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)

n = int(input())
# 各点のy=xへの写像を考える
x = []
y = []
t = []
for i in range(n):
    xi, yi = map(int, input().split())
    x.append(xi)
    y.append(yi)
    t.append([xi+yi, i])
t.sort(key=lambda x:x[0])
print(t)
min_idx = t[0][1]
max_idx = t[-1][1]
ans = abs(x[max_idx]-x[min_idx]) + abs(y[max_idx]-y[min_idx])
print(ans)