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)

// ternary operation
#[allow(unused_macros)]
macro_rules! _if {
  ($_test:expr, $_then:expr, $_else:expr) => {
    if $_test { $_then } else { $_else }
  };
  ($_test:expr, $_pat:pat, $_then:expr, $_else:expr) => {
    match $_test {
      $_pat => $_then,
      _     => $_else
    }
  };
}

use std::io::{ stdin, stdout, Write };
use my::WriteWithDelim;

#[inline(always)]
fn abc104_d() {
  let stdin  = stdin();
  let stdout = stdout();
  let (mut reader, mut writer) = my::rw(12, stdin.lock(), stdout.lock());
  let mut i2b = my::Int2Byte::with_capacity(8);

  let m = 1_000_000_000 + 7;
  let s = reader.read_byte_until_lf();

  let mut dp = [1, 0, 0, 0];
  for b in s {
    match b {
      b'A' => dp[1] = (dp[1] + dp[0]) % m,
      b'B' => dp[2] = (dp[2] + dp[1]) % m,
      b'C' => dp[3] = (dp[3] + dp[2]) % m,
      _    => {
        dp[3] = (dp[3] * 3 + dp[2]) % m;
        dp[2] = (dp[2] * 3 + dp[1]) % m;
        dp[1] = (dp[1] * 3 + dp[0]) % m;
        dp[0] = (dp[0] * 3        ) % m;
      }
    }
  }

  writer.write_lf(i2b.from_u64(dp[3])).unwrap();
  writer.flush().unwrap();
}

fn main() {
  abc104_d();
}

//------------------------------------------------------------------------
mod my {
  use std::hash::Hasher;
  use std::hash::BuildHasher;

  pub struct MyHasher(u64);

  impl Default for MyHasher {
    #[inline(always)]
    fn default() -> Self {
      MyHasher(0x00)
    }
  }

  impl BuildHasher for MyHasher {
    type Hasher = MyHasher;

    #[inline(always)]
    fn build_hasher(&self) -> Self::Hasher {
      Self::Hasher::default()
    }
  }

  impl Hasher for MyHasher {
    #[inline(always)]
    fn finish(&self) -> u64 {
      self.0
    }

    #[inline(always)]
    fn write(&mut self, bytes: &[u8]) {
      self.0 = 0;
      for i in 0..bytes.len() {
        self.0 ^= (bytes[i] as u64) << (8 * (i % 8));
      }
    }
  }

  //----------------------------------------------------------------------
  use std::io::{ self, BufRead, BufReader, Write, BufWriter };
  use std::fmt::Debug;
  use std::ops::{ Add, Sub, Mul, Neg, Rem };
  use std::str::{ self, FromStr };
  use std::mem;

  const PLUS_SIGN : u8 = b'+';
  const MINUS_SIGN: u8 = b'-';
  const ASCII_0   : u8 = b'0';
  const ASCII_9   : u8 = b'9';

  const SP        : u8 = b' ';
  const LF        : u8 = b'\n';

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn rotate_right(ary: &mut [u8]) {
    if ary.len() <= 1 {
      return;
    }

    let len = ary.len() - 1;
    let tmp = ary[len];
    for i in 0..len {
      ary[len - i] = ary[len - i - 1];
    }
    ary[0] = tmp;
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn rotate_left(ary: &mut [u8]) {
    if ary.len() <= 1 {
      return;
    }

    let len = ary.len() - 1;
    let tmp = ary[0];
    for i in 0..len {
      ary[i] = ary[i + 1];
    }
    ary[len] = tmp;
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn gcd<T>(x: T, y: T) -> T
    where T: Rem<Output=T> +
             Default +
             PartialEq +
             Copy +
             Debug
  {
    _if!(y == T::default(),
      x,
      gcd(y, x % y))
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn intersection<T>(mut x: (T, T), mut y: (T, T)) -> Option<(T, T)>
    where T: PartialOrd +
             Copy +
             Debug
  {
    if x.0 > x.1 {
      mem::swap(&mut x.0, &mut x.1);
    }
    if y.0 > y.1 {
      mem::swap(&mut y.0, &mut y.1);
    }

    if x.0 >= y.1 || x.1 <= y.0 {
      return None;
    }

    if x.0 < y.0 {
      x.0 = y.0;
    }
    if x.1 > y.1 {
      x.1 = y.1;
    }

    Some(x)
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_digit(b: u8) -> bool {
    _if!(b >= ASCII_0 && b <= ASCII_9,
      true,
      false)
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_uppercase(b: u8) -> bool {
    _if!(b >= b'A' && b <= b'Z',
      true,
      false)
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_lowercase(b: u8) -> bool {
    _if!(b >= b'a' && b <= b'z',
      true,
      false)
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn is_ascii_alphabetic(b: u8) -> bool {
    _if!(is_ascii_uppercase(b) || is_ascii_lowercase(b),
      true,
      false)
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn to_ascii_lowercase(b: u8) -> u8 {
    _if!(is_ascii_uppercase(b),
      b + 0x20,
      b)
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn to_ascii_uppercase(b: u8) -> u8 {
    _if!(is_ascii_lowercase(b),
      b - 0x20,
      b)
  }

  //----------------------------------------------------------------------
  pub trait WriteWithDelim {
    fn write_delim(&mut self, buf: &[u8], delim: &[u8]) -> Result<usize, io::Error>;
    fn write_sp(&mut self, buf: &[u8]) -> Result<usize, io::Error>;
    fn write_lf(&mut self, buf: &[u8]) -> Result<usize, io::Error>;
  }

  impl<W> WriteWithDelim for BufWriter<W>
    where W: io::Write
  {
    #[allow(dead_code)]
    #[inline(always)]
    fn write_delim(&mut self, buf: &[u8], delim: &[u8]) -> Result<usize, io::Error>
    {
      Ok(self.write(buf)? + self.write(delim)?)
    }

    #[allow(dead_code)]
    #[inline(always)]
    fn write_sp(&mut self, buf: &[u8]) -> Result<usize, io::Error>
    {
      self.write_delim(buf, b" ")
    }

    #[allow(dead_code)]
    #[inline(always)]
    fn write_lf(&mut self, buf: &[u8]) -> Result<usize, io::Error>
    {
      self.write_delim(buf, b"\n")
    }
  } // impl<W> WriteWithDelim for BufWriter<W>

  //----------------------------------------------------------------------
  macro_rules! pub_fn_Int2Byte_from_ty {
    (uint, $($name:ident => $_type:ty),*) => {$(
      #[allow(dead_code)]
      #[inline(always)]
      pub fn $name(&mut self, mut n: $_type) -> &[u8] {
        self.buf.clear();
        if n == 0 {
          self.buf.push(ASCII_0);
          return self.buf.as_slice();
        }

        while n > 0 {
          self.buf.push((n % 10) as u8 + ASCII_0);
          n /= 10;
        }
        self.buf.reverse();
        self.buf.as_slice()
      }
    )*};

    (int, $($name:ident => $_type:ty),*) => {$(
      #[allow(dead_code)]
      #[inline(always)]
      pub fn $name(&mut self, mut n: $_type) -> &[u8] {
        self.buf.clear();
        if n == 0 {
          self.buf.push(ASCII_0);
          return self.buf.as_slice();
        }

        let mut negative = false;
        if n.is_negative() {
          negative = true;
          n = n.abs();
        }

        while n > 0 {
          self.buf.push((n % 10) as u8 + ASCII_0);
          n /= 10;
        }
        if negative {
          self.buf.push(MINUS_SIGN);
        }
        self.buf.reverse();
        self.buf.as_slice()
      }
    )*};
  }

