
#include <numeric>
#include<iostream>
#include<set>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include<algorithm>
#include <sstream>
#include<string.h>
#include <cmath>
#include <iomanip>
using namespace std;
#define inf 1000000007
#define int long long
#define rep(i,j,n) for(int i=j;i<n;++i)
typedef pair<int,int>  P;
string alph("abcdefghijklmnopqrstuvwxyz");
struct edge{int from,to,cost;};
vector<edge> G;
double pi = 3.141592653589793;
P sg[10];
int a[55],b[55];
int n,m;
int d[16][16];
int dp[1<<16][16];
int  solve(int s,int v){
    if(dp[s][v]>=0)return dp[s][v];
    if(s==(1<<n)-1&&v==0)return dp[s][v]=0;
    int res=inf;
    rep(u,0,n){
        if(!(s>>u&1)){
            res=min(res,solve(s|1<<u,u)+d[v][u]);
        }
    }
    return dp[s][v]=res;
}

signed main(){
cin>>n>>m;
    rep(i,0,n)rep(j,0,n)d[i][j]=inf;
    rep(i,0,m){
        int a,b,c;cin>>a>>b>>c;
        d[a][b]=c;
    }
    memset(dp,-1,sizeof(dp));
    int h=solve(0,0);
    if(h==inf)cout<<-1<<endl;
    else cout<<h<<endl;
    return 0;
}

### Prompt

Please provide a CPP coded solution 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 <numeric>
#include<iostream>
#include<set>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include<algorithm>
#include <sstream>
#include<string.h>
#include <cmath>
#include <iomanip>
using namespace std;
#define inf 1000000007
#define int long long
#define rep(i,j,n) for(int i=j;i<n;++i)
typedef pair<int,int>  P;
string alph("abcdefghijklmnopqrstuvwxyz");
struct edge{int from,to,cost;};
vector<edge> G;
double pi = 3.141592653589793;
P sg[10];
int a[55],b[55];
int n,m;
int d[16][16];
int dp[1<<16][16];
int  solve(int s,int v){
    if(dp[s][v]>=0)return dp[s][v];
    if(s==(1<<n)-1&&v==0)return dp[s][v]=0;
    int res=inf;
    rep(u,0,n){
        if(!(s>>u&1)){
            res=min(res,solve(s|1<<u,u)+d[v][u]);
        }
    }
    return dp[s][v]=res;
}

signed main(){
cin>>n>>m;
    rep(i,0,n)rep(j,0,n)d[i][j]=inf;
    rep(i,0,m){
        int a,b,c;cin>>a>>b>>c;
        d[a][b]=c;
    }
    memset(dp,-1,sizeof(dp));
    int h=solve(0,0);
    if(h==inf)cout<<-1<<endl;
    else cout<<h<<endl;
    return 0;
}

```