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: Accepted)

N = int(input())

M = 10**9

x,y = map(int, input().split())
r = (x,y)
l = (x,y)
u = (x,y)
d = (x,y)

for i in range(N-1):
    x,y = map(int, input().split())
    if abs(x-0)+abs(y-0)<abs(l[0]-0)+abs(l[1]-0):
        l = (x,y)
    if abs(x-M)+abs(y-0)<abs(r[0]-M)+abs(r[1]-0):
        r = (x,y)
    if abs(x-0)+abs(y-M)<abs(u[0]-0)+abs(u[1]-M):
        u = (x,y)
    if abs(x-M)+abs(y-M)<abs(d[0]-M)+abs(d[1]-M):
        d = (x,y)

print(max(
    abs(l[0]-r[0])+abs(l[1]-r[1]),
    abs(l[0]-u[0])+abs(l[1]-u[1]),
    abs(l[0]-d[0])+abs(l[1]-d[1]),
    abs(r[0]-u[0])+abs(r[1]-u[1]),
    abs(r[0]-d[0])+abs(r[1]-d[1]),
    abs(u[0]-d[0])+abs(u[1]-d[1]),
))