  #[derive(Debug)]
  pub struct Int2Byte {
    buf: Vec<u8>,
  }

  impl Int2Byte {
    #[allow(dead_code)]
    #[inline(always)]
    pub fn new() -> Self {
      Int2Byte {
        buf: Vec::new(),
      }
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn with_capacity(capa: usize) -> Self {
      Int2Byte {
        buf: Vec::with_capacity(capa),
      }
    }

    pub_fn_Int2Byte_from_ty!(
      uint,
      from_usize => usize,
      from_u8    => u8,
      from_u16   => u16,
      from_u32   => u32,
      from_u64   => u64
    );

    pub_fn_Int2Byte_from_ty!(
      int,
      from_isize => isize,
      from_i8    => i8,
      from_i16   => i16,
      from_i32   => i32,
      from_i64   => i64
    );
  } // impl Int2Byte

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[inline(always)]
  pub fn rw<R, W>(rcap: usize, r: R, w: W) -> (ByteReader<BufReader<R>>, BufWriter<W>)
    where R: BufRead,
          W: io::Write
  {
    (
      ByteReader::with_capacity(rcap, BufReader::new(r)),
      BufWriter::new(w)
    )
  }

  #[allow(dead_code)]
  #[inline(always)]
  pub fn w<W>(w: W) -> BufWriter<W>
    where W: io::Write
  {
    BufWriter::new(w)
  }

  //----------------------------------------------------------------------
  #[allow(dead_code)]
  #[derive(Debug)]
  pub enum Direction {
    Horizontal,
    Vertical
  }

  #[derive(Debug)]
  pub struct ByteReader<R> {
    reader: R,
    buf   : Vec<u8>,
  }

  impl<R> ByteReader<R>
    where R: BufRead
  {
    #[allow(dead_code)]
    #[inline(always)]
    pub fn new(reader: R) -> Self {
      ByteReader {
        reader: reader,
        buf   : Vec::new(),
      }
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn with_capacity(capa: usize, reader: R) -> Self {
      ByteReader {
        reader: reader,
        buf   : Vec::with_capacity(capa),
      }
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn reserve(&mut self, additional: usize) {
      self.buf.reserve(additional);
    }

    //--------------------------------------------------------------------
    #[inline(always)]
    fn read_until(&mut self, delim: u8) -> usize {
      self.buf.clear();
      self.reader.read_until(delim, &mut self.buf).unwrap()
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_1byte(&mut self) -> Option<u8> {
      self.buf.resize(1, 0);
      _if!(self.reader.read(&mut self.buf).unwrap() != 0,
        Some(self.buf[0]),
        None)
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_byte_until_lf(&mut self) -> Vec<u8> {
      self.read_until(LF);
      let len = self.buf.len() - 1;
      if self.buf[len] == LF {
        self.buf.truncate(len);
      }
      self.buf.clone()
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_string_until_lf(&mut self) -> String {
      unsafe { String::from_utf8_unchecked(self.read_byte_until_lf()) }
    }

    //--------------------------------------------------------------------
    #[inline(always)]
    fn parse_int<T>(&self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let len = self.buf.len();
      let mut i = 0;
      let mut n = T::default();
      let mut minus = false;

      if self.buf[i] == MINUS_SIGN {
        minus = true;
        i += 1;
      } else if self.buf[i] == PLUS_SIGN {
        i += 1;
      }

      while i < len && is_ascii_digit(self.buf[i]) {
        n = (n * T::from(10)) + T::from(self.buf[i] - ASCII_0);
        i += 1;
      }

      _if!(minus,
        n.neg(),
        n)
    }

    #[inline(always)]
    fn parse_uint<T>(&self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let len = self.buf.len();
      let mut i = 0;
      let mut n = T::default();

      if self.buf[i] == PLUS_SIGN {
        i += 1;
      }

      while i < len && is_ascii_digit(self.buf[i]) {
        n = (n * T::from(10)) + T::from(self.buf[i] - ASCII_0);
        i += 1;
      }
      n
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_until_delim<T>(&mut self, delim: u8) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_until(delim);
      self.parse_int()
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_until_lf<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_int_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_until_sp<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_int_until_delim(SP)
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_until_delim<T>(&mut self, delim: u8) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_until(delim);
      self.parse_uint()
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_until_lf<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_uint_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_until_sp<T>(&mut self) -> T
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      self.read_uint_until_delim(SP)
    }

