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: Wrong Answer)

import sys
input = sys.stdin.readline


def main():
    n = int(input())
    points = []
    for _ in range(n):
        x, y = map(int, input().split())
        points.append((2*x, 2*y))

    points.sort(key=lambda p: p[0] + (p[1]-p[0])//2)
    x1, y1 = points[0]
    x2, y2 = points[-1]
    print((abs(x2-x1) + abs(y2-y1))//2)


if __name__ == "__main__":
    main()