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.util.*;

class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();
        int n=Integer.parseInt(bu.readLine());
        int a[][]=new int[n][2],i;
        for(i=0;i<n;i++)
        {
            String s[]=bu.readLine().split(" ");
            a[i][0]=Integer.parseInt(s[0]);
            a[i][1]=Integer.parseInt(s[1]);
        }

        long max=Long.MIN_VALUE; int pp[]={1,-1},qq[]={1,-1};
        for(int p:pp)
        for(int q:qq)
        {
            long sm=p*a[0][0]+q*a[0][1];
            for(i=1;i<n;i++)
            {
                long cur=p*a[i][0]+q*a[i][1];
                max=Math.max(max,cur-sm);
                sm=Math.min(sm,cur);
            }
        }
        System.out.print(max);
    }
}
