1122 Subsequence 2

AtCoder

IDabc433_f

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ consisting of digits. A string $T$ is called a **1122-string** if it satisfies all of the following conditions. (The definition is the same as in Problem C.) * $T$ is a non-empty string consisting of digits. * $|T|$ is even, where $|T|$ denotes the length of string $T$. * All characters from the $1$\-st through the $\frac{|T|}2$\-th character of $T$ are the same digit. * All characters from the $(\frac{|T|}2+1)$\-th through the $|T|$\-th character of $T$ are the same digit. * Adding $1$ to the digit of the $1$\-st character of $T$ gives the digit of the $|T|$\-th character. For example, `1122`, `01`, and `444555` are 1122-strings, but `1222` and `90` are not 1122-strings. Find the number, modulo $998244353$, of **(not necessarily contiguous) subsequences** of $S$ that are 1122-strings. Two subsequences are counted separately if they are extracted from different positions, even if they are identical as strings. ## Constraints * $S$ is a string consisting of digits with length between $1$ and $10^6$, inclusive. ## Input The input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

Output #1

5

The following five subsequences satisfy the condition.

*   `12` extracted from the $1$\-st and $3$\-rd characters of $S$
*   `12` extracted from the $1$\-st and $4$\-th characters of $S$
*   `12` extracted from the $2$\-nd and $3$\-rd characters of $S$
*   `12` extracted from the $2$\-nd and $4$\-th characters of $S$
*   `1122` extracted from the $1$\-st through $4$\-th characters of $S$

Thus, output $5$.
Note that two subsequences are counted separately if they are extracted from different positions, even if they are identical as strings.

Input #2

Output #2

0

There may be no subsequence that is a 1122-string.

Input #3

0777468889971

Output #3

API Response (JSON)

{
  "problem": {
    "name": "1122 Subsequence 2",
    "description": {
      "content": "You are given a string $S$ consisting of digits. A string $T$ is called a **1122-string** if it satisfies all of the following conditions. (The definition is the same as in Problem C.) *   $T$ is a 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": "abc433_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ consisting of digits.\nA string $T$ is called a **1122-string** if it satisfies all of the following conditions. (The definition is the same as in Problem C.)\n\n*   $T$ is a n...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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