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.Collections.Generic;
using System.IO;

namespace ARC065D{
    public class Program{
        public static void Main(string[] args){
            var sr = new StreamReader();
            var sw = new StreamWriter(Console.OpenStandardOutput()){AutoFlush = false};
            //---------------------------------
            var N = sr.Next<int>();
            var K = sr.Next<int>();
            var L = sr.Next<int>();

            var qf = new QuickFind[2];
            qf[0] = new QuickFind(N);
            qf[1] = new QuickFind(N);

            for(var i = 0; i < K; i++){
                var p = sr.Next<int>() - 1;
                var q = sr.Next<int>() - 1;
                qf[0].Merge(p, q);
            }

            for(var i = 0; i < L; i++){
                var r = sr.Next<int>() - 1;
                var s = sr.Next<int>() - 1;
                qf[1].Merge(r, s);
            }

            Func<int, int, long> hash = (x, y) => x * 1000000L + y; 
            var dic = new Dictionary<long, int>();
            for(var i = 0; i < N; i++){
                var h = hash(qf[0].Group[i], qf[1].Group[i]);
                if(dic.ContainsKey(h))dic[h]++;
                else dic.Add(h, 1);
            }

            for(var i = 0; i < N; i++){
                var h = hash(qf[0].Group[i], qf[1].Group[i]);
                sw.Write(dic[h] + " ");
            }
            sw.WriteLine();
            //---------------------------------
            sw.Flush();
        }
    }

    public class Ex{
        public static void Swap<T>(ref T left, ref T right){
            var tmp = left;
            left = right;
            right = tmp;
        }

        public static void Fill<T>(ref T[] src, T val){
            for(var i = 0; i < src.Length; i++){
                src[i] = val;
            }
        }
    }

    public class QuickFind{
        //データ構造をマージする一般的なテク
        public readonly int[] Group;
        public readonly List<int>[] Items;

        public QuickFind(int n){
            Group = new int[n];
            Items = new List<int>[n];
            for(var i = 0; i < n; i++){
                Group[i] = i;
                Items[i] = new List<int>{i};
            }
        }

        public void Merge(int x, int y){
            if(Items[Group[x]].Count < Items[Group[y]].Count) Ex.Swap(ref x, ref y);

            var gx = Group[x];
            var gy = Group[y];
            if(gx == gy) return;

            foreach(var iy in Items[gy]){
                Group[iy] = gx;
                Items[gx].Add(iy);
            }
        }

        public List<int> SameGroupItems(int x){
            return Items[Group[x]];
        }

        public bool IsSameGroup(int x, int y){
            return Group[x] == Group[y];
        }
    }

    public class StreamReader{
        private readonly char[] _c = {' '};
        private int _index = -1;
        private string[] _input = new string[0];
        private readonly System.IO.StreamReader _sr = new System.IO.StreamReader(Console.OpenStandardInput());

        public T Next<T>(){
            if(_index == _input.Length - 1){
                _index = -1;
                while(true){
                    string rl = _sr.ReadLine();
                    if(rl == null){
                        if(typeof(T).IsClass) return default(T);
                        return (T)typeof(T).GetField("MinValue").GetValue(null);
                    }
                    if(rl != ""){
                        _input = rl.Split(_c, StringSplitOptions.RemoveEmptyEntries);
                        break;
                    }
                }
            }
            return (T)Convert.ChangeType(_input[++_index], typeof(T), System.Globalization.CultureInfo.InvariantCulture);
        }

        public T[] Next<T>(int x){
            var ret = new T[x];
            for(var i = 0; i < x; ++i) ret[i] = Next<T>();
            return ret;
        }

        public T[][] Next<T>(int y, int x){
            var ret = new T[y][];
            for(var i = 0; i < y; ++i) ret[i] = Next<T>(x);
            return ret;
        }
    }
}