jsplitter | Minimal jQuery splitter plugin | Plugin library

I am trying to create a function that takes in a string and changes each letters value to a "(" if the character is not duplicated in the string, and a ")" if the character does have a duplicate present in the string. I have decided to go an unconventional route to solve this problem but I am running in to an issue with a double for loop. From what I understand, the inner for loop in javascript does not have access to the variables outside of the loop. I want to loop through every item in an array twice but I'm not sure what to set the inner loops length as.

Here is my code: