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
import java.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;

public class Main
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n=in.nextInt();
        long[] x=new long[n];
        long[] y=new long[n];
        TreeSet<Long> set1=new TreeSet<>();
        TreeSet<Long> set2=new TreeSet<>();
        for(int i=0;i<n;i++)
        {
            x[i]=in.nextLong();
            y[i]=in.nextLong();
            set1.add(x[i]+y[i]);
            set2.add(x[i]-y[i]);
        }
        System.out.println(Math.max(set1.last()-set1.first(), set2.last()-set2.first()));
        

    }
}