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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    val S = readLine()!!
    var count: Long = 0
    for (i in 1 until S.lastIndex) {
        if (S[i] == 'A' || S[i] == 'C') continue
        val a = S.substring(0, i)
        val c = S.substring(i + 1)

        val an = a.count { it == 'A' } //前半分のAの個数
        val q1 = a.count { it == '?' } //前半分の?の個数
        val cn = c.count { it == 'C' } //後半分のCの個数
        val q2 = c.count { it == '?' } //後半分の?の個数

        val a_c = an * cn * f(3, q1 + q2) //(A,C)
        val a_q = an * (q2 * f(2, q2 - 1)) * f(3, q1) //(A,?)
        val q_c = cn * (q1 * f(2, q1 - 1)) * f(3, q2) //(?,C)
        val q_q = q1 * f(2, q1 - 1) * q2 * f(2, q2 - 1) //(?,?)
        count += (a_c + a_q + q_c + q_q)
    }
    println(count % (1000000007))
}

fun f(a: Int, n: Int): Long {
    var count: Long = 1
    for (i in 0 until n) count *= a
    return count
}