#include <bits/stdc++.h>

using namespace std;

struct Edge {
    int to;
    int value;
};

struct Node {
    int value;
    vector<Edge> edge;
};

int v, e;
int s, t, d;
Node node[15];

int dp[15][1 << 16];

int solve(int pos, int stat){

    if(dp[pos][stat] != -1) return dp[pos][stat];

    int cost = 1 << 24;

    if(stat == (1 << v) - 1) return 0;
    else if(stat & 1) return cost;

    for(int i = 0; i < node[pos].edge.size(); ++i) {
        if(!(stat & 1 << node[pos].edge[i].to)) {
            cost = min(cost, solve(node[pos].edge[i].to, stat | 1 << node[pos].edge[i].to) + node[pos].edge[i].value);
        }
    }

    return dp[pos][stat] = cost;

}

int main() {

    cin >> v >> e;

    for(int i = 0; i < e; ++i) {
        cin >> s >> t >> d;
        node[s].edge.push_back((Edge){t, d});
    }

    memset(dp, -1, sizeof(dp));

    int dst = solve(0, 0);

    if(dst == 1 << 24) {
        cout << -1 << endl;
    } else {
        cout << dst << endl;
    }

}
### Prompt

Please formulate 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;

struct Edge {
    int to;
    int value;
};

struct Node {
    int value;
    vector<Edge> edge;
};

int v, e;
int s, t, d;
Node node[15];

int dp[15][1 << 16];

int solve(int pos, int stat){

    if(dp[pos][stat] != -1) return dp[pos][stat];

    int cost = 1 << 24;

    if(stat == (1 << v) - 1) return 0;
    else if(stat & 1) return cost;

    for(int i = 0; i < node[pos].edge.size(); ++i) {
        if(!(stat & 1 << node[pos].edge[i].to)) {
            cost = min(cost, solve(node[pos].edge[i].to, stat | 1 << node[pos].edge[i].to) + node[pos].edge[i].value);
        }
    }

    return dp[pos][stat] = cost;

}

int main() {

    cin >> v >> e;

    for(int i = 0; i < e; ++i) {
        cin >> s >> t >> d;
        node[s].edge.push_back((Edge){t, d});
    }

    memset(dp, -1, sizeof(dp));

    int dst = solve(0, 0);

    if(dst == 1 << 24) {
        cout << -1 << endl;
    } else {
        cout << dst << endl;
    }

}
```