Problem:
Score : 500 points

Problem Statement

There are N points on the 2D plane, i-th of which is located on (x_i, y_i).
There can be multiple points that share the same coordinate.
What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq x_i,y_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the answer.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in Scala (2.13.1) (judge verdict: Time Limit Exceeded)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(datN) = readLine.split(" ").map(_.toInt)
    val datA = for(i <- 1 to datN.toInt) yield {val Array(a,b) = readLine.split(" ").map(_.toInt); (a,b)}
//    val ans = datA.map{ a =>
//      datA.map{ b => math.abs(a._1 - b._1) + math.abs(a._2 - b._2) }
//    }.flatten.max
    val ans = for (i <- 0 until datA.length; j <- i until datA.length) yield {
      math.abs(datA(i)._1 - datA(j)._1) + math.abs(datA(i)._2 - datA(j)._2)
    }
    println(ans.max)
  }
}