Given a string with three each of three different letters ordered thus:

A A A B B B C C C

It is possible through a series of three moves to change the order into:

A B C A B C A B C

A ‘move’ consists of taking a section of the string and reversing the order of the items within it. The brackets show the section to be reversed in the subsequent move:

A(AABB)BCCC -> ABBA(ABC)CC -> AB(BACBAC)C -> ABCABCABC

Using the exact same idea, how many moves will it take to change between the following?

A A A A A B B B B B C C C C C D D D D D E E E E E

A B C D E A B C D E A B C D E A B C D E A B C D E