#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
#define yn {puts("Yes");}else{puts("No");}
#define MAX_N 18

const int INF = 1001001001;

int n;
int cost[MAX_N][MAX_N];
int dp[1<<MAX_N][MAX_N];

int dfs(int x, int k){
    if(dp[x][k] != -1) return dp[x][k];

    if(x == (1<<n) - 1){
        dp[x][k] = cost[k][0];
        return dp[x][k];
    }

    dp[x][k] = INF;
    bitset<MAX_N> f(x);

    rep(i,n){
        if(f[i] == 0){
            dp[x][k] = min(dp[x][k], dfs(x|(1<<i), i) + cost[k][i]);
        }
    }

    return dp[x][k];
}

int main() {
    int m;
    cin >> n >> m;
    rep(i,n)rep(j,n)cost[i][j] = INF;

    rep(i,m){
        int s, t, d;
        cin >> s >> t >> d;
        cost[s][t] = d;
        // cost[t][s] = d;
    }

    rep(i,1<<n)rep(j,n)dp[i][j] = -1;

    int ans = dfs(1,0);

    if(ans >= INF) ans = -1;
    cout << ans << 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 rep(i,n) for(int i = 0; i < (n); ++i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
#define yn {puts("Yes");}else{puts("No");}
#define MAX_N 18

const int INF = 1001001001;

int n;
int cost[MAX_N][MAX_N];
int dp[1<<MAX_N][MAX_N];

int dfs(int x, int k){
    if(dp[x][k] != -1) return dp[x][k];

    if(x == (1<<n) - 1){
        dp[x][k] = cost[k][0];
        return dp[x][k];
    }

    dp[x][k] = INF;
    bitset<MAX_N> f(x);

    rep(i,n){
        if(f[i] == 0){
            dp[x][k] = min(dp[x][k], dfs(x|(1<<i), i) + cost[k][i]);
        }
    }

    return dp[x][k];
}

int main() {
    int m;
    cin >> n >> m;
    rep(i,n)rep(j,n)cost[i][j] = INF;

    rep(i,m){
        int s, t, d;
        cin >> s >> t >> d;
        cost[s][t] = d;
        // cost[t][s] = d;
    }

    rep(i,1<<n)rep(j,n)dp[i][j] = -1;

    int ans = dfs(1,0);

    if(ans >= INF) ans = -1;
    cout << ans << endl;
    return 0;
}
 
 


```