13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T6b0,

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.

The Secret Number

Examples