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())
x = [0] * N
y = [0] * N
for i in range(N):
    x[i], y[i] = map(int, input().split())
    
def manhattan(x1, y1, x2, y2):
    return abs(x1 - x2) + abs(y1 - y2)

x1 = x[0]
y1 = y[0]
x2 = x[1]
y2 = y[1]
ans = manhattan(x1, y1, x2, y2)

for i in range(2, N):
    x3 = x[i]
    y3 = y[i]
    if manhattan(x1, y1, x3, y3) >= ans or manhattan(x2, y2, x3, y3) >= ans:
        if manhattan(x1, y1, x3, y3) >= manhattan(x2, y2, x3, y3):
            ans = manhattan(x1, y1, x3, y3)
            x2, y2 = x3, y3
        else:
            ans = manhattan(x2, y2, x3, y3)
            x1, y1 = x3, y3
    else:
        continue

print(ans)