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
X = Array.new N 
Y = Array.new N
dmax = 0
dmin = (10**9) * 2
N.times do |i|
    X[i], Y[i] = gets.split.map(&:to_i)
    d = X[i] + Y[i]
    if d > dmax
        dmax = d
    end
    if d < dmin 
        dmin = d
    end
end

puts dmax - dmin