P9873 [EC Final 2021] Beautiful String

Prof. Pang recently got a dictionary of the elvish language, including many strings representing their words. He thinks a partition of string $s$ is beautiful if both of the following conditions are satisfied: - $s = s_1 + s_2 + s_3 + s_4 + s_5 + s_6$, where $s_i (1\leq i\leq 6)$ are nonempty substrings. $a + b$ means the concatenation of string $a$ and $b$ here. - $s_1 = s_2 = s_5, s_3 = s_6$. For example, you can partition the string ``114514`` into $6$ parts : ``114514`` = ``1`` + ``1`` + ``4`` + ``5`` + ``1`` + ``4``. The first, second, fifth parts are the same, and the third and sixth parts are the same. Thus, the partition of $s=$``114514`` into $s_1=$``1``, $s_2=$``1``, $s_3=$``4``, $s_4=$``5``, $s_5=$``1``, and $s_6=$``4`` is beautiful. Accordingly, the beauty of a string $s$ is defined as the number of beautiful partitions of $s$. Given a string $t$, please help Prof. Pang to figure out the sum of beauties of all substrings of $t$.

The first line contains a single integer $T~(1\leq T \le 50)$ indicating the number of test cases. For each test case, there is one single line containing the string $t$, consisting of digits from `0' to `9'. It is guaranteed that the length of each $t$ in each test case will not exceed $5000$ and the total length will not exceed $30000$.

For each test case, output a single line containing an integer, indicating the sum of beauties of all substrings of $t$.