#include <iostream>
using namespace std;

#define repeat(i,n) for (int i = 0; i < (n); ++i)

#define MAX_V 15
#define MAX_D 1000
#define SUP (MAX_V * MAX_D + 1)
int V, E;
int d[MAX_V][MAX_V];
int memo[1<<MAX_V][MAX_V]; // nodes already walked * current node

int recur(int s, int v) {
    if (memo[s][v] != SUP) return memo[s][v];
    if (s == (1<<V)-1 and v == 0) return memo[s][v] = 0;
    int result = SUP+1;
    repeat (i,V) if (not (s&1<<i)) if (d[v][i] < SUP) {
        result = min(result, d[v][i] + recur(s|1<<i,i));
    }
    return memo[s][v] = result;
}

int main() {
    cin >> V >> E;
    repeat (i,V) repeat (j,V) d[i][j] = SUP;
    repeat (i,E) { int a, b; cin >> a >> b; cin >> d[a][b]; } // there are no multiedge
    repeat (i,1<<V) repeat (j,V) memo[i][j] = SUP;
    cout << (recur(0,0) < SUP ? recur(0,0) : -1) << endl;
    return 0;
}
### 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 <iostream>
using namespace std;

#define repeat(i,n) for (int i = 0; i < (n); ++i)

#define MAX_V 15
#define MAX_D 1000
#define SUP (MAX_V * MAX_D + 1)
int V, E;
int d[MAX_V][MAX_V];
int memo[1<<MAX_V][MAX_V]; // nodes already walked * current node

int recur(int s, int v) {
    if (memo[s][v] != SUP) return memo[s][v];
    if (s == (1<<V)-1 and v == 0) return memo[s][v] = 0;
    int result = SUP+1;
    repeat (i,V) if (not (s&1<<i)) if (d[v][i] < SUP) {
        result = min(result, d[v][i] + recur(s|1<<i,i));
    }
    return memo[s][v] = result;
}

int main() {
    cin >> V >> E;
    repeat (i,V) repeat (j,V) d[i][j] = SUP;
    repeat (i,E) { int a, b; cin >> a >> b; cin >> d[a][b]; } // there are no multiedge
    repeat (i,1<<V) repeat (j,V) memo[i][j] = SUP;
    cout << (recur(0,0) < SUP ? recur(0,0) : -1) << endl;
    return 0;
}
```