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())

for i in range(N):
  x, y = map(int, input().split())
  ans = 0
  if i==0:
    x1, y1, x2, y2, x3, y3, x4, y4, x5, y5, x6, y6 = x, y, x, y, x, y, x, y, x, y, x, y
    tmax, tmin = x+y, x+y
    xmax, xmaxy, ymaxx, ymax, xmin, xminy, yminx, ymin = x, y, x, y, x, y, x, y
  else:
    if x<x1 and y<y1:
      x1, y1 = x, y
    elif x<x2 and y>y2:
      x2, y2 = x, y
    elif x>x3 and y>y3:
      x3, y3 = x, y
    elif x>x4 and y<y4:
      x4, y4 = x, y
    elif x+y < tmin:
      x5, y5 = x, y
      tmin = x + y
    elif x+y > tmax:
      x6, y6 = x, y
      tmax = x + y
    elif x > xmax:
      xmax = x
      xmaxy = y
    elif y > ymax:
      ymax = y
      ymaxx = x
    elif x < xmin:
      xmin = x
      xminy = y
    elif y < ymin:
      ymin = y
      yminx = x
    ans = max(ans, abs(x1-x)+abs(y1-y),abs(x2-x)+abs(y2-y), abs(x3-x)+abs(y3-y),abs(x4-x)+abs(y4-y), abs(x5-x)+abs(y5-y), abs(x6-x)+abs(y6-y),abs(xmax-x)+abs(xmaxy-y),abs(ymaxx-x)+abs(ymax-y),
             abs(xmin-x)+abs(xminy-y),abs(yminx-x)+abs(ymin-y),abs(x1-x3)+abs(y1-y3),abs(x2-x4)+abs(y2-y4),
             abs(xmin-xmax)+abs(xminy-xmaxy),abs(yminx-ymaxx)+abs(ymin-ymax))
print(ans)