//解説AC

#include <bits/stdc++.h>
using namespace std;
 
#define rep(i,a,b) for(int i=a;i<b;i++)
#define int long long
const int inf = 100100100100100;
const int mod = 1000000007;
 
const int maxn = 15;
int n, m;
int dist[maxn][maxn];
int dp[1<<maxn][maxn];
 
int dfs(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 ans = inf;
    rep(u,0,n){
        if(!(s >> u & 1)){
            ans = min(ans, dfs(s | 1 << u, u) + dist[v][u]);
        }
    }
 
    dp[s][v] = ans;
    return ans;
 
 
}
 
signed main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
 
     
    cin >> n >> m;
 
    memset(dp,-1,sizeof(dp));
    fill(dist[0],dist[0]+maxn*maxn,inf);
 
     
 
     
    rep(i,0,m){
        int f, t, c;
        cin >> f >> t >> c;
        dist[f][t] = c;
    }
    int ans = dfs(0,0);
    cout << (ans == inf ? -1 : ans) << endl;
 
}

### Prompt

Generate 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
//解説AC

#include <bits/stdc++.h>
using namespace std;
 
#define rep(i,a,b) for(int i=a;i<b;i++)
#define int long long
const int inf = 100100100100100;
const int mod = 1000000007;
 
const int maxn = 15;
int n, m;
int dist[maxn][maxn];
int dp[1<<maxn][maxn];
 
int dfs(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 ans = inf;
    rep(u,0,n){
        if(!(s >> u & 1)){
            ans = min(ans, dfs(s | 1 << u, u) + dist[v][u]);
        }
    }
 
    dp[s][v] = ans;
    return ans;
 
 
}
 
signed main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
 
     
    cin >> n >> m;
 
    memset(dp,-1,sizeof(dp));
    fill(dist[0],dist[0]+maxn*maxn,inf);
 
     
 
     
    rep(i,0,m){
        int f, t, c;
        cin >> f >> t >> c;
        dist[f][t] = c;
    }
    int ans = dfs(0,0);
    cout << (ans == inf ? -1 : ans) << endl;
 
}

```