Problem Statement

Given are N distinct points in $a two-dimensional plane. Point i (1 \leq i \leq N)$ has the coordinates (x_i,y_i).
Let us define the distance between two points i and j be $\mathrm{min} (|x_i-x_j|,|y_i-y_j|)$: the smaller of the difference in the x-coordinates and the difference in the y-coordinates.
Find the maximum distance between two different points.

Input

Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
$\vdots$
x_N y_N

Output

Print the maximum distance between two different points.

Constraints

• $2 \leq N \leq 200000$
• $0 \leq x_i,y_i \leq 10^9$
• $(x_i,y_i) \neq (x_j,y_j) (i \neq j)$
• All values in input are integers.

Sample Input 1

3
0 3
3 1
4 10

Sample Output 1

4

The distances between Points 1 and 2, between Points 1 and 3, and between Points 2 and 3 are 2, 4, and 1, respectively, so your output should be 4.

Sample Input 2

4
0 1
0 4
0 10
0 6

Sample Output 2

0

Sample Input 3

8
897 729
802 969
765 184
992 887
1 104
521 641
220 909
380 378

Sample Output 3

801

见题面 Input 部分

见题面 Output 部分