K - Beautiful Permutation

We know that a sequence of $N$ integers is called a permutation if it contains all integers from $1$ to $N$ exactly once. A $K-$ *beautiful permutation* is a permutation for which $K$ is the **minimum** number of *good* consecutive segments into which the sequence can be partitioned. A *good* consecutive segment is a non-empty continuous segment where all elements of the segment have the same [