#include <bits/stdc++.h>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main(){
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n,m;
    cin>>n>>m;
    int s,t,d,maki=(1<<n);
    int dis[n][n];
    for(int i=0;i<n;i++){
    	for(int j=0;j<n;j++){
    		if(i==j)dis[i][j]=0;
    		else dis[i][j]=mod;
    	}
    }
    for(int i=0;i<m;i++){
    	cin>>s>>t>>d;
    	dis[s][t]=d;
    }
    int dp[maki][n];
    for(int i=0;i<maki;i++){
    	for(int j=0;j<n;j++){
    		dp[i][j]=mod;
    	}
    }
    dp[maki-1][0]=0;
    for(int bit=maki-2;bit>=0;bit--){
    	for(int i=0;i<n;i++){
    		for(int j=0;j<n;j++){
    			if(!((1<<j)&bit)){
    				dp[bit][i]=min(dp[bit][i],dp[bit|(1<<j)][j]+dis[i][j]);
    			}
    		}
    	}
    }
    if(dp[0][0]==mod)cout << -1<<endl;
    else cout << dp[0][0] <<endl;
    return 0;
}


### 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 <bits/stdc++.h>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main(){
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    int n,m;
    cin>>n>>m;
    int s,t,d,maki=(1<<n);
    int dis[n][n];
    for(int i=0;i<n;i++){
    	for(int j=0;j<n;j++){
    		if(i==j)dis[i][j]=0;
    		else dis[i][j]=mod;
    	}
    }
    for(int i=0;i<m;i++){
    	cin>>s>>t>>d;
    	dis[s][t]=d;
    }
    int dp[maki][n];
    for(int i=0;i<maki;i++){
    	for(int j=0;j<n;j++){
    		dp[i][j]=mod;
    	}
    }
    dp[maki-1][0]=0;
    for(int bit=maki-2;bit>=0;bit--){
    	for(int i=0;i<n;i++){
    		for(int j=0;j<n;j++){
    			if(!((1<<j)&bit)){
    				dp[bit][i]=min(dp[bit][i],dp[bit|(1<<j)][j]+dis[i][j]);
    			}
    		}
    	}
    }
    if(dp[0][0]==mod)cout << -1<<endl;
    else cout << dp[0][0] <<endl;
    return 0;
}


```