Problem:
Score : 500 points

Problem Statement

We have a two-dimensional grid with H \times W squares. There are M targets to destroy in this grid - the position of the i-th target is \left(h_i, w_i \right).

Takahashi will choose one square in this grid, place a bomb there, and ignite it. The bomb will destroy all targets that are in the row or the column where the bomb is placed. It is possible to place the bomb at a square with a target.

Takahashi is trying to maximize the number of targets to destroy. Find the maximum number of targets that can be destroyed.

Constraints

All values in input are integers.

1 \leq H, W \leq 3 \times 10^5

1 \leq M \leq \min\left(H\times W, 3 \times 10^5\right)

1 \leq h_i \leq H

1 \leq w_i \leq W

\left(h_i, w_i\right) \neq \left(h_j, w_j\right) \left(i \neq j\right)

Input

Input is given from Standard Input in the following format:

H W M
h_1 w_1
\vdots
h_M w_M

Output

Print the answer.

Sample Input 1

2 3 3
2 2
1 1
1 3

Sample Output 1

3

We can destroy all the targets by placing the bomb at \left(1, 2\right).

Sample Input 2

3 3 4
3 3
3 1
1 1
1 2

Sample Output 2

3

Sample Input 3

5 5 10
2 5
4 3
2 3
5 5
2 2
5 4
5 3
5 1
3 5
1 4

Sample Output 3

6

Solution in Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		InputReader sc = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int h = sc.nextInt();
		int w = sc.nextInt();
		int m = sc.nextInt();
		HashMap<Integer, ArrayList<Integer>> hmr = new HashMap<>();
		HashMap<Integer, Integer> hmc = new HashMap<>();
		
		for(int i = 0; i < m ;i ++){
			int r = sc.nextInt();
			int c = sc.nextInt();
			ArrayList<Integer> al = hmr.getOrDefault(r, new ArrayList<Integer>());
			al.add(c);
			hmr.put(r, al);
			hmc.put(c,  hmc.getOrDefault(c, 0)+1);
		}
		
		int max = 0, maxc = 0;
		int row = -1;
		for(int r : hmr.keySet()){
			if(hmr.get(r).size() > max){
				max = hmr.get(r).size();
				row = r;				
			}else if(hmr.get(r).size() == max){
				int max1 = 0;
				for(int c : hmr.get(r)){
					max1 = Math.max(max1, hmc.get(c));
				}
				int max2 = 0;
				for(int c : hmr.get(row)){
					max2 = Math.max(max2,  hmc.get(c));
				}
				if(max1 > max2){
					row = r;
					max = max1;
				}
			}
		}
		
		for(int c : hmr.get(row)){
			hmc.put(c, hmc.get(c)-1);
		}
		int max2 = 0;
		for(int s : hmc.values()){
			max2 = Math.max(max2, s);
		}
		
		pw.println((max+max2));
		
		pw.close();
	}


	static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[5];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}

				if (numChars <= 0)
					return -1;
			}

			return buf[curChar++];
		}

		public String nextLine() {
			BufferedReader br = new BufferedReader(new InputStreamReader(stream));
			String stock = "";
			try {
				stock = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return stock;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();

			int sgn = 1;

			if (c == '-') {
				sgn = -1;
				c = read();
			}

			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));

			return res * sgn;
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public double nextDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));

			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public String next() {
			return readString();
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

}