#include <iostream>
#include <cstring>
using namespace std;
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

const int MAX_V = 15;
const int INF = 1<<28;

int G[MAX_V][MAX_V];

int V, E;
int memo[MAX_V][1 << MAX_V];
void init() {
    memset(memo, -1, sizeof(memo));
}
int dfs(int v, int used) {
    if (used == (1 << V) - 1) return G[v][0];
    if (memo[v][used] >= 0) return memo[v][used];
    int ret = INF;
    for (int u = 0; u < V; u++) {
        if (v == u || G[v][u] == INF || (used & (1 << u))) continue;
        chmin(ret, dfs(u, used | (1 << u)) + G[v][u]);
    }
    return memo[v][used] = ret;
}
int TSP() {
    init();
    return dfs(0, 1);
}

int main() {
    cin >> V >> E;
    for (int i = 0; i < V; i++) {
        for (int j = 0; j < V; j++) G[i][j] = INF;
        G[i][i] = 0;
    }
    for (int i = 0; i < E; i++) {
        int s, t, d;
        cin >> s >> t >> d;
        G[s][t] = d;
    }
    int Ans = TSP();
    cout << (Ans >= INF ? -1 : Ans) << endl;
    return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 <cstring>
using namespace std;
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

const int MAX_V = 15;
const int INF = 1<<28;

int G[MAX_V][MAX_V];

int V, E;
int memo[MAX_V][1 << MAX_V];
void init() {
    memset(memo, -1, sizeof(memo));
}
int dfs(int v, int used) {
    if (used == (1 << V) - 1) return G[v][0];
    if (memo[v][used] >= 0) return memo[v][used];
    int ret = INF;
    for (int u = 0; u < V; u++) {
        if (v == u || G[v][u] == INF || (used & (1 << u))) continue;
        chmin(ret, dfs(u, used | (1 << u)) + G[v][u]);
    }
    return memo[v][used] = ret;
}
int TSP() {
    init();
    return dfs(0, 1);
}

int main() {
    cin >> V >> E;
    for (int i = 0; i < V; i++) {
        for (int j = 0; j < V; j++) G[i][j] = INF;
        G[i][i] = 0;
    }
    for (int i = 0; i < E; i++) {
        int s, t, d;
        cin >> s >> t >> d;
        G[s][t] = d;
    }
    int Ans = TSP();
    cout << (Ans >= INF ? -1 : Ans) << endl;
    return 0;
}

```