Pair Every Letter

You are given a lowercase English string. In one move, you may change any character to its previous or next alphabet character. For example, changing 'f' to 'e' costs 1 move, and changing 'f' to 'g' also costs 1 move. Characters cannot move before 'a' or after 'z'. Your goal is to modify the string so that every character has at least one equal neighboring character. For example, in a valid string: - "aa" is valid, - "aabb" is valid, - "aaa" is valid, - "aba" is not valid because the middle character has no equal neighbor. Return the minimum number of moves needed to make the string valid.