{"problem":{"name":"Div Game","description":{"content":"Given is a positive integer $N$. Consider repeatedly applying the operation below on $N$: *   First, choose a positive integer $z$ satisfying all of the conditions below:     *   $z$ can be represent","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc169_d"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc169_d","tags":[],"sample_group":[["24","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 $N=1$.)"],["1","0\n\nWe cannot apply the operation at all."],["64","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 $N=1$.)"],["1000000007","1\n\nWe can apply the operation once by, for example, making the following choice:\n\n*   $z=1000000007 (=1000000007^1)$. (Now we have $N=1$.)"],["997764507000","7"]],"created_at":"2026-03-03 11:01:14"}}