#include <bits/stdc++.h>

using namespace std;

const int inf = 1<<29;
const int maxn = 20;

int n;
int dis[maxn+3][maxn+3] = {};
int dp[(1<<maxn)+3][maxn+11] = {};

int solve(int s, int last){
    if (dp[s][last] == 0){
        dp[s][last] = inf;

        if (__builtin_popcount(s) == 1) dp[s][last] = dis[0][last];
        else{
            for(int i = 1;i < n;i++){
                if (i == last) continue;
                if (((1<<i)&s) == 0) continue;
                dp[s][last] = min(dp[s][last], solve(s^(1<<last), i)+dis[i][last]);
            }
        }
    }
    return dp[s][last];
}

int main(){

    cin>>n;
    int e;cin>>e;

    for(int i = 0;i < n;i++){
        for(int j = 0;j < n;j++){
            dis[i][j] = inf;
        }
    }

    while(e--){
        int a, b, d;cin>>a>>b>>d;
        dis[a][b] = d;
    }

    int ans = solve((1<<n)-1, 0);
    if (ans == inf) ans = -1;
    cout << ans << endl;

    return 0;
}

/* input
    5
    0 1 1 1 1
    1 0 1 1 1
    1 1 0 1 1
    1 1 1 0 1
    1 1 1 1 0
*/


### Prompt

Please formulate 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
#include <bits/stdc++.h>

using namespace std;

const int inf = 1<<29;
const int maxn = 20;

int n;
int dis[maxn+3][maxn+3] = {};
int dp[(1<<maxn)+3][maxn+11] = {};

int solve(int s, int last){
    if (dp[s][last] == 0){
        dp[s][last] = inf;

        if (__builtin_popcount(s) == 1) dp[s][last] = dis[0][last];
        else{
            for(int i = 1;i < n;i++){
                if (i == last) continue;
                if (((1<<i)&s) == 0) continue;
                dp[s][last] = min(dp[s][last], solve(s^(1<<last), i)+dis[i][last]);
            }
        }
    }
    return dp[s][last];
}

int main(){

    cin>>n;
    int e;cin>>e;

    for(int i = 0;i < n;i++){
        for(int j = 0;j < n;j++){
            dis[i][j] = inf;
        }
    }

    while(e--){
        int a, b, d;cin>>a>>b>>d;
        dis[a][b] = d;
    }

    int ans = solve((1<<n)-1, 0);
    if (ans == inf) ans = -1;
    cout << ans << endl;

    return 0;
}

/* input
    5
    0 1 1 1 1
    1 0 1 1 1
    1 1 0 1 1
    1 1 1 0 1
    1 1 1 1 0
*/


```