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: Accepted)

def func(x, y):
    res, n = 0, len(x)
    for p, q in [[1, 1], [1, -1], [-1, 1], [-1, -1]]:
        smallest = p * x[0] + q * y[0] + 0
        for i in range(n):
            cur = p * x[i] + q * y[i]
            res = max(res, cur - smallest)
            smallest = min(smallest, cur)
    return res

n = int(input())
x,y = [],[]
for i in range(n):
    a,b = list(map(int,input().split()))
    x.append(a)
    y.append(b)
print(func(x,y))