Description

Original problem from POJ 3421

Given a positive integer $x$, find the maximum length of a sequence composed of factors of $x$ greater than $1$, where each preceding term divides the subsequent term, and the number of sequences that achieve this maximum length.

Input Format

Multiple test cases. Each case consists of a single line containing a positive integer $x$.

Output Format

For each test case, output the maximum sequence length and the count of sequences that achieve this length.

Sample 1

2
3
4
10
100

1 1
1 1
2 1
2 2
4 6

Data Range and Hint

For all data, $1\le x\le 2^{20}$.