The equation of LCM#3242
The least common multiple (LCM) of two integers , is the smallest integer that is divisible by , and . Now consider the equation LCM(x, y) = n. Your task - to find how many different solutions this equation has in natural numbers. More formally: it is necessary to determine the number of distinct ordered pairs of natural numbers , whose LCM equals .
The input file contains a single integer (1 \le n \le 10^{18}).
Output a single number that is the answer to the problem.
مثال 1