#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=100003,INF=1<<30;

int V,cmp[MAX];
vector<int> G[MAX],rG[MAX],vs;
bool used[MAX];

void add_edge(int from,int to){
    G[from].push_back(to);
    rG[to].push_back(from);
}

void DFS(int v){
    used[v]=1;
    for(int i=0;i<G[v].size();i++){
        if(used[G[v][i]]==0) DFS(G[v][i]);
    }
    vs.push_back(v);
}

void rDFS(int v,int k){
    used[v]=1;
    cmp[v]=k;
    for(int i=0;i<rG[v].size();i++){
        if(used[rG[v][i]]==0) rDFS(rG[v][i],k);
    }
}

int scc(){
    memset(used,0,sizeof(used));
    vs.clear();
    for(int v=0;v<V;v++){
        if(used[v]==0) DFS(v);
    }
    
    memset(used,0,sizeof(used));
    int k=0;
    for(int i=vs.size()-1;i>=0;i--){
        if(used[vs[i]]==0) rDFS(vs[i],k++);
    }
    return k;
}

int main(){

    cin>>V;
    int M;cin>>M;
    for(int i=0;i<M;i++){
        int a,b;cin>>a>>b;
        a--;b--;
        add_edge(a,b);
    }
    
    scc();
    
    for(int i=0;i<V;i++){
        bool deta=false;
        for(int j=0;j<V;j++){
            if(cmp[i]==cmp[j]){
                if(deta) cout<<" ";
                cout<<j+1;
                deta=true;
            }
        }
        cout<<endl;
    }
}



### Prompt

Please formulate a Cpp solution to the following problem:

problem

There are $ N $ propositions, named $ 1, 2, \ cdots, N $, respectively. Also, $ M $ information about the propositions is given. The $ i $ th information is "$ a_i $$". Given in the form "b_i $", which means that $ a_i $ is $ b_i $. ("If" is a logical conditional and the transition law holds.) $ For each proposition $ i $ Output all propositions that have the same value as i $ in ascending order. However, proposition $ i $ and proposition $ i $ are always the same value. Proposition $ X $ and proposition $ Y $ have the same value as "$ if $ X $". It means "Y $" and "$ X $ if $ Y $".



output

On the $ i $ line, output all propositions that have the same value as the proposition $ i $, separated by blanks in ascending order. Also, output a line break at the end of each line.

Example

Input

5 2
1 2
2 1


Output

1 2
1 2
3
4
5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=100003,INF=1<<30;

int V,cmp[MAX];
vector<int> G[MAX],rG[MAX],vs;
bool used[MAX];

void add_edge(int from,int to){
    G[from].push_back(to);
    rG[to].push_back(from);
}

void DFS(int v){
    used[v]=1;
    for(int i=0;i<G[v].size();i++){
        if(used[G[v][i]]==0) DFS(G[v][i]);
    }
    vs.push_back(v);
}

void rDFS(int v,int k){
    used[v]=1;
    cmp[v]=k;
    for(int i=0;i<rG[v].size();i++){
        if(used[rG[v][i]]==0) rDFS(rG[v][i],k);
    }
}

int scc(){
    memset(used,0,sizeof(used));
    vs.clear();
    for(int v=0;v<V;v++){
        if(used[v]==0) DFS(v);
    }
    
    memset(used,0,sizeof(used));
    int k=0;
    for(int i=vs.size()-1;i>=0;i--){
        if(used[vs[i]]==0) rDFS(vs[i],k++);
    }
    return k;
}

int main(){

    cin>>V;
    int M;cin>>M;
    for(int i=0;i<M;i++){
        int a,b;cin>>a>>b;
        a--;b--;
        add_edge(a,b);
    }
    
    scc();
    
    for(int i=0;i<V;i++){
        bool deta=false;
        for(int j=0;j<V;j++){
            if(cmp[i]==cmp[j]){
                if(deta) cout<<" ";
                cout<<j+1;
                deta=true;
            }
        }
        cout<<endl;
    }
}



```