Palindromic Factors Round B 2022 - Kick Start 2022

Palindromic Factors Round B 2022 - Kick Start 2022

Problem

You are given a positive integer A$A$. Find the number of factors of A$A$ which are palindromes. A number is called a palindrome if it remains the same when the digits in decimal representation are reversed. For instance, 121 is a palindrome, while 123 is not.

Input

The first line of the input gives the number of test cases, T$T$. T$T$ lines follow.

Each line represents a test case and contains a single integer A$A$.

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Output

For each test case, output one line containing Case #x$x$: y$y$, where x$x$ is the test case number (starting from 1) and y$y$ is the number of factors of A$A$ which are palindromes.

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Limits

Time limit: 2 seconds.
Memory limit: 1 GB.
1≤T≤100$1\le \mathbf{T}\le 100$.

Test Set 1

1≤A≤103$1\le \mathbf{A}\le {10}^3$.

Test Set 2

1≤A≤1010$1\le \mathbf{A}\le {10}^{10}$.

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Sample

Sample Input

4
6
10
144
242

Sample Output

Case #1: 4
Case #2: 3
Case #3: 7
Case #4: 6

In the first test case, A$A$ has 4$4$ factors which are palindromes: 1,2,3,$1,2,3,$ and 6$6$.
In the second test case, A$A$ has 3$3$ factors which are palindromes: 1,2,$1,2,$ and 5$5$.
In the third test case, A$A$ has 7$7$ factors which are palindromes: 1,2,3,4,6,8,$1,2,3,4,6,8,$ and 9$9$.
In the fourth test case, A$A$ has 6$6$ factors which are palindromes: 1,2,11,22,121,$1,2,11,22,121,$ and 242$242$.

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