D - Delete if Equal

You are given a binary string $S$ of size $N$. You can do the following operation as many times you want: - Choose an index $i$ satisfying $1 < i < |S|$ and $S_{i - 1} = S_{i + 1}$, and delete $S_i$ from the string. Then, concatenate the $2$ parts $S[1, i - 1]$ and $S[i + 1, |S|]$ to form the new string $S$. Note that the length of $S$ reduces by $1$ after each operation. Find the minimum p