A gear-train designer breaks a gear ratio n down into its prime building blocks. She wants the TOTAL number of prime factors of n, counting a repeated prime as many times as it appears (so 12 = 2 x 2 x 3 has 3 prime factors counted this way, not 2).
Given a single integer n, output the count of its prime factors with multiplicity (this is sometimes called the big-Omega function).
Input format
Line 1: a single integer n.
Output format
A single integer: the total number of prime factors of n, counted with multiplicity.
Constraints
- 2 <= n <= 200000