#include<iostream>
#include<iomanip>
#include<cmath>
#include<string>
#include<vector>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<stack>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define mp make_pair
const int inf=1e9+7;
const ll mod=1e9+7;

int DP[50000][20];
vector<vector<pair<int, int> > > edge(20);
int V;

int solve(int S, int v){
    if(DP[S][v]>=0) return DP[S][v];
    DP[S][v] = inf;
    for(int i=0;i<edge[v].size();++i){
        if((S&(1<<edge[v][i].fi))==0){
            DP[S][v] = min(DP[S][v], solve(S|(1<<edge[v][i].fi), edge[v][i].fi) + edge[v][i].se);
        }
    }
    return DP[S][v];
}

int main() {
    for(int i=0;i<50000;++i){
        for(int j=0;j<20;++j){
            DP[i][j] = -1;
        }
    }
    int E;
    cin>>V>>E;
    DP[(1<<V)-1][0] = 0;
    int s, t, d;
    for(int i=0;i<E;++i){
        cin>>s>>t>>d;
        edge[s].push_back(make_pair(t, d));
    }
    int ans = solve(0, 0);
    if(ans==inf) cout<<-1<<endl;
    else cout<<ans<<endl;
}


### Prompt

In CPP, your task is to solve 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>
#include<iomanip>
#include<cmath>
#include<string>
#include<vector>
#include<algorithm>
#include<map>
#include<set>
#include<queue>
#include<stack>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define mp make_pair
const int inf=1e9+7;
const ll mod=1e9+7;

int DP[50000][20];
vector<vector<pair<int, int> > > edge(20);
int V;

int solve(int S, int v){
    if(DP[S][v]>=0) return DP[S][v];
    DP[S][v] = inf;
    for(int i=0;i<edge[v].size();++i){
        if((S&(1<<edge[v][i].fi))==0){
            DP[S][v] = min(DP[S][v], solve(S|(1<<edge[v][i].fi), edge[v][i].fi) + edge[v][i].se);
        }
    }
    return DP[S][v];
}

int main() {
    for(int i=0;i<50000;++i){
        for(int j=0;j<20;++j){
            DP[i][j] = -1;
        }
    }
    int E;
    cin>>V>>E;
    DP[(1<<V)-1][0] = 0;
    int s, t, d;
    for(int i=0;i<E;++i){
        cin>>s>>t>>d;
        edge[s].push_back(make_pair(t, d));
    }
    int ans = solve(0, 0);
    if(ans==inf) cout<<-1<<endl;
    else cout<<ans<<endl;
}


```