CF2215B.RReeppeettiittiioonn

As a girl born on November 11th (or 11/11), SS loves repetition. For example, her favorite English word is bookkeeper, her favorite letter is W (double-u, double vé, or whatever you call it), her favorite animals are the cat (kitten!) and the rabbit (bunny!), her favorite programming language is C++, her favorite parser is LL(1), her favorite optimization algorithm is branch and bound (BB), her favorite unit is millimeter (mm), her favorite game is LLLL, and her favorite winning hand in Mahjong is Seven Pairs. She plans to release her new songs "Silent-night Satellite" and "Siesta Stella" soon, so she wants to select a "pretty" number to decorate the cover of her new songs.

SS observes this world from a higher perspective, which means she considers an integer concurrently in all standard positional numeral systems, starting from the binary numeral system. SS then calls a positive integer $ n $ $ (b, p) $ -tidy (with $ b,p\ge 2 $ ) if and only if:

• In base- $ b $ representation, $ n $ is represented as $ \overline{d_{k\cdot p-1} d_{k\cdot p-2}\ldots d_1 d_0} $ for some positive integer $ k $ and integers $ 0\le d_i \lt b $ , such that for each $ 0\le i \lt k $ , $ d_{i\cdot p}=d_{i\cdot p+1}=\cdots=d_{(i+1)\cdot p-1} $ .

For example, $ 2233 $ and $ 3355 $ are $ (10,2) $ -tidy, $ 1111 $ is both $ (10,2) $ -tidy and $ (10,4) $ -tidy, and $ 6,737,151=(66\textrm{CCFF})_{16} $ is $ (16,2) $ -tidy. Furthermore, SS defines the tidiness of a positive integer $ n $ as the number of ordered pairs $ (b, p) $ such that $ n $ is $ (b, p) $ -tidy.

SS has given you an integer $ n $ . Your task is to determine the tidiness of $ n $ .

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 1000 $ ). The description of the test cases follows.

The only line of each test case contains a single integer $ n $ ( $ 1\le n\le 10^{12} $ ) — the integer SS has given you.

It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^{12} $ .

For each test case, output a single integer — the tidiness of $ n $ .

In the third test case, $ 115={(55)}{22}={(11)}{114} $ . Therefore, the tidiness of $ 115 $ is $ 2 $ .

In the fourth test case, $ 1111 $ is $ (10, 2) $ -tidy, $ (10, 4) $ -tidy, $ (100, 2) $ -tidy, and $ (1110, 2) $ -tidy.