One Change Subsequences

A string $t_1 t_2 \ldots t_m$ is called *good* if there is at most one position $1\le i < m$ such that $t_i \ne t_{i+1}$. For example `aaabb` and `zzz` are good strings; while `abc` and `ssdddssds` are not good. You are given a string $s$, consisting of lowercase English letters. Find the minimum $k$ such that you can split $s$ into $k$ *good* subsequences (a subsequence is not necessarily conti