#include <cstdio>
#include <algorithm>

constexpr int INF = 1000000000;
constexpr int MAX_V = 15;

int V, E;
int memo[1 << MAX_V][MAX_V] = {-1}, dis[MAX_V][MAX_V] = {-1};

int tsp(int s = 1, int v = 0);

int main(){
    scanf("%d%d", &V, &E);
    for(int i = 0; i < 1 << V; ++i){
        for(int j = 0; j < V; ++j){
            memo[i][j] = -1;
        }
    }
    for(int i = 0; i < V; ++i){
        for(int j = 0; j < V; ++j){
            dis[i][j] = INF;
        }
    }
    for(int i = 0; i < E; ++i){
        int s, t, d;
        scanf("%d%d%d", &s, &t, &d);
        dis[s][t] = d;
    }
    int tmp = tsp();
    if(tmp >= INF){
        puts("-1");
    }
    else{
        printf("%d\n", tmp);
    }
    return 0;
}

int tsp(int s, int v){
    if(memo[s][v] != -1){
        return memo[s][v];
    }
    if(s == ((1 << V) - 1)){
        return dis[v][0];
    }
    
    int res = INF;
    for(int i = 0; i < V; ++i){
        if(s & 1 << i){
            continue;
        }
        res = std::min(res, tsp(s | (1 << i), i) + dis[v][i]);
    }

    return memo[s][v] = res;
}
### Prompt

Please create a solution in Cpp 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 <cstdio>
#include <algorithm>

constexpr int INF = 1000000000;
constexpr int MAX_V = 15;

int V, E;
int memo[1 << MAX_V][MAX_V] = {-1}, dis[MAX_V][MAX_V] = {-1};

int tsp(int s = 1, int v = 0);

int main(){
    scanf("%d%d", &V, &E);
    for(int i = 0; i < 1 << V; ++i){
        for(int j = 0; j < V; ++j){
            memo[i][j] = -1;
        }
    }
    for(int i = 0; i < V; ++i){
        for(int j = 0; j < V; ++j){
            dis[i][j] = INF;
        }
    }
    for(int i = 0; i < E; ++i){
        int s, t, d;
        scanf("%d%d%d", &s, &t, &d);
        dis[s][t] = d;
    }
    int tmp = tsp();
    if(tmp >= INF){
        puts("-1");
    }
    else{
        printf("%d\n", tmp);
    }
    return 0;
}

int tsp(int s, int v){
    if(memo[s][v] != -1){
        return memo[s][v];
    }
    if(s == ((1 << V) - 1)){
        return dis[v][0];
    }
    
    int res = INF;
    for(int i = 0; i < V; ++i){
        if(s & 1 << i){
            continue;
        }
        res = std::min(res, tsp(s | (1 << i), i) + dis[v][i]);
    }

    return memo[s][v] = res;
}
```