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)

n = gets.to_i
def manhattan(a, b)
  (a[0] - b[0]).abs + (a[1] - b[1]).abs
end
points = n.times.map do
  x, y = gets.chomp.split(' ').map(&:to_i)
  [x, y]
end
init = points[0]
farest_i = (1...n).max_by do |i|
  manhattan(init, points[i])
end
farest = points[farest_i]
dist = (0...n).map do |i|
  manhattan(farest, points[i])
end
p dist.max