B. The Secret Number
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$n$$$.

Input

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 $$$(11 \le n \le 10^{18})$$$.

Output

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.

Example
Input
5
1111
12
55
999999999999999999
1000000000000000000
Output
2
11 101
0
1
5
3
999999999 999000999000999 90909090909090909
0
Note

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.