Can killua save them all

Oh no! The imposter on the Airship has sabotaged the Oxygen supply of the ship. The crewmates are now in grave danger. They need to get through a sequence of $Q$ doors in order to reach the $O_2$ tanks. Let us first define a string as a pesudo-palindrome if any rotation of the string (including the string itself) results in the formation of a palindrome. For example, "bba" is a pesudo-palindrome