#include <bits/stdc++.h>
#define rep(i,a,n) for(int i=a;i<n;i++)
#define repr(i,a,n) for(int i=a;i>=n;i--)
#define INF 99999999
#define INF_M 2147483647
#define pb(a) push_back(a)

using namespace std;
typedef pair<int, int> pii;
typedef long long int ll;
typedef vector<pii> VP;

int dy[]={0, 0, 1, -1};
int dx[]={1, -1, 0, 0};

int dist[15][15];
int dp[1 << 15][15];
int V,E;
int s,t,d;

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

    int res = INF;
    for(int r = 0; r < V; r++) {
        if(!(S & 1 << r)) {
            res = min(res, rec(S | 1 << r, r) + dist[v][r]);
        }
    }
    return dp[S][v] = res;
}

int main() {
    cin >> V >> E;
    rep(i,0,20) rep(j,0,20) dist[i][j] = INF;

    rep(i,0,E) {
        cin >> s >> t >> d;
        dist[s][t] = d;
    }
    memset(dp, -1, sizeof(dp));

    int ans = rec(0,0);
    if(ans == INF) cout << -1 << endl;
    else cout << 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 <bits/stdc++.h>
#define rep(i,a,n) for(int i=a;i<n;i++)
#define repr(i,a,n) for(int i=a;i>=n;i--)
#define INF 99999999
#define INF_M 2147483647
#define pb(a) push_back(a)

using namespace std;
typedef pair<int, int> pii;
typedef long long int ll;
typedef vector<pii> VP;

int dy[]={0, 0, 1, -1};
int dx[]={1, -1, 0, 0};

int dist[15][15];
int dp[1 << 15][15];
int V,E;
int s,t,d;

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

    int res = INF;
    for(int r = 0; r < V; r++) {
        if(!(S & 1 << r)) {
            res = min(res, rec(S | 1 << r, r) + dist[v][r]);
        }
    }
    return dp[S][v] = res;
}

int main() {
    cin >> V >> E;
    rep(i,0,20) rep(j,0,20) dist[i][j] = INF;

    rep(i,0,E) {
        cin >> s >> t >> d;
        dist[s][t] = d;
    }
    memset(dp, -1, sizeof(dp));

    int ans = rec(0,0);
    if(ans == INF) cout << -1 << endl;
    else cout << ans << endl;
    return 0;
}
```