Staircase Sequences

AtCoder

IDabc190_d

Time2000ms

Memory256MB

Difficulty—

How many arithmetic progressions consisting of integers with a common difference of $1$ have a sum of $N$? ## Constraints * $1 ≤ N ≤ 10^{12}$ * $N$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

4

We have four such progressions:

*   $[12]$
*   $[3, 4, 5]$
*   $[-2, -1, 0, 1, 2, 3, 4, 5]$
*   $[-11, -10, -9, \dots, 10, 11, 12]$

Input #2

Output #2

2

We have two such progressions:

*   $[1]$
*   $[0, 1]$

Input #3

963761198400

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Staircase Sequences",
    "description": {
      "content": "How many arithmetic progressions consisting of integers with a common difference of $1$ have a sum of $N$?",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc190_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "How many arithmetic progressions consisting of integers with a common difference of $1$ have a sum of $N$?\n\n## Constraints\n\n*   $1 ≤ N ≤ 10^{12}$\n*   $N$ is an integer.\n\n## Input\n\nInput is given from ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments