Product of Different

In this problem you are asked to represent a positive integer number n as a multiplication of as many different positive integer factors as possible.

Input

The first line of the input le contains a single positive integer number n (1 ≤ n ≤ 1000000000).

Output

In the first line on the output file, print the maximum possible number of different factors in the representation of n. In the second line, print k factors in any order separated by spaces. If there are multiple possible factorizations, output any of them.

Examples