#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<functional>
#include<assert.h>
#include<numeric>
using namespace std;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
using ll = long long;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;


struct StronglyConnectedComponents{
    vector<int> used,cmp,vs;
    vector<vector<int>> v,rv;
    StronglyConnectedComponents(int n):used(n),cmp(n,-1),v(n),rv(n){}

    void add_edge(int x,int y){
        v[x].push_back(y);
        rv[y].push_back(x);
    }
    void dfs(int x){
        used[x]=true;
        for(auto to:v[x])if(!used[to])dfs(to);
        vs.push_back(x);
    }

    void rdfs(int x,int k){
        cmp[x]=k;
        for(auto to:rv[x])if(cmp[to]==-1)rdfs(to,k);
    }

    int scc(){
        rep(i,used.size())if(!used[i])dfs(i);
        reverse(vs.begin(),vs.end());
        int k=0;
        for(auto x:vs)if(cmp[x]==-1)rdfs(x,k++);
        return k;
    }
    void build(vector<vector<int>> &g){
        int k=scc();
        g.resize(k);
        set<pair<int,int>> used;
        rep(i,v.size()){
            for(auto& to:v[i]){
                int x=cmp[i],y=cmp[to];
                if(x==y||used.count({x,y}))continue;
                g[x].push_back(y);
                used.emplace(x,y);
            }
        }
    }
};
int main(){
    int n,m;
    cin>>n>>m;
    StronglyConnectedComponents scc(n);
    rep(i,m){
        int x,y;
        cin>>x>>y;
        --x;--y;
        scc.add_edge(x, y);
    }
    int k = scc.scc();
    vector<vector<int>> ans(k);
    rep(i,n){
        ans[scc.cmp[i]].push_back(i+1);
    }
    rep(i,k)sort(ans[i].begin(),ans[i].end());
    rep(i,n){
        for(auto e : ans[scc.cmp[i]]){
            cout<<e<<" \n"[e == ans[scc.cmp[i]].back()];
        }
    }
    return 0;
}

### Prompt

In Cpp, your task is to solve 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<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
#include<functional>
#include<assert.h>
#include<numeric>
using namespace std;
#define REP(i,m,n) for(int i=(int)(m) ; i < (int) (n) ; ++i )
#define rep(i,n) REP(i,0,n)
using ll = long long;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;


struct StronglyConnectedComponents{
    vector<int> used,cmp,vs;
    vector<vector<int>> v,rv;
    StronglyConnectedComponents(int n):used(n),cmp(n,-1),v(n),rv(n){}

    void add_edge(int x,int y){
        v[x].push_back(y);
        rv[y].push_back(x);
    }
    void dfs(int x){
        used[x]=true;
        for(auto to:v[x])if(!used[to])dfs(to);
        vs.push_back(x);
    }

    void rdfs(int x,int k){
        cmp[x]=k;
        for(auto to:rv[x])if(cmp[to]==-1)rdfs(to,k);
    }

    int scc(){
        rep(i,used.size())if(!used[i])dfs(i);
        reverse(vs.begin(),vs.end());
        int k=0;
        for(auto x:vs)if(cmp[x]==-1)rdfs(x,k++);
        return k;
    }
    void build(vector<vector<int>> &g){
        int k=scc();
        g.resize(k);
        set<pair<int,int>> used;
        rep(i,v.size()){
            for(auto& to:v[i]){
                int x=cmp[i],y=cmp[to];
                if(x==y||used.count({x,y}))continue;
                g[x].push_back(y);
                used.emplace(x,y);
            }
        }
    }
};
int main(){
    int n,m;
    cin>>n>>m;
    StronglyConnectedComponents scc(n);
    rep(i,m){
        int x,y;
        cin>>x>>y;
        --x;--y;
        scc.add_edge(x, y);
    }
    int k = scc.scc();
    vector<vector<int>> ans(k);
    rep(i,n){
        ans[scc.cmp[i]].push_back(i+1);
    }
    rep(i,k)sort(ans[i].begin(),ans[i].end());
    rep(i,n){
        for(auto e : ans[scc.cmp[i]]){
            cout<<e<<" \n"[e == ans[scc.cmp[i]].back()];
        }
    }
    return 0;
}

```