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)

n = int(input())
xlis = [0]
ylis = [0]
for _ in range(n):
    x, y = map(int, input().split())
    xlis.append(x)
    ylis.append(y)

if (xlis[2]-xlis[1]) + (ylis[2]-ylis[1]) >= 0:
    defa1 = 1
    defa2 = 2
elif (xlis[2]-xlis[1]) + (ylis[2]-ylis[1]) <= 0:
    defa1 = 2
    defa2 = 1

for i in range(3, n):
    new1 = i
    defa1p = (xlis[defa1], ylis[defa1])
    defa2p = (xlis[defa2], ylis[defa2])
    new1p = (xlis[new1], ylis[new1])

    if (new1p[0]-defa2p[0])+(new1p[1]-defa2p[1]) >= 0:
        defa2 = new1
    elif (new1p[0]-defa2p[0])+(new1p[1]-defa2p[1]) <= 0 <= (new1p[0]-defa1p[0])+(new1p[1]-defa1p[1]):
        pass
    elif (new1p[0]-defa1p[0])+(new1p[1]-defa1p[1]) <= 0:
        defa1 = new1


print((xlis[defa2]-xlis[defa1]) + (ylis[defa2]-ylis[defa1]))