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 numpy as np

N = int(input())
xy = []
x  = []
y  = []

for i in range(N):
  xy.append(list(map(int, input().split())))
  x.append(xy[i][0])
  y.append(xy[i][1])

x = np.array(x)
y = np.array(y)

ans = 0

for i in range(N-1):
  x_temp = np.abs((x[i] - x[i+1:]))
  y_temp = np.abs((y[i] - y[i+1:]))
  xy_temp = x_temp + y_temp
  temp = np.max(xy_temp)
  if temp > ans:
    ans = temp
  
print(ans)