We are given a string $S$ of length $N$ consisting only of letters $\text{'}A\text{'}$ and$/$or $\text{'}B\text{'}.$ Our goal is to obtain a string in the format $"$A$...$AB $...B^{**}($all letters $\text{'}$A$\text{'}$ occur before all letters $\text{'}B\text{'})$ by deleting some letters from $S.$ In particular, strings consisting only of letters $\text{'}A\text{'}$ or only of letters $\text{'}B\text{'}$ fit this format.

Write a function:

class Solution $\{$ public int solution$($String S$)$; $\}$

that, given a string S$,$ returns the minimum number of letters that need to be deleted from $S$ in order to obtain a string in the above format.

Examples:

Given $S=$ "BAAABAB", the function should return $2.$ We can obtain "AAABB" by deleting the first occurrence of $\text{'}B\text{'}$ and the last occurrence of $\text{'}$A$\text{'}.$

Given $S=$ "BBABAA", the function should return $3.$ We can delete all occurrences of $\text{'}$A$\text{'}$ or all occurrences of $\text{'}B\text{'}.$

Given $S=$ "AABBBB", the function should return $0.$ We do not have to delete any letters, because the given string is already in the expected format.

Write an efficient algorithm for the following assumptions:

$N$ is an integer within the range $1.\mathrm{.}100,000$;

string $S$ is made only of the characters $\text{'}A\text{'}$ and$/$or $\text{'}B\text{'}.$

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