Description
In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n:
For this question, you are asked to compute the number of the given factorial's factors.
For example:
4! = 4 × 3 × 2 × 1 = 24
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Therefore, you should output 8 as the answer.
[HINT]
You should not directly calculate the answer of n!, or even unsigned long long cannot store your answer.
The best way to solve this question is to use the prime number ≤ N to do prime factorization and then use the result of it to get the final answer.
For example:
4! = 23 × 3, so the number of 4! 's factors = (3+1) × (1+1) = 8
Input
One interger N which denotes the given factorial of N.
(Note that 2 ≤ N ≤ 100)
Output
One integer which denotes the number of the given factorial's factors.
Note that you don't need to print '\n' at the end of the output
(We guarantee that the answers can be stored into unsigned long long)