Given two strings $S_1, S_2$, we write $S_1S_2$ for their concatenation. Given a string $S$ and integer $k\geq 1$, we write $(S)^k = SS\cdots S$ for the concatenation of $k$ copies of $S$. Now given a string, we can use this notation to 'compress' it, i.e. $AABAAB$ may be written as $((A)^2 B)^2$...