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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n=int(input())
l=list()
for i in range(n):
  x,y=map(int,input().split())
  l.append((x,y))

minx = sorted(l, key=lambda x: x[0])
maxx = sorted(l, key=lambda x: x[0], reverse=True)
miny = sorted(l, key=lambda x: x[1])
maxy = sorted(l, key=lambda x: x[1], reverse=True)

ans=0
c=0
for imaxx in maxx:
  for iminx in minx:
    dist=(abs(imaxx[0]-iminx[0]) + abs(imaxx[1] - iminx[1]))
    ans=max(ans, dist)
    c+=1
    if c==1000:
      c=0
      break

  else:
    continue
  break

for imaxx in maxx:
  for iminy in miny:
    dist=(abs(imaxx[0]-iminy[0]) + abs(imaxx[1] - iminy[1]))
    ans=max(ans, dist)
    c+=1
    if c==1000:
      c=0
      break

  else:
    continue
  break

for imaxy in maxy:
  for iminy in miny:
    dist=(abs(imaxy[0]-iminy[0]) + abs(imaxy[1] - iminy[1]))
    ans=max(ans, dist)
    c+=1
    if c==1000:
      c=0
      break

  else:
    continue
  break


for imaxy in maxy:
  for iminx in minx:
    dist=(abs(imaxy[0]-iminx[0]) + abs(imaxy[1] - iminx[1]))
    ans=max(ans, dist)
    c+=1
    if c==1000:
      c=0
      break

  else:
    continue
  break

print(ans)