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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Deque;
import java.util.HashMap;
import java.util.NoSuchElementException;

/**
 * Created by jaga on 9/22/16.
 */
public class Main{
    public static void solve(PrintWriter out, FastScanner in) {
        int N = in.nextInt();
        int K = in.nextInt();
        int L = in.nextInt();

        UnionFindTree tree1 = new UnionFindTree(N);
        UnionFindTree tree2 = new UnionFindTree(N);

        for(int i = 0; i < K ; i++) {
            int p = in.nextInt();
            int q = in.nextInt();
            tree1.unite(p - 1,q - 1);
        }

        for(int i = 0 ; i < L;i++) {
            int r = in.nextInt();
            int s = in.nextInt();
            tree2.unite(r -1 ,s -1 );
        }

        HashMap<String, Integer> map = new HashMap<>();

        String txt[] = new String[N];
        for(int i = 0;i < N ;i ++) {
            txt[i] = tree1.par[i] + "+" + tree2.par[i];
            if (map.containsKey(txt[i])) {
                map.replace(txt[i], map.get(txt[i]) + 1);
            } else {
                map.put(txt[i], 1);
            }
        }

        for(int i = 0;i < N - 1;i ++) {
            out.print( map.get(txt[i]) + " ");
        }
        out.println(map.get(txt[N - 1]));
    }

    static class Pair implements Comparable {
        int first, second;

        Pair(int a, int b) {
            first = a;
            second = b;
        }

        public int compareTo(Object other) {
            Pair p1 = (Pair) other;
            return this.first - ((Pair) other).first; // IDの値に従い昇順で並び替えたい場合
//         return -(this.first - ((Pair) other).first); // IDの値に従い降順で並び替えたい場合
        }
    }

    /*以下はテンプレ*/
    public static void main(String args[]) {
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        FastScanner in = new FastScanner();
        solve(out, in);
        out.close();

    }

    public static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int bufferLength = 0;

        private boolean hasNextByte() {
            if (ptr < bufferLength) {
                return true;
            } else {
                ptr = 0;
                try {
                    bufferLength = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (bufferLength <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte()) return buffer[ptr++];
            else return -1;
        }

        private static boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        private void skipUnprintable() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        }

        boolean hasNext() {
            skipUnprintable();
            return hasNextByte();
        }

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextDouble();
            }
            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][];
            for (int i = 0; i < n; i++) {
                map[i] = nextDoubleArray(m);
            }
            return map;
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) array[i] = nextInt();
            return array;
        }

        public long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++) array[i] = nextLong();
            return array;
        }

        public String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++) array[i] = next();
            return array;
        }

        public char[][] nextCharMap(int n) {
            char[][] array = new char[n][];
            for (int i = 0; i < n; i++) array[i] = next().toCharArray();
            return array;
        }

        public int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][];
            for (int i = 0; i < n; i++) {
                map[i] = nextIntArray(m);
            }
            return map;
        }
    }

}
class UnionFindTree {
    int par[];//親ノード
    int rank[];//木の根のランク
    int num[];//木に含まれるノードの数 根以外の数は0

    //n要素で初期化
    UnionFindTree(int n) {
        par = new int[n]; //初期値では自分自身が親
        rank = new int[n]; //初期値0]
        num = new int[n];
        for(int i = 0;i < n;i++) {
            par[i] = i;
            num[i] = 1;
        }
    }

    //木の根を求める
    int find(int x) {
        if (par[x] == x) {
            return x;
        } else {
            return par[x] = find(par[x]);
        }
    }

    //xとyの属する集合を併合
    void unite(int x, int y) {
        //根を求める
        x = find(x);
        y = find(y);
        if (x == y) {
            return;
        }

        //ランクが大きい方の木に併合
        if (rank[x] < rank[y]) {
            par[x] = y;
            num[y] += num[x];
            num[x] = 0;
        } else {
            par[y] = x;
            num[x] += num[y];
            num[y] = 0;
            if (rank[x] == rank[y]) {
                //ランクが同じ場合はxに併合してランクを増やす
                rank[x]++;
            }
        }
    }

    //xとyが同じ木に属するかどうか
    boolean same(int x , int y){
        return find(x) == find(y);
    }

    int getNum(int x) {
        return num[x];
    }

    //xと親ノードが同じノードの数を求める
}