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.

Examples

Input

3
1 1
2 4
3 2

Output

4

Input

2
1 1
1 1

Output

0

见题面

见题面