#include<bits/stdc++.h>
using namespace std;
int TSP(const vector<vector<int>>& edge) {
  const int INF = 1e9;
  vector<vector<int>> dp(1 << edge.size(), vector<int>(edge.size(), INF));
  dp[1][0] = 0;
  for(int bit = 1; bit < (1 << edge.size()); ++bit)
    for(int last = 0; last < edge.size(); ++last)
      if((bit >> last) & 1) for(int next = 0; next < edge.size(); ++next)
        if(!((bit >> next) & 1)) dp[bit | (1 << next)][next] = min(dp[bit | (1 << next)][next], dp[bit][last] + edge[last][next]);
  int result = INF;
  for(int last = 0; last < edge.size(); ++last) result = min(result, dp[(1 << edge.size()) - 1][last] + edge[last][0]);
  return result;
}
int main() {
  int V, E;
  cin >> V >> E;
  vector<vector<int>> edge(V, vector<int>(V, 1e9));
  for(int i = 0; i < E; ++i) {
    int s, t, d;
    cin >> s >> t >> d;
    edge[s][t] = d;
  }
  auto result = TSP(edge);
  cout << (result == 1e9 ? -1 : result) << endl;
}
### 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<bits/stdc++.h>
using namespace std;
int TSP(const vector<vector<int>>& edge) {
  const int INF = 1e9;
  vector<vector<int>> dp(1 << edge.size(), vector<int>(edge.size(), INF));
  dp[1][0] = 0;
  for(int bit = 1; bit < (1 << edge.size()); ++bit)
    for(int last = 0; last < edge.size(); ++last)
      if((bit >> last) & 1) for(int next = 0; next < edge.size(); ++next)
        if(!((bit >> next) & 1)) dp[bit | (1 << next)][next] = min(dp[bit | (1 << next)][next], dp[bit][last] + edge[last][next]);
  int result = INF;
  for(int last = 0; last < edge.size(); ++last) result = min(result, dp[(1 << edge.size()) - 1][last] + edge[last][0]);
  return result;
}
int main() {
  int V, E;
  cin >> V >> E;
  vector<vector<int>> edge(V, vector<int>(V, 1e9));
  for(int i = 0; i < E; ++i) {
    int s, t, d;
    cin >> s >> t >> d;
    edge[s][t] = d;
  }
  auto result = TSP(edge);
  cout << (result == 1e9 ? -1 : result) << endl;
}
```