Periods of Words

A string $P$ is considered a prefix of a string $A$ if A = PB, where either $P$ or $B$ can be empty. A string $P$ is a non-trivial prefix of $A$ if A = PB, and neither $P$ nor $B$ are empty. A string $Q$ is termed a period of the string $A$ if $Q$ is a non-trivial prefix of $A$ and $A$ is a prefix (though not necessarily a non-trivial one) of the string $QQ$. For instance, the strings abab and ababab are periods of the string abababa.

The maximum period of a string $A$ is the longest among its periods, or an empty string if $A$ has no periods. For example, the maximum period of the string ababab is abab, and the maximum period of the string abc is an empty string.

Write a program that calculates the sum of the lengths of the maximum periods for all prefixes of the given string $A$.