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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using static System.Console;
using static System.Math;
using static Atcoder.IO;

namespace Atcoder
{
    class Program
    {
        static StreamWriter sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
        static void Main(string[] args)
        {
            try
            {
                SetOut(sw);
                Solve.Answer();
                Out.Flush();
            }
            catch (Exception ex)
            {
                WriteLine(ex.ToString());
                Out.Flush();
            }
        }
    }

    public class Solve
    {
        public static void Answer()
        {
            var HWN = RSInt;

            long[] row = new long[HWN[0]];
            long[] col = new long[HWN[1]];
            var map = new int[HWN[0]][];
            for (int i = 0; i < HWN[0]; i++)
            {
                map[i] = new int[HWN[1]];
            }
            for (int i = 0; i < HWN[2]; i++)
            {
                var t = RSInt;
                //has.Add(t);
                map[t[0] - 1][t[1] - 1] = 1;
                row[t[0] - 1]++;
                col[t[1] - 1]++;
            }

            var maxRows = new List<int>();
            var maxR = row.Max();
            //for (int i = 0; i < row.Length; i++)
            //{
            //    if (row[i] == maxR)
            //        maxRows.Add(i);
            //}
            var maxCols = new List<int>();
            var maxC = col.Max();
            //for (int i = 0; i < col.Length; i++)
            //{
            //    if (col[i] == maxC)
            //        maxCols.Add(i);
            //}
            long ans = maxR + maxC;

            bool minus = true;
            for (int i = 0; i < maxRows.Count; i++)
            {
                for (int j = 0; j < maxCols.Count; j++)
                {
                    if (map[maxRows[i]][maxCols[j]] == 0)
                    {
                        minus = false;
                        break;
                    }
                }
                if (!minus) break;
            }
            if (minus)
                ans--;

            WriteLine(ans);
        }
    }

    public class IO
    {
        #region Input
        public static int RInt => int.Parse(ReadLine());
        public static long RLong => long.Parse(ReadLine());
        public static double RDouble => double.Parse(ReadLine());

        public static string[] RSString => ReadLine().Split();
        public static int[] RSInt => ReadLine().Split().Select(s => int.Parse(s)).ToArray();
        public static long[] RSLong => ReadLine().Split().Select(s => long.Parse(s)).ToArray();
        public static double[] RSDouble => ReadLine().Split().Select(s => double.Parse(s)).ToArray();
        #endregion

        #region Output
        public static void OutJoinSpace<T>(IEnumerable<T> list) => WriteLine(string.Join(" ", list));
        public static void WriteLineYes_or_No(bool flag) => WriteLine(flag ? "Yes" : "No");
        public static void WriteLineYES_or_NO(bool flag) => WriteLine(flag ? "YES" : "NO");
        #endregion
    }

    public class Mod
    {
        #region
        private readonly static long M = 1000000007;

        public static long Add(long a, long b) => (a * b) % M;
        public static long Sub(long a, long b) => (a - b) % M >= 0 ? (a - b) % M : (a - b) % M + M;
        public static long Multi(long a, long b) => (a * b) % M;
        #endregion
    }
}