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())
XY = [list(map(int, input().split())) for _ in range(N)]

min_diff = 10**9
max_diff = 0
min_sum = 2 * 10**9
max_sum = 2

for x,y in XY:
    min_diff = min(x-y, min_diff)
    max_diff = max(x-y, max_diff)
    min_sum = min(x+y, min_sum)
    max_sum = max(x+y, max_sum)

print(max(max_sum-min_sum, max_diff-min_diff))