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(dead_code)]
const MOD: u64 = 1000000007;
fn main() {
    let buf = io::read_string();
    let mut sc = io::Scanner::new(&buf);
    let s: String = sc.read();
    let s = s.into_bytes();
    let abc: Vec<u8> = "ABC".bytes().collect();
    let n = s.len();
    let mut dp = vec![vec![0u64; 4]; n+1];
    dp[n][3] = 1;
    for i in (0..n).rev() {
        for j in (0..4).rev() {
            let k = if s[i] == b'?' { 3 } else { 1 };
            dp[i][j] = k * dp[i + 1][j];
            if j < 3 {
                let k2 = if s[i] == b'?' || s[i] == abc[j] { 1 } else { 0 };
                dp[i][j] += k2 * dp[i + 1][j + 1];
            }
            dp[i][j] %= MOD;
        }
    }
    println!("{}", dp[0][0]);
}
#[allow(dead_code)]
mod io {
    use std;
    use std::io::Read;
    use std::str::{FromStr, SplitWhitespace};
    pub struct Scanner<'a> {
        pub iter: SplitWhitespace<'a>,
    }
    impl<'a> Scanner<'a> {
        pub fn new(s: &'a str) -> Scanner<'a> {
            Scanner {
                iter: s.split_whitespace(),
            }
        }
        pub fn read<T: FromStr>(&mut self) -> T {
            self.iter
                .next()
                .unwrap()
                .parse()
                .ok()
                .expect("parsing failed")
        }
        pub fn read_vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
            (0..n).map(|_| self.read()).collect()
        }
    }
    pub fn read_string() -> String {
        let mut s = String::new();
        std::io::stdin().read_to_string(&mut s).unwrap();
        s
    }
}