Cube

AtCoder

IDabc198_f

Time2000ms

Memory256MB

Difficulty—

Let us write a positive integer on each face of a cube. How many ways are there to do this so that the sum of the six numbers written is $S$? Here, two ways to write numbers are not distinguished when they only differ by rotation. (Numbers have no direction.) The count can be enormous, so find it modulo $998244353$. ## Constraints * $6 \leq S \leq 10^{18}$ * $S$ is an integer. ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

Output #1

3

We have one way to write $1,1,1,1,1,3$ on the cube and two ways to write $1,1,1,1,2,2$ (one where we write $2$ on adjacent faces and another where we write $2$ on opposite faces), for a total of three ways.

Input #2

Output #2

Input #3

Output #3

Input #4

10000000000

Output #4

2239716

Find the count modulo $998244353$.

API Response (JSON)

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    "name": "Cube",
    "description": {
      "content": "Let us write a positive integer on each face of a cube. How many ways are there to do this so that the sum of the six numbers written is $S$? Here, two ways to write numbers are not distinguished when",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc198_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let us write a positive integer on each face of a cube. How many ways are there to do this so that the sum of the six numbers written is $S$?\nHere, two ways to write numbers are not distinguished when...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments