Neither AB nor BA

AtCoder

IDagc040_c

Time4000ms

Memory256MB

Difficulty—

Given is a positive even number $N$. Find the number of strings $s$ of length $N$ consisting of `A`, `B`, and `C` that satisfy the following condition: * $s$ can be converted to the empty string by repeating the following operation: * Choose two consecutive characters in $s$ and erase them. However, choosing `AB` or `BA` is not allowed. For example, `ABBC` satisfies the condition for $N=4$, because we can convert it as follows: `ABBC` → (erase `BB`) → `AC` → (erase `AC`) → `(empty)`. The answer can be enormous, so compute the count modulo $998244353$. ## Constraints * $2 \leq N \leq 10^7$ * $N$ is an even number. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

7

Except `AB` and `BA`, all possible strings satisfy the conditions.

Input #2

Output #2

Input #3

Output #3

210055358

API Response (JSON)

{
  "problem": {
    "name": "Neither AB nor BA",
    "description": {
      "content": "Given is a positive even number $N$. Find the number of strings $s$ of length $N$ consisting of `A`, `B`, and `C` that satisfy the following condition: *   $s$ can be converted to the empty string by",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc040_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a positive even number $N$.\nFind the number of strings $s$ of length $N$ consisting of `A`, `B`, and `C` that satisfy the following condition:\n\n*   $s$ can be converted to the empty string by...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments