Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 1 - Objective Problem 1

In the world of Drown there are many islands. Every island always have an integer area. But a catastrophe hit this world suddenly and each second, every island of area $n$ larger than 3 divides into 3 island of area $\lfloor\frac{n}{3} \rfloor$ . And one of them drowns.

In the beginning you have one island of size N.

After how much time will the situation stabilize for the first time?

This problem is a part of Tessellate S.T.E.M.S (2019)