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: Time Limit Exceeded)

sen = gets.chomp.split("")
len = sen.length


arr1 = [0,0,0,0]
arr2 = [sen.count("A"),sen.count("B"),sen.count("C"),sen.count("?")]
if sen[0] == "A"
     arr2[0]-=1
 end
 
 if sen[0] == "B"
     arr2[1]-=1
 end
 
 if sen[0] == "C"
     arr2[2]-=1
 end
 
 if sen[0] == "?"
     arr2[3]-=1
 end

ans = 0
key = 10**9+7

i = 0

len.times{
    
   
    
    if sen[i]=="B" || sen[i]=="?"
        
    left = arr1[0]*(3**arr1[3])+arr1[3]*(3**(arr1[3]-1))
    right = arr2[2]*(3**arr2[3])+arr2[3]*(3**(arr2[3]-1))
    
    
    
    ans+=left*right
    ans = ans.to_i
   end
   
   
   
   
   
   if sen[i]=="A"
        arr1[0]+=1
    end
    if sen[i]=="B"
        arr1[1]+=1
    end
    
    if sen[i]=="C"
        arr1[2]+=1
    end
    
    if sen[i]=="?"
        arr1[3]+=1
    end
    
    
    if sen[i+1] == "A"
    arr2[0]-=1
    end
    if sen[i+1] == "B"
    arr2[1]-=1
    end
    if sen[i+1] == "C"
    arr2[2]-=1
    end
    if sen[i+1] == "?"
    arr2[3]-=1
    end
    
    
    
    i+=1
   
}


print ans%key