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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
x = [0]*n
y = [0]*n

xdict = {}
ydict = {}
for i in range(n):
    x,y = map(int,input().split())
    if x in xdict:
        xdict[x].add(y)
    else:
        xdict[x] = {y}
    if y in ydict:
        ydict[y].add(x)
    else:
        ydict[y] = {x}

xmin = min(xdict)
ymin = min(ydict)

xmin_ymin = min(xdict[xmin])
ymin_xmin = min(ydict[ymin])

xmax = max(xdict)
ymax = max(ydict)

xmax_ymax = max(xdict[xmax])
ymax_xmax = max(ydict[ymax])

ans = 0
ans = max(xmax - xmin + xmax_ymax - xmin_ymin,ans)
ans = max(ymax - xmin + ymax_xmax - xmin_ymin,ans)
ans = max(xmax - ymin + xmax_ymax - ymin_xmin,ans)
ans = max(ymax - ymin + ymax_xmax - ymin_xmin,ans)
print(ans)