Empty the String

You are given a string $S$, which contains only characters, $A$ and $B$, and can perform the following operation : - Choose an alternating subsequence $T$ of $S$, and delete it from $S$. For example, if our string is ABBA, we can choose **AB**B**A**, and delete the bolded characters to get B. Let $f(S) = $ the minimum number of operations to convert $S$ to an empty string. ____________ Given