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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {
	static boolean[] visited;
	static int[] ans;
	static UnionFind dsu;
	static ArrayList<Integer> temp;
	static ArrayList<Integer>[] road, rail;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int l = sc.nextInt();
		
		//idea: construct a union-find with all the roads only
		//then, for each node, run dfs on it, and add nodes to the 
		//set if and only if they're in the same road-component 
		//and theres an edge between them
		//able to count all the members in the set exactly once and 
		//at the same time; if a and b are in the same set, then 
		//their count is equal; othewrise, it might be different
		road = new ArrayList[n];
		for(int i=0;i<n;i++) {
			road[i] = new ArrayList<>();
		}
		for(int i=0;i<k;i++) {
			int p = sc.nextInt()-1;
			int q = sc.nextInt()-1;
			road[p].add(q);
			road[q].add(p);
		}
		rail = new ArrayList[n];
		for(int i=0;i<n;i++) {
			rail[i] = new ArrayList<>();
		}
		for(int i=0;i<l;i++) {
			int r = sc.nextInt()-1;
			int s = sc.nextInt()-1;
			rail[r].add(s);
			rail[s].add(r);
		}
		dsu= new UnionFind(n);
		for(int i=0;i<n;i++) {
			for(int j : road[i]) {
				dsu.union(i,j);
			}
		}
		visited = new boolean[n];
		ans = new int[n];
		for(int i=0;i<n;i++) {
			if(!visited[i]) {
				temp = new ArrayList<>();
				dfs(i);
				for(int x:  temp) {
					ans[x] = temp.size();
				}
				
			}
		}
		StringBuilder sb = new StringBuilder();
		for(int i=0;i<n;i++) {
			sb.append(ans[i]);
			sb.append("\n");
		}
		System.out.println(sb.toString());
	}
	static void dfs(int i) {
		visited[i] = true;
		temp.add(i);
		for(int j : rail[i]) {
			if(dsu.findSet(i)==dsu.findSet(j) && !visited[j]) {
				dfs(j);
			}
		}
	}
	static class UnionFind{
		int par[];
		int sz[];
		public UnionFind(int n) {
			sz = new int[n];
			par = new int[n];
			for(int i=0;i<n;i++) {
				initialize(i);
			}
		}
		private void initialize(int x) {
			par[x] = x;
			sz[x] = 1;
		}
		public int findSet(int x) {
			while(x!=par[x]) {
				par[x] = par[par[x]];
				x = par[x];
			}
			return x;
		}
		public void union(int a,int b) {
			int x= findSet(a);
			int y = findSet(b);
			if(x!=y) {
				if(sz[x]<sz[y]) {
					int temp = x;
					x = y;
					y = temp;
				}
				par[y] = x;
				sz[x]+=sz[y];
			}
		}
	}
}