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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;

namespace CompetitionPrograming2
{
    public sealed class Program : BaseProgram
    {
        public static void Main(string[] _) { using var c = new SetConsole(); Solve(); }
        public static void Solve()
        {
            //var (h, w) = GetArray<int>();
            //var (ch, cw) = GetArray<int>();
            //var (dh, dw) = GetArray<int>();
            //var sw = new List<int[]>();
            //for (int i = 0; i < h; i++)
            //{
            //    sw.Add(GetArray<int>());
            //}

            var (h, w, m) = GetArray<int>();
            var enabled = new HashSet<(int h, int w)>();

            var hDirection = new Dictionary<int, int>();
            var wDirection = new Dictionary<int, int>();
            for (int i = 0; i < m; i++)
            {
                var (hi, wi) = GetArray<int>();
                enabled.Add((hi, wi));
                if (!hDirection.ContainsKey(hi))
                {
                    hDirection.Add(hi, 1);
                }
                else
                {
                    hDirection[hi]++;
                }
                if (!wDirection.ContainsKey(wi))
                {
                    wDirection.Add(wi, 1);
                }
                else
                {
                    wDirection[wi]++;
                }
            }
            var maxH = 0L;
            var maxHKey = -1;
            foreach (var item in hDirection)
            {
                if (maxH <= item.Value)
                {
                    maxH = Math.Max(maxH, item.Value);
                    maxHKey = item.Key;
                }
            }
            var wMax = wDirection.Max(x => x.Value);
            var maxWDirection = wDirection.Where(x => x.Value == wMax).ToArray();
            var ans = 0L;
            foreach (var key in hDirection.Where(x => x.Value == maxH).Select(x => x.Key))
            {
                foreach (var item in maxWDirection)
                {
                    if (enabled.Contains((key, item.Key)))
                    {
                        ans = Math.Max(ans, maxH + item.Value - 1);
                    }
                    else
                    {
                        ans = Math.Max(ans, maxH + item.Value);
                    }
                }
            }
            Write(ans);
        }
    }
}
public abstract class BaseProgram
{
    protected readonly static long divisor = 1000000007;
    protected static Action<object> Write => Console.WriteLine;
    protected static string GetString()
    {
        var str = Console.ReadLine();
        if (str is null) { throw new NullReferenceException("標準入力がnullです Solveメソッド内の解答コードが間違っています"); }
        return str;
    }
    protected static T GetNumber<T>() where T : IComparable, IComparable<T>, IConvertible, IEquatable<T>, IFormattable
    {
        var str = GetString();
        return Activator.CreateInstance<T>() switch
        {
            int _ => (T)(object)str.ToInt(),
            long _ => (T)(object)str.ToLong(),
            double _ => (T)(object)str.ToDouble(),
            decimal _ => (T)(object)str.ToDecimal(),
            BigInteger _ => (T)(object)str.ToBigInteger(),
            _ => throw new NotSupportedException(),
        };
    }
    protected static T[] GetArray<T>() where T : IComparable, IComparable<T>, IEquatable<T> => ToArray<T>(GetString());
    protected static List<T> GetList<T>() where T : IComparable, IComparable<T>, IEquatable<T> => ToList<T>(GetString());
    protected static void Swap<T>(ref T item1, ref T item2) => (item2, item1) = (item1, item2);
    protected static IEnumerable<char> AtoZ()
    {
        for (char i = 'a'; i <= 'z'; i++)
        {
            yield return i;
        }
    }
    private static T[] ToArray<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
    {
        return ConvertEnumerator<T>(str).ToArray();
    }
    private static List<T> ToList<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
    {
        return ConvertEnumerator<T>(str).ToList();
    }
    private static IEnumerable<T> ConvertEnumerator<T>(string str) where T : IComparable, IComparable<T>, IEquatable<T>
    {
        return Activator.CreateInstance<T>() switch
        {
            byte _ => str.Split().Select(byte.Parse).Cast<T>(),
            int _ => str.Split().Select(int.Parse).Cast<T>(),
            long _ => str.Split().Select(long.Parse).Cast<T>(),
            double _ => str.Split().Select(double.Parse).Cast<T>(),
            decimal _ => str.Split().Select(decimal.Parse).Cast<T>(),
            BigInteger _ => str.Split().Select(BigInteger.Parse).Cast<T>(),
            _ => throw new NotSupportedException()
        };
    }
    protected sealed class SetConsole : IDisposable
    {
        readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
        public SetConsole()
        {
            sw.AutoFlush = false;
            Console.SetOut(sw);
        }
        public void Dispose()
        {
            Console.Out.Flush();
            sw.AutoFlush = true;
            Console.SetOut(sw);
        }
    }
}
public static class ExtentionsLibrary
{
    public static long Choose(this long n, long a, long divisor = 1000000007)
    {
        long numerator = 1, denominator = 1;
        for (int i = 0; i < a; i++)
        {
            numerator *= n - i;
            numerator %= divisor;
            denominator *= i + 1;
            denominator %= divisor;
        }
        return numerator / denominator;
    }
    public static long Choose(this int n, int a, int divisor = 1000000007)
    {
        long numerator = 1, denominator = 1;
        for (int i = 0; i < a; i++)
        {
            numerator *= n - i;
            numerator %= divisor;
            denominator *= i + 1;
            denominator %= divisor;
        }
        return numerator / denominator;
    }
    /// <summary>
    /// 階乗を求める
    /// </summary>
    /// <param name="num"></param>
    /// <returns></returns>
    public static long Factorial(this long num)
    {
        var result = 1L;
        for (int i = 1; i <= num; i++)
        {
            result *= i;
        }
        return result;
    }
    private static T[] NextPermutation<T>(this IEnumerable<T> collection, IComparer<T> cmp) where T : IComparable
    {
        var array = collection.ToArray();
        int? exchangingNumIndex = null;
        for (int i = 1; i < array.Length; i++)
        {
            if (cmp.Compare(array[i - 1], array[i]) >= 0) { continue; }

