Vadim has thought of a number (x). To ensure that no one can guess it, he appended a positive number of zeros to the right of it, thus obtaining a new number (y). However, as a precaution, Vadim decided to spread the number (n = x + y). Find all suitable (x) that Vadim could have thought of for the given (n). Each test consists of several test cases. The first line contains a single integer (t) ((1 \le t \le 10^4)) — the number of test cases. The following lines describe the test cases. In a single line of each test case, there is an integer (n) — the number spread by Vadim ((11 \le n \le 10^{18})). For each number (n), output (0) if there are no suitable (x). Otherwise, output the number of suitable (x), followed by all suitable (x) in ascending order . In the first sample, to (11) one can append two zeros to the right, then (11 + 1100 = 1111), and to (101) one can append one zero to the right, then (101 + 1010 = 1111). In the second sample, it is impossible to obtain (12) through the described actions.