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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    private struct Pair<T> { public T x, y; public Pair(T xx, T yy) { x = xx; y = yy; } }
    private static int[] dx = { 1, 0, -1, 0 };
    private static int[] dy = { 0, -1, 0, 1 };
    public static void Main()
    {
        int N = NextInt();
        int K = NextInt();
        int L = NextInt();
        UnionFind UF1 = new UnionFind(N);
        UnionFind UF2 = new UnionFind(N);
        for (int i = 0; i < K; i++)
        {
            int p = NextInt() - 1;
            int q = NextInt() - 1;
            UF1.Unite(p, q);
        }
        for (int i = 0; i < L; i++)
        {
            int r = NextInt() - 1;
            int s = NextInt() - 1;
            UF2.Unite(r, s);
        }
        
        Dictionary<Pair<int>, int> dic = new Dictionary<Pair<int>, int>();
        for (int i = 0; i < N; i++)
        {
            int pw = UF1.Root(i);
            int pt = UF2.Root(i);
            Pair<int> pair = new Pair<int>(pw, pt);
            if (!dic.ContainsKey(pair)) dic[pair] = 0;
            dic[pair]++;
        }
        for (int i = 0; i < N; i++)
            Console.Write(dic[new Pair<int>(UF1.Root(i), UF2.Root(i))] + " ");
        Console.WriteLine();
    }
}

public class UnionFind
{
    public List<int> parent = new List<int>();

    public UnionFind(int N)
    {
        for (int i = 0; i < N; i++) parent.Add(i);
    }

    public int Root(int a)
    {
        if (parent[a] == a) return a;
        else return parent[a] = Root(parent[a]);
    }

    public void Unite(int a, int b)
    {
        a = Root(a);
        b = Root(b);
        if (a == b) return;
        parent[a] = parent[b];
    }

    public bool Same(int a, int b) { return (Root(a) == Root(b)); }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}