Practice Number theory and Mathematics with the exercise "Integer pairs of AB/(A+B)"

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Number theory
Mathematics

Statement

Goal

Given an integer N, find the number of pairs of integers (A, B) that satisfies (A*B)/(A+B)=N.

Example:
If N=2, the integer solutions (A, B) to the equation (A*B)/(A+B)=N are (-2, 1), (1, -2), (3, 6), (4, 4) and (6, 3). Thus, the output is 5.

Input

An integer N.

Output

An integer for the number of pairs of integers.

Constraints

1 ≤ N ≤ 10^14

Example

Input

Output

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