Euler's Problem#6481
In this problem, we will recall the great mathematician Leonhard Euler (–) and explore his well-known function .
The value of for a positive integer is defined as the number of integers k~(1 \le k \le n) that are coprime with . Two positive integers are considered coprime if their greatest common divisor is . For example, \phi(6) = 2 because only the numbers and are coprime with , while , , , and are not.
Euler's problem is formulated as follows: given a positive integer , find all positive integers such that \phi(x) = n.
The first line contains the number of test cases t~(1 \le t \le 5). Each of the following lines contains one positive integer n~(1 \le n \le 10^{10}).
Print the answers to the given test cases. For each test, print two lines. The first line should contain the number of solutions to the equation. The second line should list all found solutions in ascending order. If the equation has no solutions, the second line should be empty.
Example 1