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I. Fake News (hard)

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputNow 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.)

Input

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

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

Example

Input

4

aa

abcd

ccc

abcc

Output

5

10

14

12

Note

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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