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.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0
import os
import sys
from atexit import register
from io import BytesIO
sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
sys.stdout = BytesIO()
register(lambda: os.write(1, sys.stdout.getvalue()))
input = lambda: sys.stdin.readline().rstrip('\r\n')
raw_input = lambda: sys.stdin.readline().rstrip('\r\n')

n = int(input())
points = set()
for _ in xrange(n):
    x,y = (int(x) for x in input().split())
    points.add((x,y))

if len(points) <= 1:
    print(0)
else:
    srt1 = sorted(points, key=lambda x: x[0] + x[1])
    x1,y1 = srt1[0]
    x2,y2 = srt1[-1]
    ans1 = abs(x1+y1 - (x2+y2))
    srt2 = sorted(points, key=lambda x: x[0] - x[1])
    x1,y1 = srt2[0]
    x2,y2 = srt2[-1]
    ans2 = abs((x1-y1) - (x2-y2))
    print(max(ans1, ans2))
