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)

def main():
	N = int(input())
	p = []
	for i in range(N):
		x, y = [int(a) for a in input().split(" ")]
		p.append({"x" : x, "y" : y})
	aveX = 0
	aveY = 0
	for i in range(N):
		aveX += p[i]["x"]
		aveY += p[i]["y"]
	aveX /= N
	aveY /= N
	for i in range(N):
		p[i]["d"] = abs(aveX - p[i]["x"]) + abs(aveY - p[i]["y"])
	p.sort(key=lambda z: z["d"])
	D = []
	P = [p[-1]]
	k = 1
	while k < min([len(P), 7]) and abs(p[-k-1]["d"] - P[0]["d"]) < 1:
		P.append(p[-k-1])
		k += 1
	for i in range(N - 1):
		for j in range(len(P)):
			D.append(abs(P[j]["x"] - p[i]["x"]) + abs(P[j]["y"] - p[i]["y"]))
	print(max(D))

main()