After reaching Râmnicu Sărat, Little IR12660 felt the weary aura the city has after being the battleground of multiple crucial historic battles.
Little IR12660 heard a very interesting rumor about Râmnicu Sărat; more specifically, he heard that exactly $$$N$$$ different rulers controlled this city during the middle ages. Moreover, while some were ruled centuries apart from each other, a constant seemed to foretell this statistic: if we were to take the list of casualties in all the battles fought in Râmnicu Sărat, the lowest common multiple of any two numbers in this list was equal to $$$N$$$.
However, this list of casualties has been long lost in history. The number $$$N$$$ hasn't. Little IR12660 wonders what the maximum size of this list could be and what one such maximal size list can look like. Of course, he then asks you to find this maximum size and one list of this size.
The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 100$$$) — the number of test cases.
Each of the next $$$T$$$ lines contains a single integer $$$N$$$ ($$$1 \leq N \leq 10^{12}$$$).
For each test case, output an integer $$$K$$$ — the maximum size of a list satisfying the given condition.
On the following line, output $$$K$$$ integers that respect the given propriety.
If there are multiple solutions, output any of them.
4 1 2 9 12
1 1 2 1 2 2 1 9 3 3 4 12
