A calibration routine needs the number of divisors of n that are perfect squares. A positive integer d is a perfect square if d = k * k for some non-negative integer k (so 1, 4, 9, 16, ... are perfect squares). Count the divisors of n that are perfect squares, including 1.
Input format
A single line with one integer n.
Output format
A single integer: the number of divisors of n that are perfect squares.
Constraints
- 1 <= n <= 1000000000000