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)

n = int(input())
a = []
b = []
for i in range(n):
    x, y = [int(i) for i in input().split()]
    a.append(x)
    b.append(y)
ans = 0
for s, t in [(-1, -1), (-1, 1), (1, -1), (1, 1)]:
    cur_min = float('inf')
    cur_max = float('-inf')
    for i in range(n):
        tmp = s*a[i] + t*b[i]
        cur_min = min(cur_min, tmp)
        cur_max = max(cur_max, tmp)
    ans = max(ans, cur_max - cur_min)
print(ans)