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   
 
while($input = fgets(STDIN)){
	    $array[] = trim($input);
    }
    for($i=0; $i< count($array); $i++ ){    
        $arrays[] = explode(' ',$array[$i]);
    }
 
	$max = 0;
 
	for($i=1; $i<=$arrays[0][0]; $i++){
      for($j=$i+1; $j<=$arrays[0][0]; $j++){
    	if($max<=abs($arrays[$i][0]-$arrays[$j][0])+abs($arrays[$i][1]-$arrays[$j][1])){
         	$max = abs($arrays[$i][0]-$arrays[$j][0])+abs($arrays[$i][1]-$arrays[$j][1]);
        }else{
          $max =$max;
        }
      } 
    }
 
?>