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.util.*;
import java.lang.*;
import java.io.*;
class Pair<E,F>{
    E first;
    F second;
    public Pair(E first, F second){
        this.first=first;
        this.second=second;
    }
    public E getFirst(){return first;}
    public F getSecond(){return second;}
    public String toString(){
        return "<"+first.toString()+","+second.toString()+">";
    }
    public int hashCode(){
        return first.hashCode()*30011+second.hashCode()+2;
    }
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair another = (Pair) obj;
        return this.getFirst().equals(another.getFirst())&&this.getSecond().equals(another.getSecond());
    }
}
class Counter<T> extends HashMap<T,Integer>{
    public Counter(){
        super();
    }
    public Integer get(Object elm){
        return getOrDefault(elm,0);
    }
    public void add(T elm){
        put(elm, get(elm)+1);
    }
}
class UnionFind{
    int size;
    int[] parent;
    int[] height;
    public UnionFind(int size){
        this.size = size;
        parent = new int[size];
        height = new int[size];
        for(int i=0;i<size;i++){
        	parent[i]=i;
        	height[i]=0;
        }
    }
    private boolean isRoot(int node){
        return node==parent[node];
    }
    public int getRoot(int node){
        if(isRoot(node)) return node;
        else{
        	parent[node] = getRoot(parent[node]);
        	return parent[node];
        }
    }
    public void union(int node1, int node2){
        if(height[node1]>height[node2])parent[getRoot(node2)] = getRoot(node1);
        else parent[getRoot(node1)] = getRoot(node2);
    }
    public boolean find(int node1, int node2){
        return getRoot(node1)==getRoot(node2);
    }
    public int countGroup(){
        int ans = 0;
        for(int i=0;i<size;i++) if(isRoot(i)) ans++;
        return ans;
    }
}
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int K = sc.nextInt();
        int L = sc.nextInt();
        UnionFind road = new UnionFind(N);
        UnionFind rail = new UnionFind(N);
        for(int k=0;k<K;k++){
        	int p = sc.nextInt()-1;
        	int q = sc.nextInt()-1;
        	road.union(p,q);
        }
        for(int l=0;l<L;l++){
        	int r = sc.nextInt()-1;
        	int s = sc.nextInt()-1;
        	rail.union(r,s);
        }
        
        Counter<Pair<Integer,Integer>> count = new Counter<>();
        for(int n=0;n<N;n++){
        	Pair<Integer,Integer> root = new Pair<>(road.getRoot(n),rail.getRoot(n));
        	count.add(root);
        }
        for(int n=0;n<N;n++){
        	Pair<Integer,Integer> root = new Pair<>(road.getRoot(n),rail.getRoot(n));
        	System.out.print(count.get(root));
        	if(n==N-1)System.out.println();
        	else System.out.print(" ");
        }
    }
}