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 PyPy2 (5.6.0) (judge verdict: Accepted)

S=raw_input()
N=len(S)
mod=10**9+7

num=[ [ 0 for i in range(4) ] for j in range(N) ]		# i=0 A, i=1 B, i=2 C, i=3 ?

for i in range(N):
	if i==0:
		if S[i]=="A":  num[i][0]=1
		elif S[i]=="B":  num[i][1]=1		
		elif S[i]=="C":  num[i][2]=1
		elif S[i]=="?":  num[i][3]=1
	else:
		for j in range(4):
			num[i][j]=num[i-1][j]
			
		if S[i]=="A":  num[i][0]+=1
		elif S[i]=="B":  num[i][1]+=1		
		elif S[i]=="C":  num[i][2]+=1
		elif S[i]=="?":  num[i][3]+=1		

ans=0

for i in range(1,N):
	if S[i]=="B" or S[i]=="?":
		a=num[i-1][0]
		c=num[N-1][2]-num[i][2]
		ql=num[i-1][3]
		qr=num[N-1][3]-num[i][3]

		#ABC
		ans+=a*pow(3,ql,mod)*c*pow(3,qr,mod)

		#AB?
		if qr>0:
			ans+=a*pow(3,ql,mod)*pow(3,(qr-1),mod )*qr

		#?BC
		if ql>0:
			ans+=pow(3,(ql-1),mod )*ql*c*pow(3,qr,mod)

		#?B?
		if ql>0 and qr>0:
			ans+=pow(3,(ql-1),mod )*ql*pow(3,(qr-1),mod )*qr

print ans%mod