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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

module Main where

import Data.List (subsequences)

main :: IO ()
main = interact $ show . f . readABCs . head . lines

data ABC
  = A
  | B
  | C
  deriving (Show, Eq)

f :: [[ABC]] -> Int
-- f xss = length . (filter ([A, B, C] ==)) $ subsequences =<< xss
f xss = length . (filter ([A, B, C] ==)) $ combinations 3 =<< xss

readABCs :: String -> [[ABC]]
readABCs "" = [[]]
readABCs ('A' : cs) = map (A:) $ readABCs cs
readABCs ('B' : cs) = map (B:) $ readABCs cs
readABCs ('C' : cs) = map (C:) $ readABCs cs
readABCs ('?' : cs) = (:) <$> [A, B, C] <*> readABCs cs
readABCs _ = error "readABCs: parse error"

tests :: [Bool]
tests = [test1, test2]

test1, test2 :: Bool
test1 = f (readABCs "A??C") == 8
test2 = f (readABCs "ABCBC") == 3
test3 = f (readABCs "????C?????B??????A???????") == 979596887

combinations :: Int -> [a] -> [[a]]
combinations 0 _ = [[]]
combinations _ [] = []
combinations m xxs@(x : xs) = map (x:) (combinations (m - 1) xs) ++ combinations m xs