The ternary expansion of a number is that number written in base 3. A number can have more than one ternary expansion. A ternary expansion is indicated with a subscript 3. For example, 1 = 1
3 = 0.222...
3, and 0.875 = 0.212121...
3.
The Cantor set is defined as the real numbers between 0 and 1 inclusive that have a ternary expansion that does not contain a 1. If a number has more than one ternary expansion, it is enough for a single one to not contain a 1.
For example, 0 = 0.000...
3 and 1 = 0.222...
3, so they are in the Cantor set. But 0.875 = 0.212121...
3 and this is its only ternary expansion, so it is not in the Cantor set.
Your task is to determine whether a given number is in the Cantor set.