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: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int(), K = Reader.Int(), L = Reader.Int();
        int[][] E1 = Reader.IntTable(K), E2 = Reader.IntTable(L);

        var uf1 = new UnionFind(N);
        foreach (var e in E1) uf1.Unite(e[0] - 1, e[1] - 1);

        var uf2 = new UnionFind(N);
        foreach (var e in E2) uf2.Unite(e[0] - 1, e[1] - 1);

        var dic = new Dictionary<long, int>();
        Func<int, long> Key = i => (long)N * uf1.Root(i) + uf2.Root(i);
        for (int i = 0; i < N; i++)
            AddDic(dic, Key(i), 1);

        Console.WriteLine(string.Join(" ", Enu.Range(0, N).Select(i => dic[Key(i)])));
    }

    void AddDic<T>(Dictionary<T, int> dic, T key, int val)
    {
        if (dic.ContainsKey(key)) dic[key] += val;
        else dic[key] = val;
    }
}

class UnionFind
{
    private int[] parent;
    private byte[] rank;

    public UnionFind(int N)
    {
        parent = new int[N];
        rank = new byte[N];
        for (int i = 0; i < N; i++) parent[i] = -1;
    }
    public int Root(int x)
    {
        if (parent[x] < 0) return x;
        return parent[x] = Root(parent[x]);
    }
    public bool Same(int x, int y)
    {
        return Root(x) == Root(y);
    }
    public int Count(int x)
    {
        return -parent[Root(x)];
    }
    public bool Unite(int x, int y)
    {
        x = Root(x); y = Root(y);
        if (x == y) return false;
        if (rank[x] > rank[y]) { var t = x; x = y; y = t; }
        if (rank[x] == rank[y]) rank[y]++;
        parent[y] += parent[x];
        parent[x] = y;
        return true;
    }
    public Dictionary<int, List<int>> Components()
    {
        var dic = new Dictionary<int, List<int>>();
        for (int i = 0; i < parent.Length; i++)
        {
            int root = Root(i);
            if (!dic.ContainsKey(root)) dic[root] = new List<int>();
            dic[root].Add(i);
        }
        return dic;
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    public static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string[] Split(string s) { return s.Split(separator, op); }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}