\problemname{Collusion on Two Wheels}

\illustration{0.2}{collusionontwowheels/problem_statement/cyclist-black-silhouette-clipart.jpg}{}

Two bicycle courier services have been competing in Metro City for
many years, stealing customers back and forth from one
another. Recently, they have come to realize that they would be better
off if they could attract new customers instead. A problem is that,
over time, each company's customers have become so widely scattered
across the city that some of their delivery times are unacceptably
slow, leading to customer dissatisfaction and a poor reputation.

The companies would like to divide up their current customers so that
each company could run ads saying ``We guarantee delivery in no more
than M minutes", hoping to attract new customers.  The streets of
Metro City are laid out on a grid, with buildings at integer
coordinates of the grid. The couriers must travel along those roads --
they cannot cut through buildings. It takes one minute to travel one
unit of distance in the x or y direction.

Divide up the current customer base to minimize the longest delivery
time required by either company to have a courier travel from one
customer of that company to any other customer of the same company.

* A delivery is considered to have been completed when the courier
  reaches the (x,y) address of the customer. No time is counted for
  wandering the hallways of the customer's building.

* It is acceptable that a courier traveling from one customer to
  another will pass by customers of the same or of the other
  company. No extra time delay is accrued for riding past a customer.

* If it should happen that one company winds up with only a single
  customer, that company puts someone on site to deliver messages
  within that one building. This is considered a zero delivery time.


\section*{Input}

Input starts with $1$ line containing an integer N, the number of
customers to be divided up.   $2 < N \leq 1\,000$.

This is followed by N lines, each containing a pair of integers $x$
and $y$ denoting the position of one customer. $0 \leq x, y \leq 1\,000$.


\section*{Output}

Print a single line containing the longest delivery time required by
the two companies (i.e., the maximum of the two longest delivery times
offered by each company separately).

\section*{Examples}
