#include<iostream>
#include<cstring>
using namespace std;
#define INF int(1e9)
#define maxn 16

#define bset(n, bit) (n | 1<<bit)
#define bclr(n, bit) (n & ~(1<<bit))

int dp[1<<maxn][maxn];
int n,E;
int dist[maxn][maxn];

int path(int S,int v)
{
    if(dp[S][v]>=0){
        return dp[S][v];
    }
    if((S==0) && (v==0)){
        return dp[S][v]=0;
    }
    int res = INF;
    for(int u=0; u<n; u++){
        if(((S>>u)&1) == 1 && u!=v){
            res=min(res, path(bclr(S, u), u) + dist[u][v]);
        }
    }
    return dp[S][v]=res;
}

int main()
{
    cin>>n>>E;
    memset(dist,0x3f,sizeof(dist));
    for(int i=0;i<E;i++){
        int a,b,c;
        cin>>a>>b>>c;
        dist[a][b]=c;
    }
    memset(dp,-1,sizeof(dp));
    int ans = path((1<<n) - 1, 0);
    if(ans==INF) ans=-1;
    cout<<ans<<endl;
}


### Prompt

Please create a solution in CPP 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<cstring>
using namespace std;
#define INF int(1e9)
#define maxn 16

#define bset(n, bit) (n | 1<<bit)
#define bclr(n, bit) (n & ~(1<<bit))

int dp[1<<maxn][maxn];
int n,E;
int dist[maxn][maxn];

int path(int S,int v)
{
    if(dp[S][v]>=0){
        return dp[S][v];
    }
    if((S==0) && (v==0)){
        return dp[S][v]=0;
    }
    int res = INF;
    for(int u=0; u<n; u++){
        if(((S>>u)&1) == 1 && u!=v){
            res=min(res, path(bclr(S, u), u) + dist[u][v]);
        }
    }
    return dp[S][v]=res;
}

int main()
{
    cin>>n>>E;
    memset(dist,0x3f,sizeof(dist));
    for(int i=0;i<E;i++){
        int a,b,c;
        cin>>a>>b>>c;
        dist[a][b]=c;
    }
    memset(dp,-1,sizeof(dp));
    int ans = path((1<<n) - 1, 0);
    if(ans==INF) ans=-1;
    cout<<ans<<endl;
}


```