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.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(buffer.readLine());
        long minval = Integer.MAX_VALUE, maxVal = Integer.MIN_VALUE;
        long minVal2 = minval, maxVal2 = maxVal;
        for (int pos = 0; pos < n; pos++) {
            String [] inp = buffer.readLine().split(" ");
            long a = Integer.parseInt(inp[0]), b = Integer.parseInt(inp[1]);
            long res = a+b, res2 = a-b;
            minval = Math.min(minval, res);
            maxVal = Math.max(maxVal, res);
            minVal2 = Math.min(minVal2, res2);
            maxVal2 = Math.max(maxVal2, res2);
        }
        long res = Math.max(maxVal-minval, maxVal2-minVal2);
        System.out.println(res);
    }
}
