Problem:
Score : 400 points

Problem Statement

There are N cities. There are also K roads and L railways, extending between the cities.
The i-th road bidirectionally connects the p_i-th and q_i-th cities, and the i-th railway bidirectionally connects the r_i-th and s_i-th cities.
No two roads connect the same pair of cities. Similarly, no two railways connect the same pair of cities.

We will say city A and B are connected by roads if city B is reachable from city A by traversing some number of roads. Here, any city is considered to be connected to itself by roads.
We will also define connectivity by railways similarly.

For each city, find the number of the cities connected to that city by both roads and railways.

Constraints

2 ≦ N ≦ 2*10^5

1 ≦ K, L≦ 10^5

1 ≦ p_i, q_i, r_i, s_i ≦ N

p_i < q_i

r_i < s_i

When i ≠ j, (p_i, q_i) ≠ (p_j, q_j)

When i ≠ j, (r_i, s_i) ≠ (r_j, s_j)

Input

The input is given from Standard Input in the following format:

N K L
p_1 q_1
:
p_K q_K
r_1 s_1
:
r_L s_L

Output

Print N integers. The i-th of them should represent the number of the cities connected to the i-th city by both roads and railways.

Sample Input 1

4 3 1
1 2
2 3
3 4
2 3

Sample Output 1

1 2 2 1

All the four cities are connected to each other by roads.

By railways, only the second and third cities are connected. Thus, the answers for the cities are 1, 2, 2 and 1, respectively.

Sample Input 2

4 2 2
1 2
2 3
1 4
2 3

Sample Output 2

1 2 2 1

Sample Input 3

7 4 4
1 2
2 3
2 5
6 7
3 5
4 5
3 4
6 7

Sample Output 3

1 1 2 1 2 2 2

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.awt.geom.*;
import java.math.*;

public class Main {

	static final Reader in = new Reader();
	static final PrintWriter out = new PrintWriter(System.out,false);
	static boolean debug = false;

	static void solve(){
		int n = in.nextInt();
		int k = in.nextInt();
		int l = in.nextInt();

		DisjointSet clus = new DisjointSet(n);

		for (int i=0; i<k; i++) {
			int p = in.nextInt() - 1;
			int q = in.nextInt() - 1;
			clus.unite(p, q);
		}


		HashMap<Integer,Integer> map = new HashMap<>();
		int p = 0;
		for (int i=0; i<n; i++) {
			if (map.containsKey(clus.find(i))) {
			} else {
				map.put(clus.find(i), p++);
			}
		}

		int m = p;

		DisjointSet ans = new DisjointSet(n);
		HashMap<Integer, ArrayList<Integer>> lists = new HashMap<>();

		for (int i=0; i<l; i++) {
			int s = in.nextInt() - 1;
			int t = in.nextInt() - 1;
			if (clus.same(s, t)) {
				ans.unite(s, t);
			} else {
				int sid = map.get(clus.find(s));
				int tid = map.get(clus.find(t));
				if (lists.containsKey(sid*m+tid)) {
					lists.get(sid*m+tid).add(t);
				} else {
					ArrayList<Integer> list = new ArrayList<>();
					list.add(t);
					lists.put(sid*m+tid, list);
				}

				if (lists.containsKey(tid*m+sid)) {
					lists.get(tid*m+sid).add(s);
				} else {
					ArrayList<Integer> list = new ArrayList<>();
					list.add(s);
					lists.put(tid*m+sid, list);
				}
			}
		}

		for (Integer key : lists.keySet()) {
			ArrayList<Integer> list = lists.get(key);
			for (int i=0; i<list.size()-1; i++) {
				ans.unite(list.get(i), list.get(i+1));
			}
		}

		boolean f = false;
		for (int i=0; i<n; i++) {
			out.print((f ? " ": "") + ans.size(i));
			f = true;
		}
		out.println();
	}

	public static void main(String[] args) throws Exception {
		debug = args.length > 0;
		long start = System.nanoTime();

		solve();
		out.flush();

		long end = System.nanoTime();
		dump((end - start) / 1000000 + " ms");
		in.close();
		out.close();
	}

	static void dump(Object... o) { if (debug) System.err.println(Arrays.deepToString(o)); }
}

class DisjointSet {

	private int[] par, cnt;

	public DisjointSet(int n){
		par = new int[n];
		cnt = new int[n];
		for (int i=0; i<n; i++) {
			par[i] = i;
			cnt[i] = 1;
		}
	}

	public int find(int x){
		return par[x] == x ? x : (par[x] = find(par[x]));
	}

	public boolean same(int x, int y){
		return find(x) == find(y);
	}

	public void unite(int x, int y){
		x = find(x); y = find(y);
		if (x == y) return;
		cnt[x] = cnt[y] = cnt[x] + cnt[y];
		par[x] = y;
	}

	public int size(int x) {
		return cnt[find(x)];
	}

	public String toString() {
		return Arrays.toString(par);
	}
}

class Reader {
	private final InputStream in;
	private final byte[] buf = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public Reader() { this(System.in);}
	public Reader(InputStream source) { this.in = source;}

	private boolean hasNextByte() {
		if (ptr < buflen) return true;
		ptr = 0;
		try{
			buflen = in.read(buf);
		}catch (IOException e) {e.printStackTrace();}
		if (buflen <= 0) return false;
		return true;
	}

	private int readByte() { if (hasNextByte()) return buf[ptr++]; else return -1;}

	private boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}

	private void skip() { while(hasNextByte() && !isPrintableChar(buf[ptr])) ptr++;}

	public boolean hasNext() {skip(); return hasNextByte();}

	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		boolean minus = false;
		long num = readByte();

		if(num == '-'){
			num = 0;
			minus = true;
		}else if (num < '0' || '9' < num){
			throw new NumberFormatException();
		}else{
			num -= '0';
		}

		while(true){
			int b = readByte();
			if('0' <= b && b <= '9')
				num = num * 10 + (b - '0');
			else if(b == -1 || !isPrintableChar(b))
				return minus ? -num : num;
			else
				throw new NoSuchElementException();
		}
	}

	public int nextInt() {
		long num = nextLong();
		if (num < Integer.MIN_VALUE || Integer.MAX_VALUE < num)
			throw new NumberFormatException();
		return (int)num;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}

	public char nextChar() {
		if (!hasNext()) throw new NoSuchElementException();
		return (char)readByte();
	}

	public String nextLine() {
		while (hasNextByte() && (buf[ptr] == '\n' || buf[ptr] == '\r')) ptr++;
		if (!hasNextByte()) throw new NoSuchElementException();

		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b != '\n' && b != '\r' && b != -1) {
			sb.appendCodePoint(b);
			b = readByte();
		}

		return sb.toString();
	}

	public int[] nextIntArray(int n) {
		int[] res = new int[n];
		for (int i=0; i<n; i++) res[i] = nextInt();
		return res;
	}

	public char[] nextCharArray(int n) {
		char[] res = new char[n];
		for (int i=0; i<n; i++) res[i] = nextChar();
		return res;
	}

	public void close() {try{ in.close();}catch(IOException e){ e.printStackTrace();}};
}