/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<map>
#include<set>
#include<unordered_map>
#include<utility>
#include<cmath>
#include<random>
#include<cstring>
#include<queue>
#include<stack>
#include<bitset>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#include<typeinfo>
#define loop(i,a,b) for(long long i=a;i<b;i++)
#define rep(i,a) loop(i,0,a)
#define FOR(i,a) for(auto i:a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define show1d(v) {rep(_,v.size())cout<<" "<<v[_];cout<<endl;}
#define show2d(v) {rep(__,v.size())show1d(v[__]);}
using namespace std;
//kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
#define mt make_tuple
typedef tuple<int,int,int,int> tp;
typedef vector<tp> vt;
template<typename A,typename B>bool cmin(A &a,const B &b){return a>b?(a=b,true):false;}
template<typename A,typename B>bool cmax(A &a,const B &b){return a<b?(a=b,true):false;}
const double PI=acos(-1);
const double EPS=1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9+10;
#define yes cout<<"Yes\n"
#define no cout<<"No\n"

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}
class SCC{//cmp(0 - kk-1) is scc's return. Same number is group. The number is no relatoin.
	public:
	int n,N;
	vvi G,rG;
	vector<bool>used;
	vi vs,cmp;
	SCC(int size){
		n=size;
		G=rG=vvi(n);
		used=vector<bool>(n);
		cmp=vi(n);
		vs=vi(0);
	}
	void add_edge(int s,int t){
		G[s].pb(t);
		rG[t].pb(s);
	}
	void rdfs(int v,int k){
		used[v]=true;
		cmp[v]=k;
		rep(i,rG[v].size())if(!used[rG[v][i]])rdfs(rG[v][i],k);
	}
	void dfs(int v){
		used[v]=true;
		rep(i,G[v].size())if(!used[G[v][i]])dfs(G[v][i]);
		vs.pb(v);
	}
	int scc(){
		rep(i,n)used[i]=false;
		rep(v,n)if(!used[v])dfs(v);
		rep(i,n)used[i]=false;
		N=0;
		for(int i=vs.size()-1;i>=0;i--)if(!used[vs[i]])rdfs(vs[i],N++);
		return N;
	}
	vvi make(){
		vvi tG(N);
		rep(i,n)rep(j,G[i].size())if(cmp[i]!=cmp[G[i][j]]){
			tG[cmp[i]].pb(cmp[G[i][j]]);
//			tG[cmp[G[i][j]]].pb(cmp[i]);
		}
		return tG;
	}
};
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);

    int n,m;
	cin>>n>>m;
	SCC scc(n);
	while(m--){
		int a,b;
		cin>>a>>b;a--;b--;
		scc.add_edge(a,b);
	}
	int N=scc.scc();
    vvi G(n);
    rep(i,n)G[scc.cmp[i]].pb(i+1);
    rep(i,n)sort(all(G[i]));
    rep(i,n){
        vi t=G[scc.cmp[i]];
        rep(j,t.size())cout<<t[j]<<" \n"[j==t.size()-1];
    }
}


### Prompt

Develop a solution in Cpp to the problem described below:

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
/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>
#include<map>
#include<set>
#include<unordered_map>
#include<utility>
#include<cmath>
#include<random>
#include<cstring>
#include<queue>
#include<stack>
#include<bitset>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#include<typeinfo>
#define loop(i,a,b) for(long long i=a;i<b;i++)
#define rep(i,a) loop(i,0,a)
#define FOR(i,a) for(auto i:a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define show1d(v) {rep(_,v.size())cout<<" "<<v[_];cout<<endl;}
#define show2d(v) {rep(__,v.size())show1d(v[__]);}
using namespace std;
//kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
#define mt make_tuple
typedef tuple<int,int,int,int> tp;
typedef vector<tp> vt;
template<typename A,typename B>bool cmin(A &a,const B &b){return a>b?(a=b,true):false;}
template<typename A,typename B>bool cmax(A &a,const B &b){return a<b?(a=b,true):false;}
const double PI=acos(-1);
const double EPS=1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9+10;
#define yes cout<<"Yes\n"
#define no cout<<"No\n"

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}
class SCC{//cmp(0 - kk-1) is scc's return. Same number is group. The number is no relatoin.
	public:
	int n,N;
	vvi G,rG;
	vector<bool>used;
	vi vs,cmp;
	SCC(int size){
		n=size;
		G=rG=vvi(n);
		used=vector<bool>(n);
		cmp=vi(n);
		vs=vi(0);
	}
	void add_edge(int s,int t){
		G[s].pb(t);
		rG[t].pb(s);
	}
	void rdfs(int v,int k){
		used[v]=true;
		cmp[v]=k;
		rep(i,rG[v].size())if(!used[rG[v][i]])rdfs(rG[v][i],k);
	}
	void dfs(int v){
		used[v]=true;
		rep(i,G[v].size())if(!used[G[v][i]])dfs(G[v][i]);
		vs.pb(v);
	}
	int scc(){
		rep(i,n)used[i]=false;
		rep(v,n)if(!used[v])dfs(v);
		rep(i,n)used[i]=false;
		N=0;
		for(int i=vs.size()-1;i>=0;i--)if(!used[vs[i]])rdfs(vs[i],N++);
		return N;
	}
	vvi make(){
		vvi tG(N);
		rep(i,n)rep(j,G[i].size())if(cmp[i]!=cmp[G[i][j]]){
			tG[cmp[i]].pb(cmp[G[i][j]]);
//			tG[cmp[G[i][j]]].pb(cmp[i]);
		}
		return tG;
	}
};
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);

    int n,m;
	cin>>n>>m;
	SCC scc(n);
	while(m--){
		int a,b;
		cin>>a>>b;a--;b--;
		scc.add_edge(a,b);
	}
	int N=scc.scc();
    vvi G(n);
    rep(i,n)G[scc.cmp[i]].pb(i+1);
    rep(i,n)sort(all(G[i]));
    rep(i,n){
        vi t=G[scc.cmp[i]];
        rep(j,t.size())cout<<t[j]<<" \n"[j==t.size()-1];
    }
}


```