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_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Read, Write, BufWriter};
#[allow(dead_code)]
fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}
fn get_word() -> String {
    let mut stdin = std::io::stdin();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

const MOD: i64 = 1_000_000_007;

/// Refers external ::MOD.
/// Verified by: https://beta.atcoder.jp/contests/arc099/submissions/2893648
mod mod_int {
    use ::MOD;
    use std::ops::*;
    #[derive(Copy, Clone, Debug, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt { pub x: i64 }
    impl ModInt {
        fn check_integrity(self) {
            debug_assert!(self.x >= 0);
            debug_assert!(self.x < MOD);
        }
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt { x: x % MOD } }
        #[allow(dead_code)]
        pub fn mul_fast(self, other: Self) -> Self {
            self.check_integrity();
            other.check_integrity();
            ModInt { x: self.x * other.x % MOD }
        }
        #[allow(dead_code)]
        pub fn mul_slow(self, other: Self) -> Self {
            // Naive multiplication in order to avoid overflow
            self.check_integrity();
            other.check_integrity();
            let mut sum = ModInt::new(0);
            let mut cur = self;
            let mut e = other.x;
            if self.x < other.x {
                cur = other;
                e = self.x;
            }
            while e > 0 {
                if e % 2 == 1 {
                    sum = sum + cur;
                }
                cur = cur + cur;
                e /= 2;
            }
            sum
        }
        pub fn pow(self, mut e: i64) -> Self {
            self.check_integrity();
            debug_assert!(e >= 0);
            let mut sum = ModInt::new(1);
            let mut cur = ModInt::new(self.x);
            while e > 0 {
                if e % 2 != 0 {
                    sum = sum * cur;
                }
                cur = cur * cur;
                e /= 2;
            }
            sum
        }
        pub fn inv(self) -> Self { self.pow(MOD - 2) }
    }
    impl Add for ModInt {
        type Output = Self;
        fn add(self, other: Self) -> Self {
            self.check_integrity();
            other.check_integrity();
            let mut sum = self.x + other.x;
            if sum >= MOD { sum -= MOD; }
            ModInt { x: sum }
        }
    }
    impl Sub for ModInt {
        type Output = Self;
        fn sub(self, other: Self) -> Self {
            self.check_integrity();
            other.check_integrity();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += MOD; }
            ModInt { x: sum }
        }
    }
    impl Mul for ModInt {
        type Output = Self;
        fn mul(self, other: Self) -> Self {
            self.mul_fast(other)
        }
    }
    impl ::std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
} // mod mod_int

use mod_int::*;


fn solve() {
    let s: Vec<_> = get_word().chars().collect();
    let n = s.len();
    let mut dp = vec![vec![ModInt::new(0); n + 1]; 4];
    dp[0][0] = ModInt::new(1);
    let abc = ['A', 'B', 'C'];
    for i in 0 .. n {
        for d in 0 .. 3 {
            if s[i] == '?' || s[i] == abc[d] {
                dp[d + 1][i + 1] = dp[d + 1][i + 1] + dp[d][i];
            }
        }
        let fac = ModInt::new(if s[i] == '?' { 3 } else { 1 });
        for d in 0 .. 4 {
            dp[d][i + 1] = dp[d][i + 1] + fac * dp[d][i];
        }
    }
    println!("{}", dp[3][n]);
}

fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}