#include<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<utility>
#include<map>
#include<set>
#include<queue>
#include<functional>
#include<math.h>
using namespace std;
#define N (1000000000+7)
#define INF 1e16
typedef long long ll;
typedef pair<ll,ll> P;
 

ll dp[(1LL<<16)-1][16];
ll n,e;
ll d[20][20];

ll rec(ll S,ll v){
    if(dp[S][v]>=0)return dp[S][v];
    if((S==(1<<n)-1)&& v==0){
        return dp[S][v]=0;
    }
    ll ans = (ll)INF;
    for(ll u=0;u<n;u++){
        if(!((S>>u)&1)){
            ans = min(ans,rec(S|(1<<u),u)+d[v][u]);
        }
    }
    return dp[S][v]=ans;
}

int main(void){
    for(ll i=0;i<20;i++){
        for(ll j=0;j<20;j++){
            d[i][j]=(ll)INF;
        }
    }
    cin>>n>>e;
    for(ll i=0;i<(1<<n);i++){
        for(ll j=0;j<=n;j++){
            dp[i][j]=-1;
        }
    }
    for(ll i=0;i<e;i++){
        ll s,t,di;
        cin>>s>>t>>di;
        d[s][t]=di;
    }
    dp[0][0] = rec(0,0);
    if(dp[0][0]==(ll)INF)cout<<-1<<endl;
    else cout<<dp[0][0]<<endl;;
    return 0;
}



### Prompt

Your task is to create a CPP solution 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<iostream>
#include<algorithm>
#include<vector>
#include<string>
#include<utility>
#include<map>
#include<set>
#include<queue>
#include<functional>
#include<math.h>
using namespace std;
#define N (1000000000+7)
#define INF 1e16
typedef long long ll;
typedef pair<ll,ll> P;
 

ll dp[(1LL<<16)-1][16];
ll n,e;
ll d[20][20];

ll rec(ll S,ll v){
    if(dp[S][v]>=0)return dp[S][v];
    if((S==(1<<n)-1)&& v==0){
        return dp[S][v]=0;
    }
    ll ans = (ll)INF;
    for(ll u=0;u<n;u++){
        if(!((S>>u)&1)){
            ans = min(ans,rec(S|(1<<u),u)+d[v][u]);
        }
    }
    return dp[S][v]=ans;
}

int main(void){
    for(ll i=0;i<20;i++){
        for(ll j=0;j<20;j++){
            d[i][j]=(ll)INF;
        }
    }
    cin>>n>>e;
    for(ll i=0;i<(1<<n);i++){
        for(ll j=0;j<=n;j++){
            dp[i][j]=-1;
        }
    }
    for(ll i=0;i<e;i++){
        ll s,t,di;
        cin>>s>>t>>di;
        d[s][t]=di;
    }
    dp[0][0] = rec(0,0);
    if(dp[0][0]==(ll)INF)cout<<-1<<endl;
    else cout<<dp[0][0]<<endl;;
    return 0;
}



```