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.*;

class Node {
  Node parent;
  int id;
  int rank;

  Node(int id) {
    this.parent = null;
    this.id = id;
    this.rank = 0;
  }

  public Node getRoot() {
    if (parent == null) {
      return this;
    }
    Node root = parent.getRoot();
    parent = root;
    return root;
  }

  public long getRootId() {
    return getRoot().id;
  }

  public static void merge(Node a, Node b) {
    Node aRoot = a.getRoot();
    Node bRoot = b.getRoot();

    if (aRoot.rank > bRoot.rank) {
      bRoot.parent = aRoot;
    } else if (aRoot.rank < bRoot.rank) {
      aRoot.parent = bRoot;
    } else if (aRoot != bRoot) {
      aRoot.parent = bRoot;
      bRoot.rank = bRoot.rank + 1;
    }
  }
}

public class Main {
  public static long getCityId(Node roadGroup, Node railGroup) {
    return (roadGroup.getRootId() << 32) | railGroup.getRootId();
  }

  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);

    String line = s.nextLine();
    String[] token = line.split(" ");
    int n = Integer.parseInt(token[0]);
    int k = Integer.parseInt(token[1]);
    int l = Integer.parseInt(token[2]);
    Node[] roadGroup = new Node[n];
    Node[] railGroup = new Node[n];
    for (int i = 0; i < n; i++) {
      roadGroup[i] = new Node(i);
      railGroup[i] = new Node(i);
    }
    for (int i = 0; i < k; i++) {
      line = s.nextLine();
      token = line.split(" ");
      int p = Integer.parseInt(token[0]) - 1;
      int q = Integer.parseInt(token[1]) - 1;
//      Node.merge(roadGroup[p], roadGroup[q]);
    }
    for (int i = 0; i < l; i++) {
      line = s.nextLine();
      token = line.split(" ");
      int r = Integer.parseInt(token[0]) - 1;
      int ss = Integer.parseInt(token[1]) - 1;
//      Node.merge(railGroup[r], railGroup[ss]);
    }
    HashMap<Long, Integer> cityCounter = new HashMap<Long, Integer>();
    for (int i = 0; i < n; i++) {
      long id = getCityId(roadGroup[i], railGroup[i]);
      if (cityCounter.get(id) == null) {
        cityCounter.put(id, 1);
      } else {
        cityCounter.put(id, cityCounter.get(id) + 1);
      }
    }
    for (int i = 0; i < n; i++) {
      long id = getCityId(roadGroup[i], railGroup[i]);
      if (i > 0) {
        System.out.print(" ");
      }
      System.out.print(cityCounter.get(id));
    }
    System.out.println();
  }
}