Solved Problem - Factorization

In the lesson, we look at an efficient way to factor a number.

Problem statement

Given a number N>1N > 1, count the number of factors of the number N.

Input format

A single line of input contains the number 1N10121 \leq N \leq 10^{12}.

Output format

Print a single integer equal to the number of factors of NN.


Sample

Input

36

Output

9

Explanation

Factors of 36:1,2,3,4,6,9,12,18,3636 : 1, 2, 3, 4, 6, 9, 12, 18, 36

Count: 99


Brute force

The brute force solution would be to loop over all the numbers from 1 to N and check if it is a factor. If it is, you would then print it.

We can use the modulus operator to check if it’s a factor or not.

Here is the code:

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