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)

def Manhattan(ans):
    return abs(ans[0][0]-ans[1][0])+abs(ans[0][1]-ans[1][1])
N=int(input())
xy=[]
for i in range(N):
    xy.append(list(map(int,input().split())))
nowans=[[xy[0][0],xy[0][1]],[xy[1][0],xy[1][1]]]
nowManhattan=Manhattan(nowans)
for i in range(1,N-1):
    nowxy=xy[i]
    if (Manhattan([nowxy,nowans[1]])>nowManhattan):
        nowans=[nowxy,nowans[1]]
        nowManhattan=Manhattan(nowans)
    elif (Manhattan([nowans[0],nowxy])>nowManhattan):
        nowans=[nowans[0],nowxy]
        nowManhattan=Manhattan(nowans)
    if (Manhattan([nowans[0],nowxy])>nowManhattan):
        nowans=[nowans[0],nowxy]
        nowManhattan=Manhattan(nowans)
print(nowManhattan)