{"raw_statement":[{"iden":"problem statement","content":"Given is a positive integer $N$. Consider repeatedly applying the operation below on $N$:\n\n*   First, choose a positive integer $z$ satisfying all of the conditions below:\n    *   $z$ can be represented as $z=p^e$, where $p$ is a prime number and $e$ is a positive integer;\n    *   $z$ divides $N$;\n    *   $z$ is different from all integers chosen in previous operations.\n*   Then, replace $N$ with $N/z$.\n\nFind the maximum number of times the operation can be applied."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 10^{12}$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"24"},{"iden":"sample output 1","content":"3\n\nWe can apply the operation three times by, for example, making the following choices:\n\n*   Choose $z=2 (=2^1)$. (Now we have $N=12$.)\n*   Choose $z=3 (=3^1)$. (Now we have $N=4$.)\n*   Choose $z=4 (=2^2)$. (Now we have $N=1$.)"},{"iden":"sample input 2","content":"1"},{"iden":"sample output 2","content":"0\n\nWe cannot apply the operation at all."},{"iden":"sample input 3","content":"64"},{"iden":"sample output 3","content":"3\n\nWe can apply the operation three times by, for example, making the following choices:\n\n*   Choose $z=2 (=2^1)$. (Now we have $N=32$.)\n*   Choose $z=4 (=2^2)$. (Now we have $N=8$.)\n*   Choose $z=8 (=2^3)$. (Now we have $N=1$.)"},{"iden":"sample input 4","content":"1000000007"},{"iden":"sample output 4","content":"1\n\nWe can apply the operation once by, for example, making the following choice:\n\n*   $z=1000000007 (=1000000007^1)$. (Now we have $N=1$.)"},{"iden":"sample input 5","content":"997764507000"},{"iden":"sample output 5","content":"7"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}