Fake News (hard)
Now that you have proposed a fake post for the HC2 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*|<=≤<=100<=000) 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.