Problem Description

Given $n$, find all $x$ such that $\varphi(x) = n$.

Input Format

The first line contains an integer $T$.

The next $T$ lines each contain an integer $n$.

Output Format

Output a total of $2 \times T$ lines.

For each test case, output an integer $m$ indicating the number of valid values.

Then output a second line containing $m$ integers $x_i$ in increasing order. If $m$ is $0$, output an empty line.

4
8
10
13
6

5
15 16 20 24 30
2
11 22
0

4
7 9 14 18

Hint

For $100\%$ of the testdata, $1 \le T \le 5$, $1 \le n \le 10^{10}$.

Translated by ChatGPT 5