We Love ABC

AtCoder

IDabc104_d

Time2000ms

Memory256MB

Difficulty—

The _ABC number_ of a string $T$ is the number of triples of integers $(i, j, k)$ that satisfy all of the following conditions: * $1 ≤ i < j < k ≤ |T|$ ($|T|$ is the length of $T$.) * $T_i =$ `A` ($T_i$ is the $i$\-th character of $T$ from the beginning.) * $T_j =$ `B` * $T_k =$ `C` For example, when $T =$ `ABCBC`, there are three triples of integers $(i, j, k)$ that satisfy the conditions: $(1, 2, 3), (1, 2, 5), (1, 4, 5)$. Thus, the ABC number of $T$ is $3$. You are given a string $S$. Each character of $S$ is `A`, `B`, `C` or `?`. Let $Q$ be the number of occurrences of `?` in $S$. We can make $3^Q$ strings by replacing each occurrence of `?` in $S$ with `A`, `B` or `C`. Find the sum of the ABC numbers of all these strings. This sum can be extremely large, so print the sum modulo $10^9 + 7$. ## Constraints * $3 ≤ |S| ≤ 10^5$ * Each character of $S$ is `A`, `B`, `C` or `?`. ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

A??C

Output #1

8

In this case, $Q = 2$, and we can make $3^Q = 9$ strings by by replacing each occurrence of `?` with `A`, `B` or `C`. The ABC number of each of these strings is as follows:

*   `AAAC`: $0$
*   `AABC`: $2$
*   `AACC`: $0$
*   `ABAC`: $1$
*   `ABBC`: $2$
*   `ABCC`: $2$
*   `ACAC`: $0$
*   `ACBC`: $1$
*   `ACCC`: $0$

The sum of these is $0 + 2 + 0 + 1 + 2 + 2 + 0 + 1 + 0 = 8$, so we print $8$ modulo $10^9 + 7$, that is, $8$.

Input #2

ABCBC

Output #2

3

When $Q = 0$, we print the ABC number of $S$ itself, modulo $10^9 + 7$. This string is the same as the one given as an example in the problem statement, and its ABC number is $3$.

Input #3

????C?????B??????A???????

Output #3

979596887

In this case, the sum of the ABC numbers of all the $3^Q$ strings is $2291979612924$, and we should print this number modulo $10^9 + 7$, that is, $979596887$.

API Response (JSON)

{
  "problem": {
    "name": "We Love ABC",
    "description": {
      "content": "The _ABC number_ of a string $T$ is the number of triples of integers $(i, j, k)$ that satisfy all of the following conditions: *   $1 ≤ i < j < k ≤ |T|$ ($|T|$ is the length of $T$.) *   $T_i =$ `A`",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc104_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The _ABC number_ of a string $T$ is the number of triples of integers $(i, j, k)$ that satisfy all of the following conditions:\n\n*   $1 ≤ i < j < k ≤ |T|$ ($|T|$ is the length of $T$.)\n*   $T_i =$ `A`...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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