Good Binary String

A binary string $S$ is said to be *good*, if there exist some $k$ binary strings $P_1, P_2, \ldots, P_k$ such that: - $S = P_1 + P_2 + \ldots + P_k$. Here, $+$ denotes string concatenation. - Each $P_i$ has even length. - Each $P_i$ contains only a single distinct character. For example, $1100, 11, $ and $11000011$ are all *good*, while $1, 1001, $ and $101010$ are not. You are given a binar