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 = [] * N
y = [] * N
for i in range(N):
    a, b = list(map(int, input().split()))
    x.append(a)
    y.append(b)
d = 0
ma = x[0] + y[0]
ima = 0
mi = x[0] + y[0]
imi = 0
for i in range(N):
    if x[i] + y[i] < mi:
        mi = x[i] + y[i]
        imi = i
    if x[i] + y[i] > ma:
        ma = x[i] + y[i]
        ima = i
print (ima, imi)
d = abs(x[ima] - x[imi]) + abs(y[ima] - y[imi])
print(d)