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: Accepted)

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

/*
			  br = new BufferedReader(new FileReader("input.txt"));
			  pw = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
			  br = new BufferedReader(new InputStreamReader(System.in));
			  pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
 */

public class Main {
	private static BufferedReader br;
	private static StringTokenizer st;
	private static PrintWriter pw;

	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		//int qq = 1;
		int qq = Integer.MAX_VALUE;
		//int qq = readInt();
		for(int casenum = 1; casenum <= qq; casenum++) {
			int n = readInt();
			int a = readInt();
			int b = readInt();
			road = init(n);
			while(a-- > 0) {
				int x = readInt()-1;
				int y = readInt()-1;
				merge(road, x, y);
			}
			rail = init(n);
			while(b-- > 0) {
				int x = readInt()-1;
				int y = readInt()-1;
				merge(rail, x, y);
			}
			int[] ret = new int[n];
			Map<Integer, ArrayList<Integer>> dp = new HashMap<>();
			for(int i = 0; i < n; i++) {
				int key = find(road, i);
				if(!dp.containsKey(key)) {
					dp.put(key, new ArrayList<>());
				}
				dp.get(key).add(i);
			}
			for(int out: dp.keySet()) {
				Map<Integer, ArrayList<Integer>> inner = new HashMap<>();
				for(int out2: dp.get(out)) {
					int key = find(rail, out2);
					if(!inner.containsKey(key)) {
						inner.put(key, new ArrayList<>());
					}
					inner.get(key).add(out2);
				}
				for(int out2: inner.keySet()) {
					for(int out3: inner.get(out2)) {
						ret[out3] = inner.get(out2).size();
					}
				}
			}
			for(int i = 0; i < n; i++) {
				pw.print(ret[i]);
				if(i == n-1) pw.println();
				else pw.print(" ");
			}
		}
		exitImmediately();
	}

	static int[] road;
	static int[] rail;

	public static int[] init(int x) {
		int[] ret = new int[x];
		for(int i = 0; i < x; i++) {
			ret[i] = i;
		}
		return ret;
	}

	public static int find(int[] p, int x) {
		return p[x] == x ? x : (p[x] = find(p, p[x]));
	}
	public static void merge(int[] p, int x, int y) {
		p[find(p, x)] = find(p, y);
	}

	private static void exitImmediately() {
		pw.close();
		System.exit(0);
	}

	private static long readLong() throws IOException {
		return Long.parseLong(readToken());
	}

	private static double readDouble() throws IOException {
		return Double.parseDouble(readToken());
	}

	private static int readInt() throws IOException {
		return Integer.parseInt(readToken());
	}

	private static String readLine() throws IOException  {
		String s = br.readLine();
		if(s == null) {
			exitImmediately();
		}
		st = null;
		return s;
	}

	private static String readToken() throws IOException  {
		while(st == null || !st.hasMoreTokens())  {
			st = new StringTokenizer(readLine().trim());
		}
		return st.nextToken();
	}
}