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
//Created by Aminul on 9/13/2020.

import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        final long inf = (long) 1e15;
        int n = in.nextInt();
        long pp = -inf, pm = -inf, mp = -inf, mm = -inf, res = -inf;
        for (int i = 0; i < n; i++) {
            int x = in.nextInt(), y = in.nextInt();
            res = max(res, x + y + mm);
            res = max(res, x - y + mp);
            res = max(res, -x + y + pm);
            res = max(res, -x - y + pp);

            pp = max(pp, x + y);
            pm = max(pm, x - y);
            mp = max(mp, -x + y);
            mm = max(mm, -x - y);
        }

        pw.println(res);
        pw.close();
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}