Block Game

AtCoder

IDagc050_c

Time4000ms

Memory256MB

Difficulty—

There is a sequence of cells that extends infinitely to both directions. You and Snuke play the following game: * The judge chooses a string $t$ consisting of `B` and `S`, called turn string, and show it to both players. * First, Snuke stands on one of the cells. * Then, for each $i = 1, ..., |t|$ in this order, the following happens: * If the $i$\-th letter of $t$ is `B`, it is your turn. You choose a cell that contains neither other blocks nor Snuke, and put a block on the cell. After that, if both of the two cells adjacent to Snuke's cell are blocked, you win and the game ends. * If the $i$\-th letter of $t$ is `S`, it is Snuke's turn. He may move to an adjacent unblocked cell, or doesn't do anything. * If the game still hasn't ended, Snuke wins and the game ends. You are given a string $s$ consisting of `B`, `S`, and `?`. If $s$ contains $Q$ `?`s, there are $2^Q$ ways to replace each `?` with `B` or `S` and get a turn string. Among those $2^Q$ strings, how many will end up with your winning, in case both players play optimally? Find the answer modulo $998,244,353$. ## Constraints * $1 \leq |s| \leq 10^6$ * $s$ consists of `B`, `S`, and `?`. ## Input Input is given from Standard Input in the following format: $s$ [samples]

Samples

Input #1

BSSBS

Output #1

0

You take the $1$st and the $4$th turn, and Snuke takes the $2$nd, the $3$rd, and the $5$th turn. In this case, if both players play optimally, it turns out that Snuke wins.

Input #2

?S?B????S????????B??????B??S??

Output #2

16777197

API Response (JSON)

{
  "problem": {
    "name": "Block Game",
    "description": {
      "content": "There is a sequence of cells that extends infinitely to both directions. You and Snuke play the following game: *   The judge chooses a string $t$ consisting of `B` and `S`, called turn string, and s",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc050_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a sequence of cells that extends infinitely to both directions. You and Snuke play the following game:\n\n*   The judge chooses a string $t$ consisting of `B` and `S`, called turn string, and s...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments