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 Python (3.4.3) (judge verdict: Wrong Answer)

class BIT():
  def __init__(self, s):
    self.str = s
    self.size = len(s)
    self.Q = s.count('?')
    self.tree = [0] * 4
    self.ab = 0
    self.aq = 0
    self.qb = 0
    self.qq = 0
    self.abc = 0
    self.ans = 0
    
  def add(self, p, x):
    if p == '?':
      self.tree[0] += x
    elif p == 'A':
      self.tree[1] += x
    elif p == 'B':
      self.tree[2] += x
    else:
      self.tree[3] += x
  
  def count(self, p):
    if p == 'C':
      self.abc += self.ab * (3 ** self.Q)
      self.abc += self.aq * (3 ** (self.Q - 1))
      self.abc += self.qb * (3 ** (self.Q - 1))
      self.abc += self.qq * (3 ** (self.Q - 2))
      
    elif p == 'B':
      self.ab += self.tree[1]
      self.qb += self.tree[0]
      
    elif p == '?':
      self.abc += self.ab * (3 ** (self.Q - 1))
      self.abc += self.qb * (3 ** (self.Q - 2))
      self.abc += self.aq * (3 ** (self.Q - 2))
      self.abc += self.qq * (3 ** (self.Q - 3))
      self.qq += self.tree[0]
      self.aq += self.tree[1]
    else:
      pass
    
s = BIT(input())

for p in s.str:
  s.count(p)
  s.add(p, 1)
  if s.abc > 10**9 + 7:
    s.abc = s.abc % (10**9 + 7)
  
print(s.abc % (10**9 + 7))