Everyone hates ugly problems.
You are given a positive integer. You must represent that number by sum of palindromic numbers.
A palindromic number is a positive integer such that if you write out that integer as a string in decimal without leading zeros, the string is an palindrome. For example, 1 is a palindromic number and 10 is not.
In the first line of input, there is an integer T denoting the number of test cases.
For each test case, there is only one line describing the given integer s ($1\leq s \leq 10^{1000}$).
For each test case, output “Case #x:” on the first line where x is the number of that test case starting from 1. Then output the number of palindromic numbers you used, n, on one line. n must be no more than 50. 阤n output n lines, each containing one of your palindromic numbers. Their sum must be exactly s.