#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <iomanip>
#include <cmath>
#include <cstdio>
#include <map>
#define REP(i,n) for (int i=0;i<(n);++i)
using namespace std;
using ll = long long;

struct Edge {
  int to, cost;
};

int v, e, s, t, d;
vector<Edge> g[16];
vector<vector<int>> dp(1 << 16, vector<int>(16, -1));

int rec(int bit, int from) {
  if (dp[bit][from] >= 0) return dp[bit][from];
  if (bit == (1 << v) - 1 && from == 0) return dp[bit][from] = 0;

  int res = 1 << 30;
  for(Edge e : g[from]) {
    if (bit >> e.to & 1) continue;
    res = min(res, rec(bit | (1 << e.to), e.to) + e.cost);
  }
  return dp[bit][from] = res;
}

int main() {
  cin >> v >> e;
  REP(i, e) {
    cin >> s >> t >> d;
    g[s].push_back(Edge{t, d});
  }
  rec(0, 0);
  cout << (dp[0][0] != (1 << 30) ? dp[0][0] : -1) << endl;
  return 0;
}




### Prompt

In cpp, your task is to solve 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>
#include <algorithm>
#include <vector>
#include <queue>
#include <iomanip>
#include <cmath>
#include <cstdio>
#include <map>
#define REP(i,n) for (int i=0;i<(n);++i)
using namespace std;
using ll = long long;

struct Edge {
  int to, cost;
};

int v, e, s, t, d;
vector<Edge> g[16];
vector<vector<int>> dp(1 << 16, vector<int>(16, -1));

int rec(int bit, int from) {
  if (dp[bit][from] >= 0) return dp[bit][from];
  if (bit == (1 << v) - 1 && from == 0) return dp[bit][from] = 0;

  int res = 1 << 30;
  for(Edge e : g[from]) {
    if (bit >> e.to & 1) continue;
    res = min(res, rec(bit | (1 << e.to), e.to) + e.cost);
  }
  return dp[bit][from] = res;
}

int main() {
  cin >> v >> e;
  REP(i, e) {
    cin >> s >> t >> d;
    g[s].push_back(Edge{t, d});
  }
  rec(0, 0);
  cout << (dp[0][0] != (1 << 30) ? dp[0][0] : -1) << endl;
  return 0;
}




```