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