No Majority

AtCoder

IDagc060_a

Time2000ms

Memory256MB

Difficulty—

A string $x$ consisting of lowercase English letters is said to be **good** if and only if the following condition is satisfied. * Every (contiguous) substring of $x$ whose length is $2$ or greater satisfies the following: * no character occupies the majority of that substring. For example, `acbca` is not good because `c` occupies the majority of the substring `cbc`. You are given a string $S$ of length $N$ consisting of lowercase English letters and `?`. You want to replace each `?` with a lowercase English letter of your choice to make $S$ a good string. Find the number of ways to make $S$ a good string, modulo $998244353$. ## Constraints * $2 \leq N \leq 5000$ * $S$ is a string of length $N$ consisting of lowercase English letters and `?`. ## Input The input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

3
a?b

Output #1

24

Every way other than `aab` and `abb` satisfies the condition.

Input #2

3
a?a

Output #2

Input #3

20
ugsyakganihodnwmktgi

Output #3

Input #4

20
??a???h?m?y?ts???tl?

Output #4

444225229

API Response (JSON)

{
  "problem": {
    "name": "No Majority",
    "description": {
      "content": "A string $x$ consisting of lowercase English letters is said to be **good** if and only if the following condition is satisfied. *   Every (contiguous) substring of $x$ whose length is $2$ or greater",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc060_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A string $x$ consisting of lowercase English letters is said to be **good** if and only if the following condition is satisfied.\n\n*   Every (contiguous) substring of $x$ whose length is $2$ or greater...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments