Please solve in typescript. Thank you.

Initially, string S of length N is given. Then $N-1$ operations are applied to it: move the first letter of S to the end. How many times is the first letter of S the same as the last letter?

For example, given $S=$ "abbaa", the obtained sequence of strings is:

abbaa longrightarrow bbaaa longrightarrow baaab longrightarrow aaabb longrightarrow aabba

Three of them have the same first and last letter.

Write a function:

function solution$($S$)$;

that, given a string $S$ of length $N,$ consisting of letters $\text{'}$a$\text{'}$ and$/$or $\text{'}$b$\text{'},$ returns the number of times the first letter is the same as the last in the obtained sequence of strings.

Examples:

Given $S=$ "abbaa", the function should return $3,$ as described above.

Given $S=$ "aaaa", the function should return $4.$ The first and last letters are always the same.

Given $S=$ "abab", the function should return $0.$ The first and last letters are always different.

Write an efficient algorithm for the following assumptions:

N is an integer within the range $[2.\mathrm{.}200,000]$;

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