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: Wrong Answer)

n = int(input())
s = []
for i in range(n):
    x = list(map(int, input().split()))
    s.append(x)
t = sorted(s)
u = sorted(s, key=lambda x: x[1])
res = 0

for X in [t[0], u[0], t[-1], u[-1], t[n // 2], u[n // 2], t[-1 + n // 2], u[-1 + n // 2]]:
    for Y in [t[0], u[0], t[-1], u[-1], t[n // 2], u[n // 2], t[-1 + n // 2], u[-1 + n // 2]]:
        tmp = abs(X[0] - Y[0]) + abs(X[1] - Y[1])
        res = max(res, tmp)
print(res)