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Competitions

2015 German Collegiate Programming Contest (GCPC)

Divisions

David is a young boy and he loves numbers. Recently he learned how to divide two numbers. David divides the whole day. He is happy if the result of the division is an integer, but he is not very amused if this is not the case. After quite a while he decided to use only a single dividend each day.

The parents of David are very careful and they would like to ensure that David experiences enough happiness. Therefore they decide which number David will use as the dividend for this day.

There is still a problem: The parents are not very good at math and don't know how to calculate the number of positive integral divisors for a given dividend n, which lead to an integral result. Now it's up to you to help David's parents.

Input

One integer n (1n1018), where n is chosen as a dividend.

Output

Print the number of positive integral divisors of n that lead to an integral result of the division.

Time limit 1 second
Memory limit 128 MiB
Input example #1
12
Output example #1
6
Input example #2
999999999999999989
Output example #2
2
Input example #3
100000007700000049
Output example #3
4
Source 2015 German Collegiate Programming Contest (GCPC), June 20, Problem F