Four Variables

AtCoder

IDabc292_c

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$. Find the number of quadruples of positive integers $(A,B,C,D)$ such that $AB + CD = N$. Under the constraints of this problem, it can be proved that the answer is at most $9 \times 10^{18}$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $N$ is an integer. ## Input The input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

8

Here are the eight desired quadruples.

*   $(A,B,C,D)=(1,1,1,3)$
*   $(A,B,C,D)=(1,1,3,1)$
*   $(A,B,C,D)=(1,2,1,2)$
*   $(A,B,C,D)=(1,2,2,1)$
*   $(A,B,C,D)=(1,3,1,1)$
*   $(A,B,C,D)=(2,1,1,2)$
*   $(A,B,C,D)=(2,1,2,1)$
*   $(A,B,C,D)=(3,1,1,1)$

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Four Variables",
    "description": {
      "content": "You are given a positive integer $N$.   Find the number of quadruples of positive integers $(A,B,C,D)$ such that $AB + CD = N$. Under the constraints of this problem, it can be proved that the answer ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc292_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a positive integer $N$.  \nFind the number of quadruples of positive integers $(A,B,C,D)$ such that $AB + CD = N$.\nUnder the constraints of this problem, it can be proved that the answer ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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