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: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	final int _intMax = Integer.MAX_VALUE; //=2147483647>10^9
	final int _intMin = Integer.MIN_VALUE;
	final long _longMax = Long.MAX_VALUE; //=9223372036854775807L>10^18
	final long _longMin = Long.MIN_VALUE;
	static boolean bElapsed = false;

	void solve() {
		int[] ia = readNums();
		int n = ia[0];
		int k = ia[1];
		int l = ia[2];
		UnionFind uf = new UnionFind(n+1);
		UnionFind uf2 = new UnionFind(n+1);
		byte[] flg = new byte[n+1];
		for (int i=0; i<k; i++) {
			ia = readNums();
			uf.merge(ia[0], ia[1]);
			flg[ia[0]] |= 1;
			flg[ia[1]] |= 1;
		}
		for (int i=0; i<l; i++) {
			ia = readNums();
			uf2.merge(ia[0], ia[1]);
			flg[ia[0]] |= 2;
			flg[ia[1]] |= 2;
		}
		for (int i=1; i<=n; i++) {
			if (i != 1) p(" ");
			if (flg[i] != 3) {
				p("1");
				continue;
			}
			int cnt = 1;
			for (int j=1; j<=n; j++) {
				if (i != j) {
					if (uf.same(i, j)) {
						if (uf2.same(i, j)) {
							cnt++;
						}
					}
				}
			}
			p(cnt);
		}
		pln("");
	}

	class RMQ {
		int n;
		int[] element;
		public RMQ(int n) {
			n = (int)ceil2pow(n);
			this.n = n;
			element = new int[2*n-1];
			Arrays.fill(element, _intMax);
		}
		public void update(int k, int a) {
			k += n-1;
			element[k] = a;
			while (k > 0) {
				k = (k-1)/2;
				element[k] = Math.min(element[2*k+1], element[2*k+2]);
			}
		}
		public int query(int a, int b) {
			if (a == b) return element[a+n-1];
			return query(a, b+1, 0, 0, n);
		}
		private int query(int a, int b, int k, int l, int r) {
			if (r <= a || b <= l) return _intMax;
			if (a <= l && r <= b) return element[k];
			int vl = query(a, b, 2*k+1, l, (l+r)/2);
			int vr = query(a, b, 2*k+2, (l+r)/2, r);
			return Math.min(vl, vr);
		}
		public void print() {
			for (int i=0; i<element.length; i++) {
				String v = element[i] != _intMax ? ""+element[i] : "-";
				p(v+" ");
			}
			pln("");
		}
	}
	class RMQIndex {
		int n;
		int[] element;
		int[] index;
		public RMQIndex(int n) {
			n = (int)ceil2pow(n);
			this.n = n;
			element = new int[2*n-1];
			index = new int[2*n-1];
			Arrays.fill(element, _intMax);
			for (int i=0; i<n; i++) {
				index[n-1+i] = i;
			}
			for (int i=n-1-1; i>=0; i--) {
				index[i] = index[2*i+1];
			}
		}
		public void update(int k, int a) {
			k += n-1;
			element[k] = a;
			while (k > 0) {
				k = (k-1)/2;
				if (element[2*k+1] <= element[2*k+2]) {
					element[k] = element[2*k+1];
					index[k] = index[2*k+1];
				} else {
					element[k] = element[2*k+2];
					index[k] = index[2*k+2];
				}
			}
		}
		public int[] query(int a, int b) {
			if (a == b) return new int[] { element[a+n-1], index[a+n-1] };
			return query(a, b+1, 0, 0, n);
		}
		private int[] query(int a, int b, int k, int l, int r) {
			if (r <= a || b <= l) return new int[] { _intMax, 0 };
			if (a <= l && r <= b) return new int[] { element[k], index[k] };
			int[] vl = query(a, b, 2*k+1, l, (l+r)/2);
			int[] vr = query(a, b, 2*k+2, (l+r)/2, r);
			if (vl[0] <= vr[0]) {
				return new int[] { vl[0], vl[1] };
			} else {
				return new int[] { vr[0], vr[1] };
			}
		}
		public void print() {
			p("dat:");
			for (int i=0; i<element.length; i++) {
				String v = element[i] != _intMax ? ""+element[i] : "-";
				p(v+" ");
			}
			pln("");
			p("idx:");
			for (int i=0; i<index.length; i++) {
				p(index[i]+" ");
			}
			pln("");
		}
	}
	class UnionFind {
		int[] uf;
		public UnionFind(int n) {
			uf = new int[n];
			for (int i=0; i<n; i++) {
				uf[i] = i;
			}
		}
		public int root(int v) {
			if (uf[v] == v) return v;
			uf[v] = root(uf[v]);
			return uf[v];
		}
		public void merge(int u, int v) {
			u = root(u);
			v = root(v);
			if (u == v) return;
			uf[v] = u;
		}
		public boolean same(int u, int v) {
			return root(u) == root(v);
		}
		public void print() {
			for (int i=0; i<uf.length; i++) {
				p(uf[i]+" ");
			}
			pln("");
		}
	}
	class Pair {
		String a;
		String b;
		public Pair(String a, String b) {
			this.a = a;
			this.b = b;
		}
		public Pair(Pair pr) {
			this.a = pr.a;
			this.b = pr.b;
		}
		public boolean equals(Object o) {
			if (o instanceof Pair) {
				Pair that = (Pair)o;
				return (a.equals(that.a)) && (b.equals(that.b));
			}
			return false;
		}
		public int hashCode() {
			return a.hashCode() + (b.hashCode() * 31);
		}
		public String toString() {
			return "(" + a + ", " + b + ")";
		}
	}
	class Point {
		int x;
		int y;
		public Point(int x, int y) {
			this.x = x;
			this.y = y;
		}
		public Point(Point pt) {
			this.x = pt.x;
			this.y = pt.y;
		}
		public boolean equals(Object o) {
			if (o instanceof Point) {
				Point that = (Point)o;
				return (x == that.x) && (y == that.y);
			}
			return false;
		}
		public int hashCode() {
			return x + (y * 31);
		}
		public String toString() {
			return "(" + x + ", " + y + ")";
		}
	}
	class Info implements Comparable<Info> {
		int idx;
		int val;
		public Info(int idx, int val) {
			this.idx = idx;
			this.val = val;
		}
		public int compareTo(Info o) {
			if (idx < o.idx) return -1;
			else if (idx > o.idx) return 1;
			return 0;
		}
		public boolean equals(Object o) {
			if (o instanceof Info) {
				Info that = (Info)o;
				return 0 == compareTo(that);
			}
			return false;
		}
		public int hashCode() {
			return idx + (val * 31);
		}
		public String toString() {
			return "(" + idx + ", " + val + ")";
		}
	}
	class InfoComp implements Comparator<Info> {
		public int compare(Info o1, Info o2) {
			if (o1.val < o2.val) return -1;
			else if (o1.val > o2.val) return 1;
			return 0;
		}
	}
	long ceil2pow(long n) {
		if (n == 0) return 1;
		n--;
		n |= (n >>> 1);
		n |= (n >>> 2);
		n |= (n >>> 4);
		n |= (n >>> 8);
		n |= (n >>> 16);
		n++;
		return n;
		/*
		long pow = 1;
		while (pow < n) pow <<= 1;
		return pow;
		*/
	}
	int gcd(int a, int b) {
		if (a < b) return gcd(b, a);
		if (b == 0) return a;
		return gcd(b, a % b);
	}
	long sqrt(long n) {
		return (long)Math.sqrt(n);
	}
	long pow(long n, long p) {
		return (long)Math.pow(n, p);
	}
	long pow_mod(long n, long p, long m) {
		if (p == 0) return 1;
		else if (p % 2 == 1) return pow_mod(n, p-1, m) * n % m;
		long sum = pow_mod(n, p/2, m);
		return sum * sum % m;
	}
	int pint(String s) {
		return Integer.parseInt(s);
	}
	long plong(String s) {
		return Long.parseLong(s);
	}
	String readLine() {
		try {
			return _in.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}
	int readNum() {
		String line = readLine();
		return pint(line);
	}
	String[] readFlds() {
		String line = readLine();
		return line.split(" ");
	}
	int[] readNums() {
		String[] flds = readFlds();
		int[] nums = new int[flds.length];
		for (int i=0; i<flds.length; i++) {
			nums[i] = pint(flds[i]);
		}
		return nums;
	}
	void p(char c) {
		_out.print(c);
	}
	void pln(char c) {
		_out.println(c);
	}
	void p(double d) {
		_out.print(d);
	}
	void pln(double d) {
		_out.println(d);
	}
	void p(long l) {
		_out.print(l);
	}
	void pln(long l) {
		_out.println(l);
	}
	void p(String s) {
		_out.print(s);
	}
	void pln(String s) {
		_out.println(s);
	}
	static BufferedReader _in;
	static PrintWriter _out;
	public static void main(String[] args) {
		long start = System.currentTimeMillis();
		_in = new BufferedReader(new InputStreamReader(System.in));
		_out = new PrintWriter(System.out);
		new Main().solve();
		_out.flush();
		long end = System.currentTimeMillis();
		if (bElapsed) {
			System.err.println((end-start) + "ms");
		}
	}
}