Roger, having figured out how to reason in two dimensions, has crafted a tricky puzzle for Victor to crack.

Roger has highlighted several lattice points in the ~xy~-plane and wants Victor to find the rectangle with maximum area inside that has vertices among the highlighted points!

Victor takes a look at this task and scoffs. It's just a line sweep problem, what's so tricky about that?

However, Roger points out to Victor that the rectangle need not be axis-aligned. The rectangles, much like Roger, can be tilted.

Is Victor tilt-proof?

Constraints

~4 \le N \le 1500~

For at most 20% of full credit, ~N \le 500~.

~\left|x_i\right| \le 10^8~

~\left|y_i\right| \le 10^8~

All ~(x_i, y_i)~ are distinct.

Input Specification

The first line will contain a single integer, ~N~.

Each of the next ~N~ lines will contain two space-separated integers ~x_i~ and ~y_i~, indicating that Roger has highlighted point ~(x_i, y_i)~.

Output Specification

Print, on a single line, the maximum area of a rectangle with lattice points among the highlighted points. It is guaranteed that a non-degenerate rectangle exists.

Sample Input

8
-2 3
-2 -1
0 3
0 -1
1 -1
2 1
-3 1
-2 1

Sample Output

10