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.*;
import java.io.*;

public class Main {
    Scanner sc = new Scanner(System.in);
    public static void main(String[] args) throws Exception{
        new Main().run();
    }
    void run() throws IOException {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());

        int[][] arr = new int[n][2];
        for (int i=0; i<n; i++) {
            String[] s = br.readLine().split(" ");
            arr[i][0] = Integer.parseInt(s[0]);
            arr[i][1] = Integer.parseInt(s[1]);
        }

        int[] z = new int[n];
        for (int i=0; i<n; i++) z[i] = arr[i][0] + arr[i][1];
        int[] w = new int[n];
        for (int i=0; i<n; i++) w[i] = arr[i][0] - arr[i][1];

        Arrays.sort(z);
        Arrays.sort(w);

        System.out.print(Math.max(z[n-1]-z[0], w[n-1]-w[0]));
    }
}

