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)

from sys import stdin

N = int(stdin.readline().strip())
maxv = (0,0)
mixv = (float("inf"),0)
mayv = (0,0)
miyv = (0,float("inf"))
for _ in range(N):
    x,y = map(int,stdin.readline().strip().split())
    if x < mixv[0]:
        mixv = (x,y)
    elif x > maxv[0]:
        maxv = (x,y)
    if y < miyv[1]:
        miyv = (x,y)
    elif y > mayv[1]:
        mayv = (x,y)
results = [maxv,mixv,mayv,miyv]
g_max = 0
for i in range(4):
    for j in range(i+1,4):
        x_diff = abs(results[i][0] - results[j][0])
        y_diff = abs(results[i][1]-results[j][1])
        g_max = max(g_max,x_diff+y_diff)
print(g_max)