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 Ruby (2.7.1) (judge verdict: Wrong Answer)

#!/usr/bin/env ruby

N = gets.chomp.to_i

X = []
Y = []

minx = 2 * 10 ** 6
miny = 2 * 10 ** 6
maxx = -2 * 10 ** 6
maxy = -2 * 10 ** 6

def min(x, y)
  x > y ? y : x
end

def max(x, y)
  x < y ? y : x
end

N.times do |i|
  x, y = gets.chomp.split.map(&:to_i)
  x0 = (x - y)
  y0 = (x + y)

  minx = min(x0, minx)
  miny = min(y0, miny)

  maxx = max(x0, maxx)
  maxy = max(y0, maxy)
end

puts [(maxx - minx).abs, (maxy - miny).abs].max