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 Julia (0.5.0) (judge verdict: Accepted)

function main()
    MOD = 1000000007
    s = chomp(readline())
    n = length(s)
    ans = 0
    a,b,c,z = zeros(Int, (n+1,)),zeros(Int, (n+1,)),zeros(Int, (n+1,)),zeros(Int, (n+1,))
    t = zeros(Int, (n+1,))
    t[1] = 1
    for i in 2:n+1
        t[i] = t[i-1]*3%MOD
    end
    for i in 1:n
        a[i+1], b[i+1], c[i+1], z[i+1] = a[i], b[i], c[i], z[i]
        if s[i] == 'A'
            a[i+1] += 1
        elseif s[i] == 'B'
            b[i+1] += 1
        elseif s[i] == 'C'
            c[i+1] += 1
        else
            z[i+1] += 1
        end
    end
    for i in 1:n
        if s[i] == 'B'
            ans = (ans + a[i]*(c[n+1]-c[i+1])%MOD*t[z[n+1]+1]%MOD)%MOD
            ans = (ans + (z[i]*(c[n+1]-c[i+1])+a[i]*(z[n+1]-z[i+1]))%MOD*t[max(1,z[n+1])]%MOD)%MOD
            ans = (ans + z[i]*(z[n+1]-z[i+1])%MOD*t[max(1,z[n+1]-1)]%MOD)%MOD
        elseif s[i] == '?'
            ans = (ans + a[i]*(c[n+1]-c[i+1])%MOD*t[max(1,z[n+1])]%MOD)%MOD
            ans = (ans + (z[i]*(c[n+1]-c[i+1])+a[i]*(z[n+1]-z[i+1]))%MOD*t[max(1,z[n+1]-1)]%MOD)%MOD
            ans = (ans + z[i]*(z[n+1]-z[i+1])%MOD*t[max(1,z[n+1]-2)]%MOD)%MOD
        end
    end
    print("$ans\n")
end

main()