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 Scala (2.13.1) (judge verdict: Runtime Error)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(datH,datW,datM) = readLine.split(" ").map(_.toInt)
    val datS = for (i <- 1 to datM) yield {
      val Array(datY,datX) = readLine.split(" ").map(_.toInt)
      (datY - 1, datX - 1)
    }

    // initialize
    var aryH = new Array[Int](datH)
    // for (i <- 0 until aryH.length) aryH(i) = 0 // default 0
    var aryW = new Array[Int](datW)
    // for (i <- 0 until aryW.length) aryW(i) = 0 // default 0

    // counting
    datS.map{a => aryH(a._1) += 1; aryW(a._2) += 1}
    val maxH = aryH.max
    val maxW = aryW.max

    // [[crossing check]]
    // get candidate row/col idx
    val candH = aryH.zipWithIndex.filter(a => a._1 == maxH).map(a => a._2)
    val candW = aryW.zipWithIndex.filter(a => a._1 == maxW).map(a => a._2)

    // init matrix
    var aryM = Array.ofDim[Int](datH, datW)
    // for(i <- 0 until datH; j <- 0 until datW) aryM(i)(j) = 0 //default 0
    // make matrix
    datS.map{a => aryM(a._1)(a._2) = 1}

    // cross check
    val valCross = candH.map{y =>
      candW.map{x =>
        aryM(y)(x)
      }
    }.flatten.min

    val ans = maxH + maxW - valCross
    println(ans)
  }
}