Problems
The equation of LCM
The equation of LCM
The least common multiple (\textbf{LCM}) of two integers \textbf{x}, \textbf{y} is the smallest integer that is divisible by \textbf{x}, and \textbf{y}. Now consider the equation \textbf{LCM (x, y) = n}. Your task - to find how many different solutions of this equation is in the natural numbers. More formally: it is necessary to determine the number of distinct ordered pairs of integers \textbf{(x, y)}, where the \textbf{LCM} is \textbf{n}.
\InputFile
The input file contains a single integer \textbf{n} (\textbf{1} ≤ \textbf{n} ≤ \textbf{10^18}).
\OutputFile
Need to bring a unique number that is the answer to the problem.
Input example #1
3
Output example #1
3
Example description: For the first test, you can find all three pairs of numbers (1, 3), (3, 1), (3, 3). For the second test, the only pair that satisfies the condition to be (1, 1).