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)

import sys

n = int(sys.stdin.readline())

item_min = [None, None] # x_min, y_min
item_max = [None, None] # x_max, y_max
coord_min = [None, None] # x_minに相当する座標, y_minに相当する座標
coord_max = [None, None] # x_maxに相当する座標, y_maxに相当する座標
for _ in range(n):
    coord = list(map(int, sys.stdin.readline().split()))
    if item_min[0] is None:
        for i in range(2):
            item_min[i] = coord[i]
            item_max[i] = coord[i]
            coord_min[i] = coord
            coord_max[i] = coord
    else:
        for i in range(2):
            if coord[i] < item_min[i]:
                item_min[i] = coord[i]
                coord_min[i] = coord
            elif coord[i] > item_max[i]:
                item_max[i] = coord[i]
                coord_max[i] = coord

candidate = []
for i in range(2):
    # 最小
    for k in range(2):
        # 最大
        c_min = coord_min[i]
        c_max = coord_max[k]
        candidate.append(abs(c_max[0] - c_min[0]) + abs(c_max[1] - c_min[1]))
print(max(candidate))