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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ARC065.D();
        }
        class ARC065
        {
            public static void C()
            {
                var S = Read.Str();
                var strings = new string[] { "dream", "dreamer", "erase", "eraser" };
                int idx = S.Length - 1;
                while (idx >= 0)
                {
                    bool okAll = false;
                    foreach(var s in strings)
                    {
                        if (idx >= s.Length - 1)
                        {
                            bool ok = true;
                            for(int i = 0; i < s.Length; ++i)
                            {
                                if(s[i] != S[idx - s.Length + i + 1])
                                {
                                    ok = false; break;
                                }
                            }
                            if (ok)
                            {
                                okAll = true;
                                idx -= s.Length;
                                break;
                            }
                        }
                    }
                    if (!okAll) { Console.WriteLine("NO"); return; }
                }
                Console.WriteLine("YES");
            }
            public static void D()
            {
                var N = Read.Int();
                var K = Read.Int();
                var L = Read.Int();
                var PQ = Read.TupleInt(K);
                var RS = Read.TupleInt(L);
                var uft1 = new Util.UnionFindTree(N);
                var uft2 = new Util.UnionFindTree(N);
                foreach(var pq in PQ)
                {
                    uft1.Unite(pq.Item1 - 1, pq.Item2 - 1);
                }
                foreach(var rs in RS)
                {
                    uft2.Unite(rs.Item1 - 1, rs.Item2 - 1);
                }
                var dict1 = new Dictionary<int, HashSet<int>>();
                for(int i = 0; i < N; ++i)
                {
                    var r = uft1.Root(i);
                    if (!dict1.ContainsKey(r)) { dict1.Add(r, new HashSet<int>()); }
                    dict1[r].Add(i);
                }
                var ans = new int[N];
                foreach(var kvp1 in dict1)
                {
                    var dict2 = new Dictionary<int, HashSet<int>>();
                    foreach(var i in kvp1.Value)
                    {
                        var r = uft2.Root(i);
                        if (!dict2.ContainsKey(r)) { dict2.Add(r, new HashSet<int>()); }
                        dict2[r].Add(i);
                    }
                    foreach(var kvp2 in dict2)
                    {
                        foreach(var i in kvp2.Value)
                        {
                            ans[i] = kvp2.Value.Count;
                        }
                    }
                }
                Console.WriteLine(String.Join(" ", ans));
            }
        }
        class Util
        {
            public class UnionFindTree
            { //各Treeのサイズを保持する拡張仕様
                int[] parent;
                int[] count;
                public UnionFindTree(int n) { parent = new int[n]; count = new int[n]; for (int i = 0; i < n; ++i) { parent[i] = i; count[i] = 1; } }
                public int Root(int i) { if (parent[i] == i) { return i; } else { return parent[i] = Root(parent[i]); } }
                public int Count(int i) { return count[Root(i)]; }
                public bool Same(int i, int j) { return Root(i) == Root(j); }
                public void Unite(int i, int j) { var ri = Root(i); var rj = Root(j); if (ri != rj) { parent[ri] = rj; count[rj] += count[ri]; } }
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}