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.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        //int K = sc.nextInt();
        //long N = sc.nextLong();

        long[] x = new long[N];
        long[] y = new long[N];
        for(int i=0; i<N; i++){
            x[i]=sc.nextLong();
            y[i]=sc.nextLong();
            long xx = x[i];
            x[i] = x[i] + y[i];
            y[i] = xx - y[i];
        }

        Arrays.sort(x);
        Arrays.sort(y);

        long res=Math.max(Math.abs(x[N-1]-x[0]),Math.abs(y[N-1]-y[0]));
        

        
        System.out.println(res);
        }
    }