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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net;
using System.Security.Cryptography;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder.ABC
{
    class QuestionE
    {
        public class HW
        {
            public long H;
            public long W;

            public HW(long[] hw)
            {
                H = hw[0];
                W = hw[1];
            }
        }

        public static void Main(string[] args)
        {
            var hwm = Console.ReadLine().Split(" ").Select(z => long.Parse(z)).ToArray();
            var h = hwm[0];
            var w = hwm[1];
            var m = hwm[2];

            var arrayMax = 300000;

            var hlineBombs = new long[arrayMax];
            var wlineBombs = new long[arrayMax];

            var bombs = new HW[arrayMax];

            //それぞれの行列での爆弾の個数を求める
            for (int i = 0; i < m; i++) {
                var hw = new HW(Console.ReadLine().Split(" ").Select(z => long.Parse(z)).ToArray());
                var y = --hw.H;
                var x = --hw.W;
                bombs[i] = hw;

                hlineBombs[y]++;
                wlineBombs[x]++;
            }

            var hMax = hlineBombs.Max();
            var wMax = wlineBombs.Max();

            //最大数の爆弾を保持する行列のIndex
            var hIndexes = new HashSet<long>();
            var wIndexes = new HashSet<long>();

            for (int i = 0; i < h; i++) {
                if (hlineBombs[i] == hMax) {
                    if (hIndexes.Contains(i) == false) {
                        hIndexes.Add(i);
                    }
                }
            }

            for (int i = 0; i < w; i++) {
                if (wlineBombs[i] == wMax) {
                    if (wIndexes.Contains(i) == false) {
                        wIndexes.Add(i);
                    }
                }
            }

            var max = hMax + wMax;

            //爆破したいマスの候補数
            var remain = ((long)hIndexes.Count) * wIndexes.Count;

            for (int i = 0; i < m; i++) {
                //なるべく爆弾のない候補マスを爆破したいので
                //候補マスに爆弾が存在していた時は候補数を減らす
                if (hIndexes.Contains(bombs[i].H) && wIndexes.Contains(bombs[i].W)) {
                    remain--;
                }
            }

            //すべての爆弾を調べた後、爆破するマスの候補が残っていなければ、仕方なく爆弾のあるマスを爆破する
            if (remain <= 0) {
                max--;
            }

            Console.WriteLine(max);
        }
    }
}