CF802I 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

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.