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: Time Limit Exceeded)

N = int(input())

def m_dis(x1, y1, x2, y2):
	return abs(x2 - x1) + abs(y2 - y1)

table_p = {}
table_m = {}

points = []
for _ in range(N):
	x, y = map(int, input().split())
	points.append((x, y))
	a = x + y
	b = x - y
	if a in table_p:
		table_p[a].append((x, y))
	else:
		table_p[a] = [(x, y)]
	if b in table_m:
		table_m[b].append((x, y))
	else:
		table_m[b] = [(x, y)]

list_p = []
list_m = []
for a, ps in table_p.items():
	list_p.append((a, ps[0]))

for b, ps in table_m.items():
	list_m.append((b, ps[0]))

list_p.sort()
list_m.sort()

topvalue = 0

for x, y in points:
	topvalue = max(topvalue, 
		m_dis(x, y, list_p[0][1][0], list_p[0][1][1]),
		m_dis(x, y, list_p[-1][1][0], list_p[-1][1][1]),
		m_dis(x, y, list_m[0][1][0], list_m[0][1][1]),
		m_dis(x, y, list_m[-1][1][0], list_m[-1][1][1]))

print(topvalue)