Palindromic Factors

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

The first line of the input gives the number of test cases, $T$. $T$ lines follow. Each line contains a single integer $A$.

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

$1≤T≤100$.

In the first test case, $A$ has 4 palindromic factors: 1, 2, 3, and 6.

In the second test case, $A$ has 3 palindromic factors: 1, 2, and 5.

In the third test case, $A$ has 7 palindromic factors: 1, 2, 3, 4, 6, 8, and 9.

In the fourth test case, $A$ has 6 palindromic factors: 1, 2, 11, 22, 121, and 242.