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 Python (3.8.2) (judge verdict: Wrong Answer)

N = int(input())
hw = [[int(i) for i in input().split()] for _ in range(N)]

minD = 2 * 10**9
min = 0
maxD = 0
max = 0

for i in range(N):
    if (minD > (hw[i][0]*hw[i][0] + hw[i][1]*hw[i][1])):
        minD = hw[i][0]*hw[i][0] + hw[i][1]*hw[i][1]
        min = i
    if (maxD < hw[i][0]*hw[i][0] + hw[i][1]*hw[i][1]):
        maxD = hw[i][0]*hw[i][0] + hw[i][1]*hw[i][1]
        max = i

print(abs(hw[max][0] - hw[min][0]) + abs(hw[max][1] - hw[min][1]))