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 Julia (1.4.0) (judge verdict: Accepted)

parseInt(x)=parse(Int, x)
parseMap(x::Array{SubString{String},1})=map(parseInt, x)

function main()
	n = readline() |> parseInt
	a = Tuple{Int,Int}[(0,0) for i in 1:n]
	for i in 1:n
		x,y = readline() |> split |> parseMap
		a[i] = (x,y)
	end
	a = sort(a,by=x->(x[1]+x[2]))
	b = sort(a,by=x->(x[1]-x[2]))
	println(max(abs(a[1][1]-a[n][1])+abs(a[1][2]-a[n][2]), abs(b[1][1]-b[n][1])+abs(b[1][2]-b[n][2])))
end

main()