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Contest: Task: Related: TaskD TaskF

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

Sample Output 1

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