Input: a whole positive number greater than 4
Output: A whole positive number that describes the highest possible period an oscillator could have inside a square space of size (input)x(input) in a "life" grid that follows the rules of Conway's Game of Life. The oscillator never leaves this area throughout its cycles. It may not interact with any outside cells. There is no wall, cells outside this area are just dead by default.
Your program should be able to theoretically calculate as high of a number as the 32 bit Integer Limit.
Winner: this is code-golf, so shortest code in bytes wins!