Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in C (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

long int dis(long int a[], long int b[]) {
    long int x = a[0] - b[0], y = a[1] - b[1];
    if (x < 0) x *= -1;
    if (y < 0) y *= -1;
    return x + y;
}

int main (void) {
    int n, i, j;
    scanf("%d", &n);
    long int xy[n][2], max = 0;
    for (i = 0; i < n; i++) {
        scanf("%ld %ld", &xy[i][0], &xy[i][1]);
    }
    for (i = 0; i < n - 1; i++) {
        for (j = i + 1; j < n; j++) {
            if (dis(xy[i], xy[j]) > max)
                max = dis(xy[i], xy[j]);
        }
    }
    printf("%ld\n", max);
    return 0;
}