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: Accepted)


import scala.io.StdIn

object Main extends App {
  val n = StdIn.readInt()
  val points :Seq[(Int,Int)] = for(i <- 1 to n) yield {
    val Array(a,b,_*) = StdIn.readLine().split(' ').map(_.toInt)
    (a,b)
  }
  val sin45 = math.sin(Math.PI/4)
  val cos45 = math.cos(Math.PI/4)
  def rotate(point:(Int,Int)):(Double,Double)={
    val (x,y) = point
    (x*cos45-y*sin45,x*sin45+y*cos45)
  }

  def dist(point1:(Int,Int),point2:(Int,Int)):Int={
    val (x1,y1) = point1
    val (x2,y2) = point2
    math.abs(x1-x2) + math.abs(y1-y2)
  }
  val pointRot = points.map(rotate)

  val maxX = pointRot.map(_._1).zipWithIndex.maxBy(_._1)._2
  val minX = pointRot.map(_._1).zipWithIndex.minBy(_._1)._2
  val maxY = pointRot.map(_._2).zipWithIndex.maxBy(_._1)._2
  val minY = pointRot.map(_._2).zipWithIndex.minBy(_._1)._2
  val ans = math.max(dist(points(maxX),points(minX)),dist(points(maxY),points(minY)))
  println(ans)
}