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.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        class Node<T>
        {
            private int m_height;
            private Node<T> m_parent;
            public T Item { get; private set; }
            public Node(T item)
            {
                m_height = 0;
                m_parent = this;
                Item = item;
            }
            public Node<T> Find()
            {
                if (m_parent == this) { return this; }

                Node<T> parent = m_parent.Find();
                m_parent = parent;
                return parent;
            }
            public static void Unite(Node<T> a, Node<T> b)
            {
                Node<T> p = a.Find();
                Node<T> q = b.Find();
                if (p.m_height < q.m_height)
                {
                    p.m_parent = q;
                    q.m_height = Math.Max(p.m_height + 1, q.m_height);
                }
                else
                {
                    q.m_parent = p;
                    p.m_height = Math.Max(q.m_height + 1, p.m_height);
                }
            }
        }

        static IEnumerable<int> Solve(int N, Node<int>[] nodes1, Node<int>[] nodes2)
        {
            var dict = new Dictionary<Tuple<int, int>, int>();
            for (int i = 0; i < N; ++i)
            {
                int a = nodes1[i].Find().Item;
                int b = nodes2[i].Find().Item;
                var key = new Tuple<int, int>(a, b);
                if (!dict.ContainsKey(key)) { dict[key] = 0; }
                ++dict[key];
            }
            int[] ans = new int[N];
            for (int i = 0; i < N; ++i)
            {
                int a = nodes1[i].Find().Item;
                int b = nodes2[i].Find().Item;
                var key = new Tuple<int, int>(a, b);
                ans[i] = dict[key];
            }
            return ans;
        }
        static void Main(string[] args)
        {
            int[] v1 = ReadInts();
            int N = v1[0];
            int K = v1[1];
            int L = v1[2];
            var nodes1 = new Node<int>[N];
            var nodes2 = new Node<int>[N];
            for (int i = 0; i < N; ++i)
            {
                nodes1[i] = new Node<int>(i);
                nodes2[i] = new Node<int>(i);
            }
            for (int i = 0; i < K; ++i)
            {
                int[] v2 = ReadInts();
                int p = v2[0] - 1;
                int q = v2[1] - 1;
                Node<int>.Unite(nodes1[p], nodes1[q]);
            }
            for (int i = 0; i < L; ++i)
            {
                int[] v2 = ReadInts();
                int r = v2[0] - 1;
                int s = v2[1] - 1;
                Node<int>.Unite(nodes2[r], nodes2[s]);
            }
            Console.WriteLine(string.Join(" ", Solve(N, nodes1, nodes2)));
        }
    }
}