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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
 
class Program
{
    static void Main(string[] args)
    {
        var nkl = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var union1 = new UnionFind<int>();
        var union2 = new UnionFind<int>();
        for(var i = 0; i < nkl[0]; i++)
        {
            union1.MakeSet(i + 1);
            union2.MakeSet(i + 1);
        }
        for(var i = 0; i < nkl[1]; i++)
        {
            var input = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            union1.Union(input[0], input[1]);
        }
        for(var i = 0; i < nkl[2]; i++)
        {
            var input = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            union2.Union(input[0], input[1]);
        }
        var proad = new int[nkl[0]];
        var ptrain = new int[nkl[0]];
        for(var i = 0; i < nkl[0]; i++)
        {
            proad[i] = union1.parent(i + 1);
            ptrain[i] = union2.parent(i + 1);
        }
        var dic = new Dictionary<int, Dictionary<int,int>>();
        for(var i = 0; i < nkl[0]; i++)
        {
            if (!dic.ContainsKey(proad[i]))
                dic[proad[i]] = new Dictionary<int, int>();
            if (dic[proad[i]].ContainsKey(ptrain[i])) dic[proad[i]][ptrain[i]]++;
            else dic[proad[i]][ptrain[i]] = 1;
        }
        WriteLine(string.Join(" ", Enumerable.Range(0, nkl[0]).Select(v => dic[proad[v]][ptrain[v]]).ToArray()));
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}
 
 
public class UnionFind<T>
{
    private class Vertex
    {
        public T Key { get; set; }
        public Vertex Parent { get; set; }
        public int Rank { get; set; }
 
        public Vertex(T key) : this(key, null, 0)
        {
 
        }
        public Vertex(T key, Vertex Parent, int rank)
        {
            this.Key = key;
            this.Parent = Parent;
            this.Rank = rank;
        }
    }
    private readonly Dictionary<T, Vertex> dics;
    private readonly Vertex NIL;
 
    public int Count { get; private set; }
 
    public UnionFind()
    {
        NIL = new Vertex(default(T));
        dics = new Dictionary<T, Vertex>();
    }
 
    public T parent(T key)
        => dics[key].Parent.Key;
 
    public bool IsSame(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            throw new ArgumentException("対応する頂点が存在しません");
        return ReferenceEquals(FindSet(dics[key1]), FindSet(dics[key2]));
    }
 
    public bool MakeSet(T key)
    {
        if (dics.ContainsKey(key))
            throw new ArgumentException($"{key}をキーとして持つ頂点が既に存在します");
        dics[key] = new Vertex(key, NIL, 0);
        dics[key].Parent = dics[key];
        Count++;
        return true;
    }
 
    public bool Union(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            throw new ArgumentException("対応する頂点が存在しません");
        if (IsSame(key1,key2)) return false;
        Link(FindSet(dics[key1]), FindSet(dics[key2]));
        Count--;
        return true;
    }
 
    private bool Link(Vertex vex1, Vertex vex2)
    {
        if (vex1.Rank > vex2.Rank)
            vex2.Parent = vex1;
        else
        {
            vex1.Parent = vex2;
            if (vex1.Rank == vex2.Rank)
                vex2.Rank++;
        }
        return true;
    }
 
    private Vertex FindSet(Vertex vex)
    {
        if (!ReferenceEquals(vex.Parent, vex))
            vex.Parent = FindSet(vex.Parent);
        return vex.Parent;
    }
}