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: Accepted)

#[allow(unused_macros)]
macro_rules! vec_md {
    ( $ init : expr ; $ ( $ dim : expr ) ;* ) => { vec_md ! ( $ ( $ dim ) ;* => $ init ) };
    ( $ head : expr ; $ ( $ tail : expr ) ;* => $ init : expr ) => { vec ! [ vec_md ! ( $ ( $ tail ) ;* => $ init ) ; $ head ] };
    ( $ head : expr => $ init : expr ) => { vec ! [ $ init ; $ head ] };
}

#[allow(dead_code)]
pub const M: u64 = 1_000_000_007;

fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let s: Vec<char> = iter.next().unwrap().chars().collect();
    let n = s.len() as usize;
    let mut dp = vec_md![0u64;n + 1;4];
    dp[0][0] = 1;
    for i in 0..n {
        let k = match s[i] {
            'A'|'B'|'C' => 1,
            _ => 3
        };
        for j in 0..4 {
            dp[i+1][j] = k * dp[i][j] % M;
        }
        match s[i] {
            'A' => {
                dp[i+1][1] += dp[i][0];
                dp[i+1][1] %= M;
            },
            'B' => {
                dp[i+1][2] += dp[i][1];
                dp[i+1][2] %= M;
            },
            'C' => {
                dp[i+1][3] += dp[i][2];
                dp[i+1][3] %= M;
                
            },
            _ => {
                for j in 0..3 {
                    dp[i+1][j+1] += dp[i][j];
                    dp[i+1][j+1] %= M;
                }
            }
        }
    }
    println!("{}", dp[n][3]);
}