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

n = int(raw_input())
points = set([])
for _ in range(n):
	p = map(int, raw_input().split())
	points.add(tuple(p))
points = list(points)
def distance(p,q): return abs(p[0] - q[0]) + abs(p[1] - q[1])


def f(points):
	r = 0
	for u in [-1,1]:
		for v in [-1,1]:
			pps = [u*x + v*y for x,y in points]
			r = max(r, max(pps) - min(pps))
	return r
print f(points)