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)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

const MOD: i64 = 1e+9 as i64 + 7;

fn main() {
    let s = read::<String>().chars().collect::<Vec<char>>();
    let n = s.len();
    let mut acnt = vec![0; n + 1];
    let mut ccnt = vec![0; n + 1];
    let mut qcnt = vec![0; n + 1];
    let mut threes = vec![1; n + 1];
    for i in 0..n {
        threes[i + 1] = threes[i] * 3 % MOD;
    }
    for i in 0..n {
        acnt[i + 1] += acnt[i];
        ccnt[i + 1] += ccnt[i];
        qcnt[i + 1] += qcnt[i];
        if s[i] == 'A' {
            acnt[i + 1] += 1;
        } else if s[i] == 'C' {
            ccnt[i + 1] += 1;
        } else if s[i] == '?' {
            qcnt[i + 1] += 1;
        }
    }
    let mut ans = 0;
    for i in 0..n {
        if s[i] != 'B' && s[i] != '?' {
            continue;
        }
        let lq = qcnt[i];
        let la = acnt[i];
        let mut l = la * threes[lq as usize] % MOD;
        if lq > 0 {
            l = (l + lq * threes[lq as usize - 1]) % MOD;
        }
        let rq = qcnt[n] - qcnt[i + 1];
        let rc = ccnt[n] - ccnt[i + 1];
        let mut r = rc * threes[rq as usize] % MOD;
        if rq > 0 {
            r = (r + rq * threes[rq as usize - 1]) % MOD;
        }
        ans = (ans + l * r) % MOD;
    }
    println!("{}", ans);
}