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 (1.42.0) (judge verdict: Accepted)

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

#[derive(Copy, Clone, Debug, Eq, PartialEq)]
pub struct ModInt(u32);
impl ModInt {
    pub const MOD: u32 = 1_000_000_007;
    pub fn inv(self) -> Self {
        if self.0 == 0 {
            panic!();
        }
        self.pow(Self::MOD - 2)
    }
    pub fn one() -> Self {
        Self(1)
    }
    pub fn pow(self, e: u32) -> Self {
        if e == 0 {
            return Self::new(1);
        }
        let mut res = self.pow(e >> 1);
        res *= res;
        if e & 1 == 1 {
            res *= self;
        }
        res
    }
    pub fn zero() -> Self {
        Self(0)
    }
    fn new(n: i64) -> Self {
        let mut n = n % (Self::MOD as i64);
        if n.is_negative() {
            n += Self::MOD as i64;
        }
        Self(n as u32)
    }
}
impl From<i32> for ModInt {
    fn from(n: i32) -> Self {
        ModInt::from(n as i64)
    }
}
impl From<i64> for ModInt {
    fn from(n: i64) -> Self {
        Self::new(n)
    }
}
impl From<isize> for ModInt {
    fn from(n: isize) -> Self {
        ModInt::from(n as i64)
    }
}
impl From<u32> for ModInt {
    fn from(n: u32) -> Self {
        ModInt::from(n as u64)
    }
}
impl From<u64> for ModInt {
    fn from(n: u64) -> Self {
        Self::new(n as i64)
    }
}
impl From<usize> for ModInt {
    fn from(n: usize) -> Self {
        ModInt::from(n as u64)
    }
}
impl Into<i32> for ModInt {
    fn into(self) -> i32 {
        self.0 as i32
    }
}
impl Into<i64> for ModInt {
    fn into(self) -> i64 {
        self.0 as i64
    }
}
impl Into<isize> for ModInt {
    fn into(self) -> isize {
        self.0 as isize
    }
}
impl Into<u32> for ModInt {
    fn into(self) -> u32 {
        self.0
    }
}
impl Into<u64> for ModInt {
    fn into(self) -> u64 {
        self.0 as u64
    }
}
impl Into<usize> for ModInt {
    fn into(self) -> usize {
        self.0 as usize
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        Self::new((self.0 + rhs.0) as i64)
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.inv()
    }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        Self::new((self.0 as i64) * (rhs.0 as i64))
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        Self::new((self.0 as i64) - (rhs.0 as i64))
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

fn solve() {
    input! {
        s: Chars
    };

    let len = s.len();
    // dp[i][j] = 個数
    // j = 1 / Aの個数
    // j = 2 / ABの個数
    // j = 3 / ABCの個数
    let mut dp = vec![vec![ModInt::zero(); 3]; len + 1];
    let mut pat = ModInt::one();
    for i in 0..len {
        match s[i] {
            'A' => {
                dp[i + 1][0] = pat + dp[i][0];
                dp[i + 1][1] = dp[i][1];
                dp[i + 1][2] = dp[i][2];
            }
            'B' => {
                dp[i + 1][0] = dp[i][0];
                dp[i + 1][1] = dp[i][1] + dp[i][0];
                dp[i + 1][2] = dp[i][2];
            }
            'C' => {
                dp[i + 1][0] = dp[i][0];
                dp[i + 1][1] = dp[i][1];
                dp[i + 1][2] = dp[i][2] + dp[i][1];
            }
            _ => {
                // ?
                dp[i + 1][0] = pat + dp[i][0] * ModInt::from(3);
                dp[i + 1][1] = dp[i][1] * ModInt::from(3) + dp[i][0];
                dp[i + 1][2] = dp[i][2] * ModInt::from(3) + dp[i][1];
                pat *= ModInt::from(3);
            }
        }
    }
    println!("{}", dp[len][2]);
}

fn main() {
    std::thread::Builder::new()
        .name("big stack size".into())
        .stack_size(256 * 1024 * 1024)
        .spawn(|| {
            solve();
        })
        .unwrap()
        .join()
        .unwrap();
}