409282: GYM103476 C Divisor Circle
Memory Limit：512 MB
Time Limit：1 S
Judge Style：Text Compare
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Description
C. Divisor Circletime limit per test1 secondmemory limit per test512 megabytesinputstandard inputoutputstandard output
ExampleInput
Consider all divisors of some integer $$$n$$$. Choose some of these divisors, then arrange them in a circle so that the ratio of any two adjacent numbers is a prime number.
Find the maximum number of divisors of $$$n$$$ you can choose, and find the appropriate arrangement.
InputThe first line of input contains the integer $$$n$$$ ($$$2 \le n \le 10^9$$$).
OutputIn the first line, print a single integer $$$k$$$ — the maximum number of divisors of $$$n$$$ you can choose.
In the second line, print $$$k$$$ integers — different divisors of $$$n$$$ in the order they appear on the circle. Any two adjacent and the first and last numbers in this list must differ by multiplication by some prime number.
Scoring| Subtask | Score | Constraints |
| $$$1$$$ | $$$10$$$ | $$$n \le 10$$$ |
| $$$2$$$ | $$$15$$$ | $$$n \le 50$$$ |
| $$$3$$$ | $$$20$$$ | $$$n \le 150$$$ |
| $$$4$$$ | $$$20$$$ | $$$n = 10^m$$$ for integer $$$m \ge 0$$$ |
| $$$5$$$ | $$$15$$$ | $$$n = 2^x \cdot 3^y \cdot 5^z$$$ for integers $$$x, y, z \ge 0$$$ |
| $$$6$$$ | $$$10$$$ | $$$n$$$ is not a square of an integer |
| $$$7$$$ | $$$10$$$ | No additional constraints |
10Output
4 1 2 10 5