A10887. Fake News (hard)

Now that you have proposed a fake post for the HC $^{2}$ Facebook page, Heidi wants to measure the quality of the post before actually posting it. She recently came across a (possibly fake) article about the impact of fractal structure on multimedia messages and she is now trying to measure the self-similarity of the message, which is defined as

where the sum is over all nonempty strings $p$ and  is the number of occurences of $p$ in $s$ as a substring. (Note that the sum is infinite, but it only has a finite number of nonzero summands.)

Heidi refuses to do anything else until she knows how to calculate this self-similarity. Could you please help her? (If you would like to instead convince Heidi that a finite string cannot be a fractal anyway – do not bother, we have already tried.)

The input starts with a line indicating the number of test cases $T$ ( $1<=T<=10$ ). After that, $T$ test cases follow, each of which consists of one line containing a string $s$ ( $1<=|s|<=100000$ ) composed of lowercase letters (a-z).

Output $T$ lines, every line containing one number – the answer to the corresponding test case.

A string $s$ contains another string $p$ as a substring if $p$ is a contiguous subsequence of $s$ . For example, ab is a substring of cab but not of acb.