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