code javascript:

Given a string, count the minimum number of letters that need to be deleted in order to obtain a string in the format $"$A$...$AB$...$B$".$

Task description

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:

function solution$($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:

$1.$ 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$\text{'}.$

$2.$ Given S $=$ "BBABAA", the function should return $3.$ We can delete all occurrences of $\text{'}$A$\text{'}$ or all occurrences of $\text{'}$B$\text{'}.$

$3.$ 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$\text{'}.$