#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... Args> void assign(V<T>& v, int n, const Args&... args) { v.resize(n); for (auto&& e : v) assign(e, args...); }


int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int n, m; cin >> n >> m;
  VV<> d; assign(d, n, n, (int) 1e9);
  for (int i = 0; i < n; ++i) d[i][i] = 0;
  for (int i = 0; i < m; ++i) {
    int s, t, _d; cin >> s >> t >> _d;
    d[s][t] = _d;
  }
  VV<> dp; assign(dp, 1 << n, n, (int) 1e9);
  dp[0][0] = 0;
  for (int bit = 0; bit < 1 << n; ++bit) for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) {
    dp[bit][i] = min(dp[bit][i], dp[bit ^ 1 << i][j] + d[j][i]);
  }
  int res = dp.back()[0] != 1e9 ? dp.back()[0] : -1;
  cout << res << '\n';
}

### Prompt

Your task is to create 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;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... Args> void assign(V<T>& v, int n, const Args&... args) { v.resize(n); for (auto&& e : v) assign(e, args...); }


int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int n, m; cin >> n >> m;
  VV<> d; assign(d, n, n, (int) 1e9);
  for (int i = 0; i < n; ++i) d[i][i] = 0;
  for (int i = 0; i < m; ++i) {
    int s, t, _d; cin >> s >> t >> _d;
    d[s][t] = _d;
  }
  VV<> dp; assign(dp, 1 << n, n, (int) 1e9);
  dp[0][0] = 0;
  for (int bit = 0; bit < 1 << n; ++bit) for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) {
    dp[bit][i] = min(dp[bit][i], dp[bit ^ 1 << i][j] + d[j][i]);
  }
  int res = dp.back()[0] != 1e9 ? dp.back()[0] : -1;
  cout << res << '\n';
}

```