#include <bits/stdc++.h>
using namespace std;

struct edge {int to,cost;};

const int INF = 1001001001;

vector<edge> g[16];
int dp[1<<15][16][16];

int main(){
    int v,e;
    cin>>v>>e;
    for(int i=0;i<e;i++){
        int s,t,d;
        cin>>s>>t>>d;
        g[t].push_back((edge){s,d});
    }
    for(int bit=0;bit<1<<15;bit++)for(int i=0;i<16;i++)for(int j=0;j<16;j++){
        dp[bit][i][j]=INF;
        if(bit==0&&i==j)dp[bit][i][j]=0;
    }
    for(int bit=1;bit<1<<v;bit++){
        for(int u=0;u<v;u++){
            if(!(bit>>u&1))continue;
            for(int a=0;a<v;a++){
                if(bit!=(1<<v)-1&&(u==a||bit>>a&1))continue;
                for(auto x:g[u]){
                    dp[bit][u][a]=min(dp[bit][u][a],dp[bit&~(1<<u)][x.to][a]+x.cost);
                }
            }
        }
    }
    int ans=INF;
    for(int u=0;u<v;u++){
        ans=min(ans,dp[(1<<v)-1][u][u]);
    }
    if(ans==INF)ans=-1;
    cout<<ans<<endl;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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>
using namespace std;

struct edge {int to,cost;};

const int INF = 1001001001;

vector<edge> g[16];
int dp[1<<15][16][16];

int main(){
    int v,e;
    cin>>v>>e;
    for(int i=0;i<e;i++){
        int s,t,d;
        cin>>s>>t>>d;
        g[t].push_back((edge){s,d});
    }
    for(int bit=0;bit<1<<15;bit++)for(int i=0;i<16;i++)for(int j=0;j<16;j++){
        dp[bit][i][j]=INF;
        if(bit==0&&i==j)dp[bit][i][j]=0;
    }
    for(int bit=1;bit<1<<v;bit++){
        for(int u=0;u<v;u++){
            if(!(bit>>u&1))continue;
            for(int a=0;a<v;a++){
                if(bit!=(1<<v)-1&&(u==a||bit>>a&1))continue;
                for(auto x:g[u]){
                    dp[bit][u][a]=min(dp[bit][u][a],dp[bit&~(1<<u)][x.to][a]+x.cost);
                }
            }
        }
    }
    int ans=INF;
    for(int u=0;u<v;u++){
        ans=min(ans,dp[(1<<v)-1][u][u]);
    }
    if(ans==INF)ans=-1;
    cout<<ans<<endl;
}

```