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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[] x = new int[n];
		int[] y = new int[n];
		for (int i = 0; i < n; i++) {
			String[] sa = br.readLine().split(" ");
			int a = Integer.parseInt(sa[0]);
			int b = Integer.parseInt(sa[1]);
			x[i] = a + b;
			y[i] = a - b;
		}
		br.close();

		Arrays.sort(x);
		Arrays.sort(y);
		System.out.println(Math.max(x[n - 1] - x[0], y[n - 1] - y[0]));
	}
}
