Problem:
Score : 400 points

Problem Statement

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

Output

Print the sum of the ABC numbers of all the 3^Q strings, modulo 10^9 + 7.

Sample Input 1

A??C

Sample 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.

Sample Input 2

ABCBC

Sample 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.

Sample Input 3

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

Sample 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.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import java.util.Scanner

object Main {
  val MOD = 1000000007L

  def main(args: Array[String]): Unit = {
    val sc = new Scanner(System.in)
    val S = sc.next()

    println(solve(S))
  }

  def solve(S: String): String = {
    val N = S.length
    val dp = new Array[(Long, Long, Long, Long)](N + 1) // A, AB, ABC, X
    dp.update(0, (0, 0, 0, 1))
    for (i <- 1 to N) {
      if (S.charAt(i - 1) == 'A') {
        dp.update(
          i,
          (
            (dp(i - 1)._1 + dp(i - 1)._4) % MOD,
            dp(i - 1)._2,
            dp(i - 1)._3,
            dp(i - 1)._4
          )
        )
      } else if (S.charAt(i - 1) == 'B') {
        dp.update(
          i,
          (
            dp(i - 1)._1,
            (dp(i - 1)._2 + dp(i - 1)._1) % MOD,
            dp(i - 1)._3,
            dp(i - 1)._4
          )
        )
      } else if (S.charAt(i - 1) == 'C') {
        dp.update(
          i,
          (
            dp(i - 1)._1,
            dp(i - 1)._2,
            (dp(i - 1)._3 + dp(i - 1)._2) % MOD,
            dp(i - 1)._4
          )
        )
      } else if (S.charAt(i - 1) == '?') {
        dp.update(
          i,
          (
            (dp(i - 1)._1 * 3 % MOD + dp(i - 1)._4) % MOD,
            (dp(i - 1)._2 * 3 % MOD + dp(i - 1)._1) % MOD,
            (dp(i - 1)._3 * 3 % MOD + dp(i - 1)._2) % MOD,
            dp(i - 1)._4 * 3 % MOD
          )
        )
      }
    }
    dp(N)._3.toString
  }
}