#include <bits/stdc++.h>
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

const int INF = 1e9;

int V, E;
vector< vector<int> > dist(22, vector<int>(22, -1));
int dp[(1<<20)+1][22];

int main() {
    cin >> V >> E;
    for(int i = 0; i < E; ++i) {
        int s, t, d;
        cin >> s >> t >> d;
        dist[s][t] = d;
    }

    for(int bit = 0; bit < (1<<V); ++bit) {
        for(int v = 0; v < V; ++v) {
            dp[bit][v] = INF;
        }
    }

    dp[0][0] = 0;
    for(int bit = 0; bit < (1<<V); ++bit) {
        for(int now = 0; now < V; ++now) {
            for(int to = 0; to < V; ++to) {
                if((bit & (1<<to)) == 0 && dist[now][to] != -1) {
                    chmin(dp[bit|1<<to][to], dp[bit][now]+dist[now][to]);
                }
            }
        }
    }

    if(dp[(1<<V)-1][0] == INF) {
        cout << -1 << endl;
    }else {
        cout << dp[(1<<V)-1][0] << endl;
    }
}

### Prompt

Your challenge is to write 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;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

const int INF = 1e9;

int V, E;
vector< vector<int> > dist(22, vector<int>(22, -1));
int dp[(1<<20)+1][22];

int main() {
    cin >> V >> E;
    for(int i = 0; i < E; ++i) {
        int s, t, d;
        cin >> s >> t >> d;
        dist[s][t] = d;
    }

    for(int bit = 0; bit < (1<<V); ++bit) {
        for(int v = 0; v < V; ++v) {
            dp[bit][v] = INF;
        }
    }

    dp[0][0] = 0;
    for(int bit = 0; bit < (1<<V); ++bit) {
        for(int now = 0; now < V; ++now) {
            for(int to = 0; to < V; ++to) {
                if((bit & (1<<to)) == 0 && dist[now][to] != -1) {
                    chmin(dp[bit|1<<to][to], dp[bit][now]+dist[now][to]);
                }
            }
        }
    }

    if(dp[(1<<V)-1][0] == INF) {
        cout << -1 << endl;
    }else {
        cout << dp[(1<<V)-1][0] << endl;
    }
}

```