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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

N = int(input())
x, y = map(int, input().split())
A = B = C = D = [x, y]
for _ in range(N - 1):
    x, y = map(int, input().split())
    if x <= A[0] and y <= A[1]:
        A = [x, y]
    elif x <= B[0] and y >= B[1]:
        B = [x, y]
    elif x >= C[0] and y >= C[1]:
        C = [x, y]
    elif x >= D[0] and y <= D[1]:
        D = [x, y]
L1 = abs(A[0] - B[0]) + abs(A[1] - B[1])
L2 = abs(A[0] - C[0]) + abs(A[1] - C[1])
L3 = abs(A[0] - D[0]) + abs(A[1] - D[1])
L4 = abs(B[0] - C[0]) + abs(B[1] - C[1])
L5 = abs(B[0] - D[0]) + abs(B[1] - D[1])
L6 = abs(C[0] - D[0]) + abs(C[1] - D[1])
L = max([L1, L2, L3, L4, L5, L6])
print(L)