Div Game

AtCoder

IDabc169_d

Time2000ms

Memory256MB

Difficulty—

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 represented as $z=p^e$, where $p$ is a prime number and $e$ is a positive integer; * $z$ divides $N$; * $z$ is different from all integers chosen in previous operations. * Then, replace $N$ with $N/z$. Find the maximum number of times the operation can be applied. ## Constraints * All values in input are integers. * $1 \leq N \leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

3

We can apply the operation three times by, for example, making the following choices:

*   Choose $z=2 (=2^1)$. (Now we have $N=12$.)
*   Choose $z=3 (=3^1)$. (Now we have $N=4$.)
*   Choose $z=4 (=2^2)$. (Now we have $N=1$.)

Input #2

Output #2

0

We cannot apply the operation at all.

Input #3

Output #3

3

We can apply the operation three times by, for example, making the following choices:

*   Choose $z=2 (=2^1)$. (Now we have $N=32$.)
*   Choose $z=4 (=2^2)$. (Now we have $N=8$.)
*   Choose $z=8 (=2^3)$. (Now we have $N=1$.)

Input #4

1000000007

Output #4

1

We can apply the operation once by, for example, making the following choice:

*   $z=1000000007 (=1000000007^1)$. (Now we have $N=1$.)

Input #5

997764507000

Output #5

API Response (JSON)

{
  "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 represent...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments