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 Rust (1.15.1) (judge verdict: Wrong Answer)

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn main() {
    let s: String = read();
    let s = s.chars().collect::<Vec<char>>();
    let mut dp: Vec<Vec<i64>> = vec![vec![0; 4]; s.len() + 1];
    let big_num: i64 = 1000_0000 + 7;
    dp[0][0] = 1;
    for i in 0..s.len() {
        for j in 0..4 {
            if s[i] == '?' {
                dp[i + 1][j] = (dp[i + 1][j] + 3 * dp[i][j]) % big_num;
            } else {
                dp[i + 1][j] = (dp[i + 1][j] + dp[i][j]) % big_num;
            }
            if (s[i] == 'A' && j == 0)
                || (s[i] == 'B' && j == 1)
                || (s[i] == 'C' && j == 2)
                || (s[i] == '?')
            {
                if j != 3 {
                    dp[i + 1][j + 1] = (dp[i + 1][j + 1] + dp[i][j]) % big_num;
                }
            }
        }
    }
    // println!("{:?}", dp);
    println!("{:?}", dp[s.len()][3]);
}