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 Python (2.7.6) (judge verdict: Accepted)

#!/usr/bin/env python

from collections import deque
import itertools as it
import sys
import math

sys.setrecursionlimit(10000000)

S = raw_input()
sz = len(S)

A = [0 for i in range(sz)]
C = [0 for i in range(sz)]

cnt = 0
for i in range(sz):
    if S[i] == 'A':
        cnt += 3
    if S[i] == '?':
        cnt += 1
    A[i] = cnt

cnt = 0
for i in range(sz - 1, -1, -1):
    if S[i] == 'C':
        cnt += 3
    if S[i] == '?':
        cnt += 1
    C[i] = cnt

ans = 0
MOD = 10 ** 9 + 7
for i in range(1, sz - 1):
    if S[i] == 'B':
        ans += A[i - 1] * C[i + 1] * 3
        ans %= MOD
    if S[i] == '?':
        ans += A[i - 1] * C[i + 1]
        ans %= MOD

def inv(n):
    POW = MOD - 2
    mul = n
    ret = 1
    while POW > 0:
        if POW % 2 == 1:
            ret *= mul
            ret %= MOD
        mul *= mul
        mul %= MOD
        POW /= 2
    return ret

q_num = S.count('?')
if q_num < 3:
    ans *= inv(3 ** (3 - q_num))
    ans %= MOD
else:
    for i in range(q_num - 3):
        ans *= 3
        ans %= MOD
print ans