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# Input 

A single integer \1ドル \leq x \leq 10^{15}\$.

# Output

The maximum number of distinct positive integers that have the product \$x\$.

# Examples

Input: 1099511627776. Output: 9. One possible optimal list of factors is: (1, 2, 4, 8, 16, 32, 64, 128, 4096).

Input: 127381. Output 4. One possible optimal list of factors is: (1, 17, 59, 127).

Related to this [old question][1].


 [1]: https://codegolf.stackexchange.com/questions/104707/list-all-multiplicative-partitions-of-n?rq=1