The equation of LCM

The least common multiple (LCM) of two integers x, y is the smallest integer that is divisible by x, and y. Now consider the equation 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 (x, y), where the LCM is n.

Input

The input file contains a single integer n (1 ≤ n ≤ 10^18).

Output

Need to bring a unique number that is the answer to the problem.

Examples