Problem:
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

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

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php 

$n = fgets(STDIN);
$l[0] = explode(" ", trim(fgets(STDIN)) );
$l[1] = explode(" ", trim(fgets(STDIN)) );

$a = $l[0];
$b = $l[1];
$d = abs($a[0] - $b[0]) + abs($a[1] - $b[1]);

for($i=2; $i<$n; $i++){
    $l = explode(" ", trim(fgets(STDIN)) );  
    $d1 = abs($a[0] - $l[0]) + abs($a[1] - $l[1]);
    $d2 = abs($l[0] - $b[0]) + abs($l[1] - $b[1]);

    if($d1 > $d){
        $d = $d1;
    }
    if($d2 > $d){
        $d = $d2;
    }
}

print $d;