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 Kotlin (1.3.71) (judge verdict: Accepted)

// solution is at the bottom

import kotlin.math.*

@JvmField val INPUT = System.`in`
@JvmField val OUTPUT = System.out

const val _BUFFER_SIZE = 1 shl 16
@JvmField val _buffer = ByteArray(_BUFFER_SIZE)
@JvmField var _bufferPt = 0
@JvmField var _bytesRead = 0

tailrec fun readChar(): Char {
    if(_bufferPt == _bytesRead) {
        _bufferPt = 0
        _bytesRead = INPUT.read(_buffer, 0, _BUFFER_SIZE)
    }
    return if(_bytesRead < 0) Char.MIN_VALUE
    else {
        val c = _buffer[_bufferPt++].toChar()
        if (c == '\r') readChar()
        else c
    }
}

fun readLine(): String? {
    var c = readChar()
    return if(c == Char.MIN_VALUE) null
    else buildString {
        while(true) {
            when(c) {
                '\n', Char.MIN_VALUE -> return@buildString
                else -> {
                    append(c)
                    c = readChar()
                }
            }
        }
    }
}
fun readLn() = readLine()!!

fun read() = buildString {
    var c = readChar()
    while(c <= ' ') {
        if(c == Char.MIN_VALUE) return@buildString
        c = readChar()
    }
    do {
        append(c)
        c = readChar()
    } while(c > ' ')
}
fun readInt() = read().toInt()
fun readDouble() = read().toDouble()
fun readLong() = read().toLong()
fun readStrings(n: Int) = List(n) { read() }
fun readLines(n: Int) = List(n) { readLn() }
fun readInts(n: Int) = List(n) { read().toInt() }
fun readIntArray(n: Int) = IntArray(n) { read().toInt() }
fun readDoubles(n: Int) = List(n) { read().toDouble() }
fun readDoubleArray(n: Int) = DoubleArray(n) { read().toDouble() }
fun readLongs(n: Int) = List(n) { read().toLong() }
fun readLongArray(n: Int) = LongArray(n) { read().toLong() }


fun main() {
    val (n, m, k) = readIntArray(3)
    val colCount = IntArray(m) {0}
    val rowCount = IntArray(n) {0}

    val points = mutableSetOf<Pair<Int, Int>>()
    for (kk in 1..k) {
        var (row, col) = readIntArray(2)
        row--
        col--

        colCount[col]++
        rowCount[row]++

        points.add(Pair(row, col))
    }

//    println(colCount.joinToString(" "))
//    println(rowCount.joinToString(" "))

    val colMax = colCount.max()!!
    val col = colCount.indexOf(colMax)

    var result = 0

    for (row in 0 until n) {
        var ths = colCount[col] + rowCount[row]
        if (Pair(row, col) in points) {
            ths--
        }

        result = max(result, ths)
    }

    val rowMax = rowCount.max()!!
    val row = rowCount.indexOf(rowMax)

    for (col in 0 until m) {
        var ths = colCount[col] + rowCount[row]
        if (Pair(row, col) in points) {
            ths--
        }

        result = max(result, ths)
    }

    println(result)
}