#include <bits/stdc++.h>

#define rep(i, n) for(int i = 0; i < n; i++)
using namespace std;

typedef long long ll;

const ll INF = 1 << 30;

struct edge{
    int to;
    int cost;
    edge(int t, int c){
        to = t;
        cost = c;
    }
};

ll G[15][15];
ll dp[(1 << 15)][15];
int states;
int V,E;

void init(){
    rep(i, 15) rep(j, 15) G[i][j] = INF;
}

ll dfs(int S, int v){
    //S -> S | to への遷移
    if(dp[S][v] >= 0) return dp[S][v];
    if(S == states-1 && v == 0) return dp[S][v] = 0;

    ll ans = INF;
    for(int to = 0; to < V; to++){
        //まだtoに行っていない
        if(!((S >> to) & 1)) ans = min(ans, dfs(S|(1 << to), to) + G[v][to]);
    }
    dp[S][v] = ans;
    return ans;
}

int main(void){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    init();
    cin >> V >> E;
    states = (1 << V);
    memset(dp, -1, sizeof(dp));
    rep(i, E){
        int f, t, c; cin >> f >> t >> c;
        G[f][t] = c;
    }

    ll ans = min(INF, dfs(0, 0));
    if(ans != INF) cout << ans << endl;
    else cout << -1 << endl;
    return 0;
}

### Prompt

Create a solution in cpp for 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++)
using namespace std;

typedef long long ll;

const ll INF = 1 << 30;

struct edge{
    int to;
    int cost;
    edge(int t, int c){
        to = t;
        cost = c;
    }
};

ll G[15][15];
ll dp[(1 << 15)][15];
int states;
int V,E;

void init(){
    rep(i, 15) rep(j, 15) G[i][j] = INF;
}

ll dfs(int S, int v){
    //S -> S | to への遷移
    if(dp[S][v] >= 0) return dp[S][v];
    if(S == states-1 && v == 0) return dp[S][v] = 0;

    ll ans = INF;
    for(int to = 0; to < V; to++){
        //まだtoに行っていない
        if(!((S >> to) & 1)) ans = min(ans, dfs(S|(1 << to), to) + G[v][to]);
    }
    dp[S][v] = ans;
    return ans;
}

int main(void){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    init();
    cin >> V >> E;
    states = (1 << V);
    memset(dp, -1, sizeof(dp));
    rep(i, E){
        int f, t, c; cin >> f >> t >> c;
        G[f][t] = c;
    }

    ll ans = min(INF, dfs(0, 0));
    if(ans != INF) cout << ans << endl;
    else cout << -1 << endl;
    return 0;
}

```