In some house in some place, John and Jane were playing a game, the game consist on a pile of $$$N$$$ chips and they will be alternating turns with Jane starting. In each turn they need to remove at least one chip from the pile, and the winner will be the one that takes the last chip.

But there is an interesting way in wich each one can take chips, in first turn (Jane's turn) she can only pick 1 chip, in the second turn (John's turn) he can choose to take 1 or 2 chips, in the third turn (Jane's turn again) she can choose between taking 1, 2 or 3 chips. Generally speaking, on the $$$i$$$-th turn, the player in turn should take at least $$$1$$$ chip and maximum $$$i$$$ chips.

Knowing the amount of chips in the pile when the game started, and assuming both John and Jane will play optimally. Can you determine who will win?