    //--------------------------------------------------------------------
    #[inline(always)]
    fn from_utf8_unchecked(&mut self) -> &str {
      unsafe { str::from_utf8_unchecked(&self.buf) }
    }

    #[inline(always)]
    fn parse_tok<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.from_utf8_unchecked()
        .trim()
        .parse()
        .unwrap()
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn parse_until_delim<T>(&mut self, delim: u8) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.read_until(delim);
      self.parse_tok()
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn parse_until_lf<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.parse_until_delim(LF)
    }

    // s -> n
    #[allow(dead_code)]
    #[inline(always)]
    pub fn parse_until_sp<T>(&mut self) -> T
      where T: FromStr + Debug,
            <T as FromStr>::Err: Debug
    {
      self.parse_until_delim(SP)
    }

    //--------------------------------------------------------------------
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_vec<T>(&mut self, n: usize, dir: Direction) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let delim = _if!(dir, Direction::Horizontal, SP, LF);
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n - 1 {
        vec.push(self.read_int_until_delim(delim));
      }
      vec.push(self.read_int_until_delim(LF));
      vec
    }

    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_vec<T>(&mut self, n: usize, dir: Direction) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let delim = _if!(dir, Direction::Horizontal, SP, LF);
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n - 1 {
        vec.push(self.read_uint_until_delim(delim));
      }
      vec.push(self.read_uint_until_delim(LF));
      vec
    }

    // horizontal
    //
    // N
    // s1 s2 s3, ..., sN -> [n1, n2, n3, ..., nN]
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_vec_h<T>(&mut self) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let n: usize = self.read_uint_until_lf();
      self.read_int_vec(n, Direction::Horizontal)
    }

    // horizontal
    //
    // N
    // s1 s2 s3, ..., sN -> [n1, n2, n3, ..., nN]
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_vec_h<T>(&mut self) -> Vec<T>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let n: usize = self.read_uint_until_lf();
      self.read_uint_vec(n, Direction::Horizontal)
    }

    // N M
    // s11 s12 s13 ... s1M
    // s21 s22 s23 ... s2M
    // s31 s32 s33 ... s3M
    //   :
    // sN1 sN2 sN3 ... sNM
    // -> [
    //      [n11, n12, n13, ..., n1M],
    //      [n21, n22, n23, ..., n2M],
    //      [n31, n32, n33, ..., n3M],
    //          :
    //      [nN1, nN2, nN3, ..., nNM],
    //    ]
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_uint_vec2<T>(&mut self, n: usize, m: usize) -> Vec<Vec<T>>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n {
        vec.push(self.read_uint_vec(m, Direction::Horizontal));
      }
      vec
    }

    // N M
    // s11 s12 s13 ... s1M
    // s21 s22 s23 ... s2M
    // s31 s32 s33 ... s3M
    //   :
    // sN1 sN2 sN3 ... sNM
    // -> [
    //      [n11, n12, n13, ..., n1M],
    //      [n21, n22, n23, ..., n2M],
    //      [n31, n32, n33, ..., n3M],
    //          :
    //      [nN1, nN2, nN3, ..., nNM],
    //    ]
    #[allow(dead_code)]
    #[inline(always)]
    pub fn read_int_vec2<T>(&mut self, n: usize, m: usize) -> Vec<Vec<T>>
      where T: Add<Output=T> +
               Sub<Output=T> +
               Mul<Output=T> +
               Neg<Output=T> +
               Default +
               From<u8> +
               Debug
    {
      let mut vec = Vec::with_capacity(n);
      for _ in 0..n {
        vec.push(self.read_int_vec(m, Direction::Horizontal));
      }
      vec
    }

  } // impl<R> ByteReader<R>

} // mod my