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.

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.

Constraints

• 3 ≤ |S| ≤ 10^5
• Each character of S is A, B, C or ?.

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.

见题面 Input 部分

见题面 Output 部分