            exchangingNumIndex = i - 1;
        }

        if (exchangingNumIndex is null) { return null; }

        for (int j = array.Length - 1; j >= 0; j--)
        {
            if (cmp.Compare(array[(int)exchangingNumIndex], array[j]) >= 0) { continue; }

            var tmp = array[j];
            array[j] = array[(int)exchangingNumIndex];
            array[(int)exchangingNumIndex] = tmp;
            array = array.Take((int)exchangingNumIndex + 1).Concat(array.Skip((int)exchangingNumIndex + 1).Reverse()).ToArray();
            break;
        }
        return array;
    }
    public static string[] NextPermutation(this IEnumerable<string> collection)
    {
        return NextPermutation(collection, StringComparer.Ordinal);
    }
    public static T[] NextPermutation<T>(this IEnumerable<T> collection) where T : IComparable
    {
        return NextPermutation(collection, Comparer<T>.Default);
    }
    public static IEnumerable<T[]> Permutations<T>(this IEnumerable<T> collection) where T : IComparable
    {
        var next = collection.NextPermutation();

        while (next != null)
        {
            yield return next;

            next = next.NextPermutation();
        }
    }
    public static long Gcd(this long a, long b)
    {
        if (a < b) { return Gcd(b, a); }
        long tmp;
        do
        {
            tmp = a % b;
            a = b;
            b = tmp;
        } while (tmp != 0);
        return a;
    }
    public static long Lcm(this long a, long b) => a * b / Gcd(a, b);
    /// <summary>
    /// 素因数分解を行う
    /// </summary>
    /// <param name="num"></param>
    /// <returns></returns>
    public static IEnumerable<(long num, int count)> Factorize(this long n)
    {
        yield return (1, 1);
        var rootN = Math.Sqrt(n);
        for (long i = 2; i <= rootN; i++)
        {
            if (n % i != 0) { continue; }

