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::stdin;

const MOD: i64 = 1000000007;

fn powmod(x: i64, n: i64) -> i64 {
    if n == 0 {
        1
    } else {
        let sq = powmod(x, n / 2);
        let sqsq = sq * sq % MOD;
        if n % 2 == 1 {
            sqsq * x % MOD
        } else {
            sqsq
        }
    }
}

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    let s = buf.trim_right();
    let count = |ch| {
        s.chars().filter(|&c| c == ch).count() as i64
    };


    let ccount = count('C');
    let qcount = count('?');

    let mut preva = 0 as i64;
    let mut prevb = 0 as i64;
    let mut prevc = 0 as i64;
    let mut prevq = 0 as i64;

    let mut ans = 0 as i64;

    for ch in s.chars() {
        if ch == 'B' || ch == '?' {
            let afterc = ccount - prevc;
            let afterq = (qcount - prevq) - ((ch == '?') as i64);

            let freeq = prevq + afterq;
            ans += preva * afterc % MOD * powmod(3, freeq) % MOD;
            ans %= MOD;

            if prevq > 0 {
                ans += prevq * afterc % MOD * powmod(3, freeq - 1) % MOD;
                ans %= MOD;
            }
            if afterq > 0 {
                ans += preva * afterq % MOD * powmod(3, freeq - 1) % MOD;
                ans %= MOD;
            }
            if prevq > 0 && afterq > 0 {
                ans += prevq * afterq % MOD * powmod(3, freeq - 2) % MOD;
                ans %= MOD;
            }
        }
        let upd = if ch == 'A' {
            &mut preva
        } else if ch == 'B' {
            &mut prevb
        } else if ch == 'C' {
            &mut prevc
        } else {
            &mut prevq
        };
        *upd += 1;
    }

    println!("{}", ans)
}