX 15
int v,e;
int d[MAX][MAX] = {{0}};

int dp[1 << MAX][MAX] = {{0}};

int dfs(int s, int n){
  // cout << dp[s][n] << endl;
  if(dp[s][n] >= 0) return dp[s][n];
  if(s == (1 << v) - 1 && n == 0) return dp[s][n] = 0;
  int res = INF;
  for(int u = 0; u < v; u++){
    if(!(s >> u & 1) && d[n][u] != -1){
      // cout << s << " " << n << " " << u << endl;
      res = min(res, dfs( s | (1 << u), u) + d[n][u]);
    }
  }
  return dp[s][n] = res;
}

int main(){
  cin >> v >> e;
  for(int i = 0; i < v; i++){
    for(int j = 0; j < v; j++){
      d[i][j] = -1;
    }
  }
  for(int i = 0; i < (1<<v); i++){
    for(int j = 0; j < v; j++){
      dp[i][j] = -1;
    }
  }
  // cout << dp[0][0] << endl;
  for(int i = 0; i < e; i++){
    int s,t,c;
    cin >> s >> t >> c;
    d[s][t] = c;
  }
   // cout << "hi" << endl;
  int ans = dfs(0, 0);
  if(ans == INF) cout << -1 << endl;
  else cout << ans << 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<iostream>
#include<algorithm>
#include<math.h>

using namespace std;

#define INF 1000000007
#define MAX 15
int v,e;
int d[MAX][MAX] = {{0}};

int dp[1 << MAX][MAX] = {{0}};

int dfs(int s, int n){
  // cout << dp[s][n] << endl;
  if(dp[s][n] >= 0) return dp[s][n];
  if(s == (1 << v) - 1 && n == 0) return dp[s][n] = 0;
  int res = INF;
  for(int u = 0; u < v; u++){
    if(!(s >> u & 1) && d[n][u] != -1){
      // cout << s << " " << n << " " << u << endl;
      res = min(res, dfs( s | (1 << u), u) + d[n][u]);
    }
  }
  return dp[s][n] = res;
}

int main(){
  cin >> v >> e;
  for(int i = 0; i < v; i++){
    for(int j = 0; j < v; j++){
      d[i][j] = -1;
    }
  }
  for(int i = 0; i < (1<<v); i++){
    for(int j = 0; j < v; j++){
      dp[i][j] = -1;
    }
  }
  // cout << dp[0][0] << endl;
  for(int i = 0; i < e; i++){
    int s,t,c;
    cin >> s >> t >> c;
    d[s][t] = c;
  }
   // cout << "hi" << endl;
  int ans = dfs(0, 0);
  if(ans == INF) cout << -1 << endl;
  else cout << ans << endl;
}


```