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())

P = []

for _ in range(N):
    x, y = [int(n) for n in input().split(" ")]
    P.append([x, y])


def getMan(p1, p2):
    return abs(p1[0] - p2[0]) + abs(p1[1] - p2[1])


def getLengest(nowIndex, points):
    maxscore = 0
    maxIndex = -1

    for i in range(N):
        if i != nowIndex:
            ll = getMan(points[nowIndex], points[i])
            if maxscore <= ll:
                maxscore = ll
                maxIndex = i

    return maxIndex, maxscore

import random

now = random.randint(0, N - 1)
already = [now]
while True:
    nextIndex, score = getLengest(now, P)
    if nextIndex in already:
        print(score)
        break
    else:
        already.append(nextIndex)
    now = nextIndex