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)

dots = []
gets.to_i.times do
  dots << gets.split.map{|i| i.to_i-1}
end
x_max,y_max = 0,0
x_min,y_min = Float::INFINITY,Float::INFINITY
dots.each do |x,y|
  x_max = [x_max,x].max
  x_min = [x_min,x].min
  y_max = [y_max,y].max
  y_min = [y_min,y].min
end
puts (x_max - x_min) + (y_max - y_min)