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: Accepted)

n = int(input())
inf = float('inf')

M1, M2 = -inf, -inf
m1, m2 = inf, inf

for i in range(n):
  x, y = map(int, input().split())
  d1 = x+y
  d2 = x-y
  M1 = max(M1, d1)
  m1 = min(m1, d1)
  M2 = max(M2, d2)
  m2 = min(m2, d2)

D1 = M1-m1
D2 = M2-m2

print(max(D1, D2))