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)

import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())

upper = []
lower = []
for _ in range(N):
    x, y = mapint()
    if x<=y:
        upper.append((x, y))
    else:
        lower.append((x, y))
upper.sort(key=lambda x:x[0]+x[1])
lower.sort(key=lambda x:x[0]+x[1])

if len(upper):
    upper_max = abs(upper[0][0]-upper[-1][0]) + abs(upper[0][1]-upper[-1][1])
else:
    upper_max = 0

if len(lower):
    lower_max = abs(lower[0][0]-lower[-1][0]) + abs(lower[0][1]-lower[-1][1])
else:
    lower_max = 0

if len(upper) and len(lower):
    upper.sort(key=lambda x:abs(x[0]-x[1]), reverse=True)
    lower.sort(key=lambda x:abs(x[0]-x[1]), reverse=True)
    upper_lower = abs(upper[0][0]-lower[0][0]) + abs(upper[0][1]-lower[0][1])
else:
    upper_lower = 0

print(max(upper_max, lower_max, upper_lower))