Shorten ABC

AtCoder

IDarc110_e

Time2000ms

Memory256MB

Difficulty—

We have a string $S$ of length $N$ consisting of `A`, `B`, and `C`. You can do the following operation on $S$ zero or more times: * Choose $i$ $(1 \leq i \leq |S| - 1)$ such that $S_i \neq S_{i + 1}$. Replace $S_i$ with the character (among `A`, `B`, and `C`) that is different from both $S_i$ and $S_{i + 1}$, and remove $S_{i + 1}$ from $S$. Find the number of distinct strings that $S$ can be after zero or more operations, and print the count modulo $(10^9+7)$. ## Constraints * $1 \leq N \leq 10^6$ * $S$ is a string of length $N$ consisting of `A`, `B`, and `C`. ## Input Input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

5
ABAAC

Output #1

11

For example, the following sequence of operations turns $S$ into `ACB`:

*   First, choose $i=2$. We replace $S_2$ with `C` and remove $S_3$, turning $S$ into `ACAC`.
*   Then, choose $i=3$. We replace $S_3$ with `B` and remove $S_4$, turning $S$ into `ACB`.

Input #2

50
AACCCCBBBACCCCABABCCCCABACCACACACCACABABBBABABACCB

Output #2

256972022

API Response (JSON)

{
  "problem": {
    "name": "Shorten ABC",
    "description": {
      "content": "We have a string $S$ of length $N$ consisting of `A`, `B`, and `C`. You can do the following operation on $S$ zero or more times: *   Choose $i$ $(1 \\leq i \\leq |S| - 1)$ such that $S_i \\neq S_{i + 1",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc110_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a string $S$ of length $N$ consisting of `A`, `B`, and `C`.\nYou can do the following operation on $S$ zero or more times:\n\n*   Choose $i$ $(1 \\leq i \\leq |S| - 1)$ such that $S_i \\neq S_{i + 1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments