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: Accepted)

<?php
list($n) = ints();
$base = [
    [0, 0],
    [0, 10 ** 9],
    [10 ** 9, 0],
    [10 ** 9, 10 ** 9]
];
$mins = array_fill(0, 4, PHP_INT_MAX);
$maxs = array_fill(0, 4, 0);
for ($i = 0; $i < $n; ++$i) {
    list($x, $y) = ints();
    for ($j = 0; $j < 4; ++$j) {
        $d = abs($base[$j][0] - $x) + abs($base[$j][1] - $y);
        if ($d < $mins[$j]) $mins[$j] = $d;
        if ($d > $maxs[$j]) $maxs[$j] = $d;
    }
}
$max = 0;
for ($i = 0; $i < 4; ++$i) {
    if ($maxs[$i] - $mins[$i] > $max) $max = $maxs[$i] - $mins[$i];
}
echo $max;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}