string S of length N is given. Then N$-1$ operations are applied to it: move the first letter 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 $-->$ bbaaa $->$ baaab aaabb $->$ aabba Three of them have the same first and last letter. Write a function: class Solution $\{$ public int solution$($String S$)$: $1$ 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: $1.$ Given S $=$ "abbaa", the function should return $3,$ as described above. $2.$ Given S $=$ "aaaa", the function should return $4.$ The first and last letters are always the same. $3.$ 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 Sis made only of the characters $\text{'}$a$\text{'}$ and$/$or$\text{'}$b$*.$