DNA Sequence

AtCoder

IDarc104_b

Time2000ms

Memory256MB

Difficulty—

We have a string $S$ of length $N$ consisting of `A`, `T`, `C`, and `G`. Strings $T_1$ and $T_2$ of the same length are said to be complementary when, for every $i$ ($1 \leq i \leq l$), the $i$\-th character of $T_1$ and the $i$\-th character of $T_2$ are complementary. Here, `A` and `T` are complementary to each other, and so are `C` and `G`. Find the number of non-empty contiguous substrings $T$ of $S$ that satisfies the following condition: * There exists a string that is a permutation of $T$ and is complementary to $T$. Here, we distinguish strings that originate from different positions in $S$, even if the contents are the same. ## Constraints * $1 \leq N \leq 5000$ * $S$ consists of `A`, `T`, `C`, and `G`. ## Input Input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

4 AGCT

Output #1

2

The following two substrings satisfy the condition:

*   `GC` (the $2$\-nd through $3$\-rd characters) is complementary to `CG`, which is a permutation of `GC`.
*   `AGCT` (the $1$\-st through $4$\-th characters) is complementary to `TCGA`, which is a permutation of `AGCT`.

Input #2

4 ATAT

Output #2

4

The following four substrings satisfy the condition:

*   `AT` (the $1$\-st through $2$\-nd characters) is complementary to `TA`, which is a permutation of `AT`.
*   `TA` (the $2$\-st through $3$\-rd characters) is complementary to `AT`, which is a permutation of `TA`.
*   `AT` (the $3$\-rd through $4$\-th characters) is complementary to `TA`, which is a permutation of `AT`.
*   `ATAT` (the $1$\-st through $4$\-th characters) is complementary to `TATA`, which is a permutation of `ATAT`.

Input #3

10 AAATACCGCG

Output #3

API Response (JSON)

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  "problem": {
    "name": "DNA Sequence",
    "description": {
      "content": "We have a string $S$ of length $N$ consisting of `A`, `T`, `C`, and `G`. Strings $T_1$ and $T_2$ of the same length are said to be complementary when, for every $i$ ($1 \\leq i \\leq l$), the $i$\\-th ch",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc104_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a string $S$ of length $N$ consisting of `A`, `T`, `C`, and `G`.\nStrings $T_1$ and $T_2$ of the same length are said to be complementary when, for every $i$ ($1 \\leq i \\leq l$), the $i$\\-th ch...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments