String Reduction

Given a string consisting of the letters $a$, $b$ and $c$, we can perform the following operation: -Take any two adjacent distinct characters and replace them with the third character. Find the shortest string obtainable through applying this operation repeatedly. For example, given the string $aba$ we can reduce it to a 1 character string by replacing $ab$ with $c$ and $ca$ with $b$: $aba$ ->