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 (2.4.0) (judge verdict: Runtime Error)

S = input()


MOD = 10**9 + 7
# time complexity: O(|S|)
def focus_on_B(S):
    cuml = {"A": [], 
            "C": [],
            "?": []}
    current_nums = {"A": 0,
                    "C": 0,
                    "?": 0}
    for char in S:
        if char in cuml.keys():
            current_nums[char] += 1
        for key in cuml.keys():
            cuml[key].append(current_nums[key])

    num_combinations = 0
    for i in range(1, len(S) - 1):
        if S[i] in {"B", "?"}:
            A_L = cuml["A"][i-1]
            Q_L = cuml["?"][i-1]
            C_R = cuml["C"][-1] - cuml["C"][i]
            Q_R = cuml["?"][-1] - cuml["?"][i]
            num_combinations += int((A_L * 3 + Q_L) * 3**(Q_L - 1)\
                            * (C_R * 3 + Q_R) * 3**(Q_R - 1))
            num_combinations %= MOD
        else:
            continue
    print(num_combinations)


focus_on_B(S)