Let $n = p_1^{a_1}p_2^{a_2}...p_k^{a_k}\:(p_1 < p_2 < ... < p_k)$ be a factorization of positive integer $n$. Find the value of $a_1 + a_2 + ... + a_k$. \InputFile One positive integer $n\:(1 < n \le 10^9)$. \OutputFile Find the factorization of $n$ and print the value of $a_1 + a_2 + ... + a_k$. \Examples For example, $72 = 2^3 \cdot 3^2$. The answer is $a_1 + a_2 = 3 + 2 = 5$.