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: Time Limit Exceeded)

def manhattan(cor_1, cor_2)
  x = cor_1[0] - cor_2[0]
  y = cor_1[1] - cor_2[1]
  x *= -1 if x < 0
  y *= -1 if y < 0
  x + y
end


N = gets.to_i

coordinates = []



N.times do
  coordinates << gets.split(' ').map(&:to_i)
end

ans = 0
(0..N-2).each do |i|
  (i+1..N-1).each do |j|
    manhattan_distance = manhattan(coordinates[i],coordinates[j])
    ans = manhattan_distance if manhattan_distance > ans
  end
end

puts ans