#include <bits/stdc++.h>
template<class T> inline void chmin(T &a,T b){if(a > b) a = b;}
#define REP(i,n) for(int i=0;i<n;++i)

using namespace std;
using ll = long long;
constexpr int INF = 1e9;

int dp[1 << 16][16];
int V,E,s,t,d;

struct Edge {
    int to,cost;
    Edge(int to,int cost) : to(to), cost(cost){}
};

using Graph = vector<vector<Edge> >;

int main(){
    cin >> V >> E;
    Graph g(V);
    REP(i,E){
        cin >> s >> t >> d;
        g[s].emplace_back(t,d);
    }
    REP(i,1<<V) REP(j,V) dp[i][j] = INF;
    dp[(1<<V)-1][0] = 0; // start is 0
    for(int i = (1<<V)-2; i >= 0; --i){
        // x to somewhere
        for(int v = 0; v < V; ++v){
            for(Edge e : g[v]){
                int nv = e.to;
                int nc = e.cost;
                if(!(i & (1<<nv))){
                    chmin(dp[i][nv],dp[i | (1<<nv)][v] + nc);
                }
            }
        }
    }
    cout << (dp[0][0]==INF ? -1 : dp[0][0]) << endl;
    return 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>
template<class T> inline void chmin(T &a,T b){if(a > b) a = b;}
#define REP(i,n) for(int i=0;i<n;++i)

using namespace std;
using ll = long long;
constexpr int INF = 1e9;

int dp[1 << 16][16];
int V,E,s,t,d;

struct Edge {
    int to,cost;
    Edge(int to,int cost) : to(to), cost(cost){}
};

using Graph = vector<vector<Edge> >;

int main(){
    cin >> V >> E;
    Graph g(V);
    REP(i,E){
        cin >> s >> t >> d;
        g[s].emplace_back(t,d);
    }
    REP(i,1<<V) REP(j,V) dp[i][j] = INF;
    dp[(1<<V)-1][0] = 0; // start is 0
    for(int i = (1<<V)-2; i >= 0; --i){
        // x to somewhere
        for(int v = 0; v < V; ++v){
            for(Edge e : g[v]){
                int nv = e.to;
                int nc = e.cost;
                if(!(i & (1<<nv))){
                    chmin(dp[i][nv],dp[i | (1<<nv)][v] + nc);
                }
            }
        }
    }
    cout << (dp[0][0]==INF ? -1 : dp[0][0]) << endl;
    return 0;
}



```