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)

nums = []
for i in range(0, int(input())):
  nums.append(input())

max_num = 0
curr = 0
for start in nums:
  x1 = int(start.split(" ")[0])
  y1 = int(start.split(" ")[1])
  for end in nums:
    x2 = int(end.split(" ")[0])
    y2 = int(end.split(" ")[1])
    curr = abs(x1 - x2) + abs(y1 - y2)
    if curr > max_num:
      max_num = curr
      
print(max_num)