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: Time Limit Exceeded)

S = input()

max_S = 10**9 + 7

N_Q = S.count("?")
N_C = S.count("C")

t_A = 0
t_Q = 0
if(S[0:1] == "C"):
    t_C = N_C - 1
else:
    t_C = N_C

S_list = [{"bA": t_A, "bQ": t_Q, "aC": t_C, "aQ": N_Q - t_Q}]
for i in range(1, len(S)):
    if(S[i - 1:i] == "A"):
        t_A += 1
    elif(S[i - 1:i] == "?"):
        t_Q += 1

    ba_dic = {}
    ba_dic["bA"] = t_A
    ba_dic["bQ"] = t_Q
    if(S[i:i + 1] == "?"):
        ba_dic["aQ"] = N_Q - t_Q - 1
    else:
        ba_dic["aQ"] = N_Q - t_Q
    if(S[i:i + 1] == "C"):
        t_C -= 1
    ba_dic["aC"] = t_C

    S_list.append(ba_dic)

ans = 0
for i in range(len(S)):
    if(S[i:i + 1] == "A" or S[i:i + 1] == "C"):
        continue

    bA = S_list[i]["bA"]
    bQ = S_list[i]["bQ"]
    aC = S_list[i]["aC"]
    aQ = S_list[i]["aQ"]

    ans += bA * aC * int(3**(bQ + aQ))
    ans = ans % max_S

    ans += bQ * aQ * int(3**(bQ + aQ - 2))
    ans = ans % max_S

    ans += (bA * aQ + bQ * aC) * int(3**(bQ + aQ - 1))
    ans = ans % max_S

print(ans)