Jaime has been successful building fences to keep his sheep safe, the fences he builds are very classic wooden fences forming a rectangle or a square. Seeing the success he has with sheep, he plans on expanding his business and will build fences for hogs. He built the first fence for some hogs and after a couple days, the fence was broken, hogs are really clever to find a way out of the fence.

Jaime has developed a new fence that uses an unbreakable metal wire, he will build a fence and verify the hogs are not able to escape from it, nor break it. To build the fence Jaime has $$$N$$$ units of this metal wire, each unit with a $$$1$$$ meter size. Since the metal wire is unbreakable he has to build each of the $$$4$$$ walls for the fence using complete metal wire units and then join them at their ending points forming the rectangular fence. Note the metal wire units can not be broken, and a wall containing $$$L$$$ metal wire units will have $$$L$$$ meters in length.

Jaime has a lot of hogs now, and no fence ready, this is why he wants to build the fence that encloses the maximum possible area he can using this new metal wire. Jaime is not really good at math, so he asked your help to find the maximum area he can enclose building his fence with the $$$N$$$ units he has.