#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef pair<ll, ll> LP;
typedef vector<ll> vec;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-5;
const ld pi = acos(-1.0);

struct graph {
private:
	int n;
	vector<vector<int>> G, rG;
	vector<bool> used;
	vector<int> vs;

	int mk;
	vector<vector<int>> fG;
	vector<vector<int>> ori;
	vector<int> trans;
public:
	graph(int sz) {
		n = sz;
		G.resize(n);
		rG.resize(n);
		used.resize(n);

		fG.resize(n);
		trans.resize(n, -1);
		ori.resize(n);
	}
	void add_edge(int a, int b) {
		G[a].push_back(b);
		rG[b].push_back(a);
	}
	void dfs(int v) {
		used[v] = true;
		rep(i, G[v].size()) {
			if (!used[G[v][i]])dfs(G[v][i]);
		}
		vs.push_back(v);
	}
	void rdfs(int v, int k) {
		used[v] = true;
		queue<int> q; q.push(v);
		vector<int> c;
		while (!q.empty()) {
			int id = q.front(); q.pop();
			ori[k].push_back(id);
			rep(j, rG[id].size()) {
				int to = rG[id][j];
				if (used[to]) {
					if (trans[to] >= 0)c.push_back(trans[to]);
					continue;
				}
				used[to] = true; q.push(to);
			}
		}
		sort(c.begin(), c.end());
		int len = unique(c.begin(), c.end()) - c.begin();
		rep(i, len) {
			fG[c[i]].push_back(k);
		}
		rep(i, ori[k].size()) {
			trans[ori[k][i]] = k;
		}
	}
	void scc() {
		fill(used.begin(), used.end(), false);
		rep(i, n) {
			if (!used[i])dfs(i);
		}
		fill(used.begin(), used.end(), false);
		int k = 0;
		per(i, (int)vs.size()) {
			if (!used[vs[i]]) {
				rdfs(vs[i], k); k++;
			}
		}
		mk = k;
	}
	void query() {
		rep(i, mk)sort(ori[i].begin(), ori[i].end());
		rep(i, n) {
			int id = trans[i];
			rep(j, ori[id].size()) {
				if (j > 0)cout << " ";
				cout << ori[id][j]+1;
			}
			cout << endl;
		}
	}
};

void solve() {
	int n, m; cin >> n >> m;
	graph g(n);
	rep(i, m) {
		int a, b; cin >> a >> b; a--; b--;
		g.add_edge(a, b);
	}
	g.scc();
	g.query();
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	solve();
	//stop
	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<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
const ll mod = 998244353;
const ll INF = mod * mod;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef pair<ll, ll> LP;
typedef vector<ll> vec;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-5;
const ld pi = acos(-1.0);

struct graph {
private:
	int n;
	vector<vector<int>> G, rG;
	vector<bool> used;
	vector<int> vs;

	int mk;
	vector<vector<int>> fG;
	vector<vector<int>> ori;
	vector<int> trans;
public:
	graph(int sz) {
		n = sz;
		G.resize(n);
		rG.resize(n);
		used.resize(n);

		fG.resize(n);
		trans.resize(n, -1);
		ori.resize(n);
	}
	void add_edge(int a, int b) {
		G[a].push_back(b);
		rG[b].push_back(a);
	}
	void dfs(int v) {
		used[v] = true;
		rep(i, G[v].size()) {
			if (!used[G[v][i]])dfs(G[v][i]);
		}
		vs.push_back(v);
	}
	void rdfs(int v, int k) {
		used[v] = true;
		queue<int> q; q.push(v);
		vector<int> c;
		while (!q.empty()) {
			int id = q.front(); q.pop();
			ori[k].push_back(id);
			rep(j, rG[id].size()) {
				int to = rG[id][j];
				if (used[to]) {
					if (trans[to] >= 0)c.push_back(trans[to]);
					continue;
				}
				used[to] = true; q.push(to);
			}
		}
		sort(c.begin(), c.end());
		int len = unique(c.begin(), c.end()) - c.begin();
		rep(i, len) {
			fG[c[i]].push_back(k);
		}
		rep(i, ori[k].size()) {
			trans[ori[k][i]] = k;
		}
	}
	void scc() {
		fill(used.begin(), used.end(), false);
		rep(i, n) {
			if (!used[i])dfs(i);
		}
		fill(used.begin(), used.end(), false);
		int k = 0;
		per(i, (int)vs.size()) {
			if (!used[vs[i]]) {
				rdfs(vs[i], k); k++;
			}
		}
		mk = k;
	}
	void query() {
		rep(i, mk)sort(ori[i].begin(), ori[i].end());
		rep(i, n) {
			int id = trans[i];
			rep(j, ori[id].size()) {
				if (j > 0)cout << " ";
				cout << ori[id][j]+1;
			}
			cout << endl;
		}
	}
};

void solve() {
	int n, m; cin >> n >> m;
	graph g(n);
	rep(i, m) {
		int a, b; cin >> a >> b; a--; b--;
		g.add_edge(a, b);
	}
	g.scc();
	g.query();
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	solve();
	//stop
	return 0;
}


```