1111gal password

AtCoder

IDabc242_c

Time2000ms

Memory256MB

Difficulty—

Given an integer $N$, find the number of integers $X$ that satisfy all of the following conditions, modulo $998244353$. * $X$ is an $N$\-digit positive integer. * Let $X_1,X_2,\dots,X_N$ be the digits of $X$ from top to bottom. They satisfy all of the following: * $1 \le X_i \le 9$ for all integers $1 \le i \le N$; * $|X_i-X_{i+1}| \le 1$ for all integers $1 \le i \le N-1$. ## Constraints * $N$ is an integer. * $2 \le N \le 10^6$ ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

203

Some of the $4$\-digit integers satisfying the conditions are $1111,1234,7878,6545$.

Input #2

Output #2

Input #3

Output #3

248860093

Be sure to find the count modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "1111gal password",
    "description": {
      "content": "Given an integer $N$, find the number of integers $X$ that satisfy all of the following conditions, modulo $998244353$. *   $X$ is an $N$\\-digit positive integer. *   Let $X_1,X_2,\\dots,X_N$ be the d",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc242_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given an integer $N$, find the number of integers $X$ that satisfy all of the following conditions, modulo $998244353$.\n\n*   $X$ is an $N$\\-digit positive integer.\n*   Let $X_1,X_2,\\dots,X_N$ be the d...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments