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: Time Limit Exceeded)

import itertools

N = int(input())
dis_max = 0

XY = []
for i in range(N):
  xy = list(map(int,input().split()))
  XY.append(xy)

l = [i for i in range(1,N+1)]
c = itertools.combinations(l, 2)

for v in itertools.combinations(l, 2):
  distance = abs(XY[v[0]-1][0]-XY[v[1]-1][0])+abs(XY[v[0]-1][1]-XY[v[1]-1][1])
  if distance > dis_max:
    dis_max = distance
print(dis_max)