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)

import heapq
N = int(input())
xy_s = [list(map(int,input().split())) for _ in range(N)]
XPYMAX = []
XPYMIN = []
XMYMAX = []
XMYMIN = []
heapq.heapify(XPYMAX)
heapq.heapify(XPYMIN)
heapq.heapify(XMYMAX)
heapq.heapify(XMYMIN)
answer = 0
for i, xy in enumerate(xy_s):
    x = xy[0]
    y = xy[1]
    heapq.heappush(XPYMAX,-(x+y))
    heapq.heappush(XMYMAX,-(x-y))
    heapq.heappush(XPYMIN,(x+y))
    heapq.heappush(XMYMIN,(x-y))

    if i == 0:
        continue

    xpy = x+y
    xmy = x-y
    xpymax = -XPYMAX[0]
    xpymin = XPYMIN[0]
    xmymax = -XMYMAX[0]
    xmymin = XMYMIN[0]
    dist = max(abs(xpymax-xpy), abs(xpymin-xpy), abs(xmymax-xmy), abs(xmymin-xmy))
    answer = max(dist, answer)
print(answer)