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.Arrays;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// AtCoder_E
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		long d[] = new long[N];
		long dR[] = new long[N];


		for(int i=0; i<N; i++) {
			long x = sc.nextLong();
			long y = sc.nextLong();
			d[i] = x + y;
			dR[i] = 1000000000 - x + y;
		}

		Arrays.sort(d);
		Arrays.sort(dR);

		if(d[N-1]-d[0] > dR[N-1]-dR[0]) {
			System.out.println(d[N-1]-d[0]);
		} else {
			System.out.println(dR[N-1]-dR[0]);
		}

		// Scannerクラスのインスタンスをクローズ
		sc.close();
	}
}
