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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static int modP = 1000000007;

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt(), k = in.nextInt(), l = in.nextInt();
			DisjointSet road = new DisjointSet(n);
			DisjointSet rail = new DisjointSet(n);

			for (int i = 0; i < k; i++) {
				int x = in.nextInt()-1, y = in.nextInt()-1;
				road.unite(x, y);
			}

			for (int i = 0; i < l; i++) {
				int x = in.nextInt()-1, y = in.nextInt()-1;
				rail.unite(x, y);
			}

			Map<Long, Integer> map = new HashMap<>();
			for (int i = 0; i < n; i++) {
				long key = (long)road.findSet(i) << 32 | rail.findSet(i);
				int count = map.containsKey(key) ? map.get(key) : 0;
				map.put(key, ++count);
			}
			for (int i = 0; i < n; i++) {
				long key = (long)road.findSet(i) << 32 | rail.findSet(i);
				if (i == 0) {
					out.print(map.get(key));
				} else {
					out.print(" "+map.get(key));
				}
			}
			out.print("\n");

		}
		public class DisjointSet {

			int[] p, rank;

			public DisjointSet(int size) {
				p = new int[size];
				rank = new int[size];

				for (int j = 0; j < size; j++) {
					makeSet(j);
				}
			}

			private void makeSet(int x) {
				p[x] = x;
				rank[x] = 0;
			}

			public int findSet(int x) {
				return p[x] == x ? x : findSet(p[x]);
			}

			public void link(int x, int y) {
				if (rank[x] > rank[y]) {
					p[y] = x;
				} else if (rank[x] < rank[y]) {
					p[x] = y;
				} else if (rank[x] == rank[y]) {
					p[x] = y;
					rank[y]++;
				}
			}

			public void unite(int x, int y) {
				link(findSet(x), findSet(y));
			}

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

	static class InputReader {
		BufferedReader in;
		StringTokenizer tok;

		public String nextString() {
			while (!tok.hasMoreTokens()) {
				try {
					tok = new StringTokenizer(in.readLine(), " ");
				} catch (IOException e) {
					throw new InputMismatchException();
				}
			}
			return tok.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(nextString());
		}

		public long nextLong() {
			return Long.parseLong(nextString());
		}

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

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

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public InputReader(InputStream inputStream) {
			in = new BufferedReader(new InputStreamReader(inputStream));
			tok = new StringTokenizer("");
		}

	}

}