E - Dist Max

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.

3
1 1
2 4
3 2

4

The Manhattan distance between the first point and the second point is $|1-2|+|1-4|=4$, which is maximum possible.

2
1 1
1 1

0