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 Ruby (2.3.3) (judge verdict: Accepted)

S = gets.chomp
M = 1e9.to_i + 7

def mpow(x, n)
  ret = 1
  while n > 0
    if n.even?
      x = x * x % M
      n >>= 1
    else
      ret = ret * x % M
      n -= 1
    end
  end
  ret
end

N = S.length
as, cs, qs = [], [], []
as[0], cs[0], qs[0] = 0, 0, 0
(1 .. N).each do |i|
  as[i], cs[i], qs[i] = as[i - 1], cs[i - 1], qs[i - 1]
  case S[i - 1]
  when 'A'
    as[i] += 1
  when 'C'
    cs[i] += 1
  when '?'
    qs[i] += 1
  end
end
res = 0
(2 ... N).each do |i|
  if S[i - 1] == 'B' || S[i - 1] == '?'
    a, q = as[i - 1], qs[i - 1]
    la = a * mpow(3, q) + q * mpow(3, q - 1)
    c, q = cs[N] - cs[i], qs[N] - qs[i]
    rc = c * mpow(3, q) + q * mpow(3, q - 1)
    res = (res + la*rc) % M
  end
end
puts res