Counting Gift Combinations with LCM

wyh has a lucky number (n). Two friends, hke and ljc, plan to give him gifts with "heart levels" (a) and (b) respectively. When combined, the gift has a heart level equal to the least common multiple (\operatorname{lcm}(a, b)). wyh will be happy if (\operatorname{lcm}(a, b) = n).

Your task is to count the number of pairs ((a, b)) of positive integers such that (\operatorname{lcm}(a, b) = n).

Hint: If (n = \prod_{i=1}^{k} p_i^{e_i}) is the prime factorization of (n), then the number of valid pairs ((a,b)) is given by (\prod_{i=1}^{k} (2e_i+1)).

inputFormat

The input consists of a single integer (n) on one line, where (n) is the lucky number of wyh.

outputFormat

Output a single integer representing the number of pairs ((a, b)) such that (\operatorname{lcm}(a, b) = n).

sample

6

9