            var count = 1;
            n /= i;
            while (n % i == 0)
            {
                n /= i;
                count++;
            }
            yield return (i, count);
        }
        if (n != 1) { yield return (n, 1); }
    }
    public static int ToInt(this string str) => int.Parse(str);
    public static int ToInt(this char chr) => int.Parse(chr.ToString());
    public static long ToLong(this string str) => long.Parse(str);
    public static double ToDouble(this string str) => double.Parse(str);
    public static decimal ToDecimal(this string str) => decimal.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
    public static string StringJoin<T>(this IEnumerable<T> collection, string separator = "") => string.Join(separator, collection.Select(c => c.ToString()));
    public static string StringConcat(this IEnumerable<char> collection) => string.Concat(collection);
    public static int LowerBound<T>(this IReadOnlyList<T> a, T v) => LowerBound(a, v, Comparer<T>.Default);
    public static int LowerBound(this IReadOnlyList<string> str, string v) => LowerBound(str, v, StringComparer.Ordinal);
    public static int LowerBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
    {
        var l = 0;
        var r = a.Count - 1;
        while (l <= r)
        {
            var mid = l + (r - l) / 2;
            var result = cmp.Compare(a[mid], v);
            if (result == -1)
            {
                l = mid + 1;
            }
            else
            {
                r = mid - 1;
            }
        }
        return l;
    }
    public static int UpperBound(this IReadOnlyList<string> str, string v) => UpperBound(str, v, StringComparer.Ordinal);
    public static int UpperBound<T>(this IReadOnlyList<T> a, T v) => UpperBound(a, v, Comparer<T>.Default);
    public static int UpperBound<T>(this IReadOnlyList<T> a, T v, IComparer<T> cmp)
    {
        var l = 0;
        var r = a.Count - 1;
        while (l <= r)
        {
            var mid = l + (r - l) / 2;
            var res = cmp.Compare(a[mid], v);
            if (res <= 0) l = mid + 1;
            else r = mid - 1;
        }
        return l;
    }
    public static IOrderedEnumerable<TSource> OrderBy<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
    {
        return source.OrderBy(keySelector, StringComparer.Ordinal);
    }
    public static IOrderedEnumerable<TSource> OrderByDescending<TSource>(this IEnumerable<TSource> source, Func<TSource, string> keySelector)
    {
        return source.OrderByDescending(keySelector, StringComparer.Ordinal);
    }
    public static void Deconstruct<T>
    (
        this IList<T> self,
        out T first
    )
    {
        first = self[0];
    }

    public static void Deconstruct<T>
    (
        this IList<T> self,
        out T first,
        out T second
    )
    {
        first = self[0];
        second = self[1];
    }

    public static void Deconstruct<T>
    (
        this IList<T> self,
        out T first,
        out T second,
        out T third
    )
    {
        first = self[0];
        second = self[1];
        third = self[2];
    }

    public static void Deconstruct<T>
    (
        this IList<T> self,
        out T first,
        out T second,
        out T third,
        out T forth
    )
    {
        first = self[0];
        second = self[1];
        third = self[2];
        forth = self[3];
    }
    public static void Deconstruct<T>
    (
        this IList<T> self,
        out T first,
        out T second,
        out T third,
        out T forth,
        out T fifth
    )
    {
        first = self[0];
        second = self[1];
        third = self[2];
        forth = self[3];
        fifth = self[4];
    }
}

public struct Mint
{
    private static readonly long MOD = (long)1e9 + 7;

    /// <summary>
    /// 0以上MOD未満の整数
    /// </summary>
    public long Value;

    public Mint(long val)
    {
        Value = val % MOD;
        if (Value < 0) Value += MOD;
    }

    private static Mint Ctor(long val) => new Mint() { Value = val };
    public static Mint operator +(Mint a, Mint b)
    {
        long res = a.Value + b.Value;
        if (res > MOD) res -= MOD;
        return Ctor(res);
    }
    public static Mint operator -(Mint a, Mint b)
    {
        long res = a.Value - b.Value;
        if (res < 0) res += MOD;
        return Ctor(res);
    }
    public static Mint operator *(Mint a, Mint b)
    {
        long res = a.Value * b.Value;
        if (res > MOD) res %= MOD;
        return Ctor(res);
    }
    public static Mint operator /(Mint a, Mint b) => a * Inv(b);
    public static Mint Pow(Mint a, long n)
    {
        if (n == 0) return new Mint(1);
        Mint b = Pow(a, n >> 1);
        b *= b;
        if ((n & 1) == 1) b *= a;
        return b;
    }
    public static Mint Inv(Mint n)
    {
        long a = n.Value;
        long b = MOD;

        long x = 1;
        long u = 0;
        while (b != 0)
        {
            long k = a / b;
            long _x = u;
            u = x - k * u;
            x = _x;

            long _a = a;
            a = b;
            b = _a - (k * b);
        }

        return new Mint(x);
    }
    public override string ToString() => Value.ToString();
    public static implicit operator Mint(long a) => new Mint(a);
    public static explicit operator long(Mint a) => a.Value;
    public static Mint Choose(long n, long k)
    {
        Mint numerator = 1, denominator = 1;
        for (int i = 0; i < k; i++)
        {
            numerator *= n - i;
            denominator *= i + 1;
        }
        return numerator / denominator;
    }
}
public enum Priority : byte
{
    Smaller = 0,
    Larger = 1
}