You are given a string letters made of N English letters. Count the number of different letters that appear in both uppercase and lowercase where all lowercase occurrences of the given letter appear before any uppercase occurrence.

For example, for letters $=$ "aaAbcCABBc" the answer is $2.$ The condition is met for letters $‘$a$’$ and $‘$b$’,$ but not for $‘$c$’.$

Write a function:

function solution$($letters: string$)$: number;

that, given a string letters, returns the number of different letters fulfilling the conditions above.

Examples:

Given letters $=$ "aaAbcCABBc", the function should return $2,$ as explained above.

Given letters $=$ "xyzXYZabcABC", the function should return $6.$

Given letters $=$ "ABCabcAefG", the function should return $0.$

Write an efficient algorithm for the following assumptions:

N is an integer within the range $[1.\mathrm{.}100,000]$; string letters is made only of letters $($a$-$z and$/$or A$-$Z$).$