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 PyPy3 (7.3.0) (judge verdict: Accepted)

def getval():
    s = input()
    return s
    
def main(s):
    #dp for "a","ab","abc"
    mod = 10**9 + 7
    dp = [0,0,0,0]
    p3 = [1]
    for i in range(len(s)):
        p3.append((3*p3[i])%mod)
    for i in s:
        if i=="A":
            dp[0] += p3[dp[3]]
            dp[0] %= mod
        elif i=="B":
            dp[1] += dp[0]
            dp[1] %= mod
        elif i=="C":
            dp[2] += dp[1]
            dp[2] %= mod
        else:
            temp1 = dp[0]*2
            temp2 = dp[1]*2
            temp3 = dp[2]*2
            dp[2] += dp[1]
            dp[1] += dp[0]
            dp[0] += p3[dp[3]]
            dp[2] += temp3
            dp[1] += temp2
            dp[0] += temp1
            dp[3] += 1
            for j in range(3):
                dp[j] %= mod
            #print(dp)
    print(dp[2])

if __name__=="__main__":
    s = getval()
    main(s)