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1816. Troubles with Pollard

Time limit: 0.5 second
Memory limit: 64 MB
Once Alexander decided to learn Pollard's method. However, he didn't understand this method well enough, and as a result he implemented the following algorithm which decomposes an integer n:
  1. If n is prime, return n.
  2. Otherwise, choose a random r in the range [1, 1018] and calculate g, the greatest common divisor of n and r.
  3. If g = 1 or g = n, repeat step 2, otherwise run the algorithm recursively for numbers g and n/g and return the union of the resulting divisor lists.
Alexander wants to know the number of times the greatest common divisor will be calculated at step 2 for a given n. Help him find this number.

Input

The only input line contains an integer n (2 ≤ n ≤ 109).

Output

Output the expected number of times the greatest common divisor will be calculated, with absolute or relative error not exceeding 10−6.

Samples

inputoutput
12
4.8571428571
8
6.6666666667
Problem Source: Tavrida NU Akai Contest. Petrozavodsk Summer Session, August 2010