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: Wrong Answer)

# p ['A', ?'].map(&:ord) #=> [65, 63]
s = gets.to_s.chomp.bytes.map{ |i| i == 63 ? 0 : i - 64 }
n = s.size

dp = Array.new(s.size+1){ [0] * 3 }
m = 10 ** 9 + 7
v = 0
s.each_with_index do |c,i|
  # p [c, i]
  
  # v += 1 if c == 0
  
  if c == 0
    v += 1
    v %= m
    # x = 3** v
    dp[i+1][0] = (dp[i][0] * 3 + 3**(v -1) ) % m
    dp[i+1][1] = (dp[i][1] * 3 + dp[i][0]) % m
    dp[i+1][2] = (dp[i][2] * 3 + dp[i][1]) % m
  else
    dp[i+1][0] = (dp[i][0])
    dp[i+1][1] = (dp[i][1])
    dp[i+1][2] = (dp[i][2])
  end
  
  dp[i+1][0] += 1 if c == 1
  dp[i+1][1] += dp[i][0] % m if c == 2
  dp[i+1][2] += dp[i][1] % m if c == 3
end
# pp dp
puts dp[n][2] % m