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)

def dist(v1, v2):
    return abs(v1[0]-v2[0]) + abs(v1[1]-v2[1])

def main():
    N = int(input())
    o = (1, 1)
    v = []
    min_dist = 1000000
    min_dist_index = 0
    for i in range(N):
        vx, vy = map(int, input().split())
        v.append((vx, vy))
        if min_dist > dist(o, (vx, vy)):
            min_dist = dist(o, (vx, vy))
            min_dist_index = i

    m = v[min_dist_index]

    max_dist = 0
    for vi in v:
        if max_dist < dist(m, vi):
            max_dist = dist(m, vi)

    print(max_dist)

if __name__ == "__main__":
    main()