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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int addmod(int a, int b, int m)
{
    return ((a % m) + (b % m)) % m;
}

int mulmod(int a, int b, int m)
{
    int result = a;
    for (int i = 1; i < b; i++) {
        result = addmod(result, a, m);
    }
    return result;
}

int main()
{
    char str[100007];
    int wNum = 1;
    int aCount = 0, aCountNew = 0, abCount = 0, abCountNew = 0, abcCount = 0, abcCountNew = 0, len, modNum = 1e9 + 7;
    gets(str);
    if (str[0] == 'A')
    {
        aCountNew = ++aCount;
    }
    else if (str[0] == '?')
    {
        aCountNew = ++aCount;
        wNum = 3;
    }
    len = strlen(str);
    for (int i = 1; i < len; i++) {
        if (str[i] == 'A') {
            aCountNew = addmod(aCount, wNum, modNum);
        }
        else if (str[i] == 'B') {
            abCountNew = addmod(aCount, abCount, modNum);
        }
        else if (str[i] == 'C') {
            abcCountNew = addmod(abCount, abcCount, modNum);
        }
        else {
            aCountNew = addmod(mulmod(aCount, 3, modNum), wNum, modNum);
            abCountNew = addmod(mulmod(abCount, 3, modNum), aCount, modNum);
            abcCountNew = addmod(mulmod(abcCount, 3, modNum), abCount, modNum);
            wNum = mulmod(wNum, 3, modNum);
        }
        aCount = aCountNew;
        abCount = abCountNew;
        abcCount = abcCountNew;
    }
    printf("%d", abcCount);
    return 0;
}