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 xPlusYMax = Integer.MIN_VALUE;
    int xPlusYMin = Integer.MAX_VALUE;
    int xMinusYMax = Integer.MIN_VALUE;
    int xMinusYMin = Integer.MAX_VALUE;
    for (int i = 0; i < N; i++) {
      int x = sc.nextInt();
      int y = sc.nextInt();
      xPlusYMax = Math.max(xPlusYMax, x + y);
      xPlusYMin = Math.min(xPlusYMin, x + y);
      xMinusYMax = Math.max(xMinusYMax, x - y);
      xMinusYMin = Math.min(xMinusYMin, x - y);
    }
    int ans = Math.max(xPlusYMax - xPlusYMin, xMinusYMax - xMinusYMin);
    System.out.println(ans);
  }
}
