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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    static final int MODULUS = 1_000_000_007;
    static String TARGET = "ABC";

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        String S = sc.next();

        System.out.println(solve(S));

        sc.close();
    }

    static int solve(String S) {
        int wildCount = (int) S.chars().filter(ch -> ch == '?').count();
        int[] threePowers = new int[wildCount + 1];
        threePowers[0] = 1;
        for (int i = 1; i < threePowers.length; ++i) {
            threePowers[i] = multiplyMod(threePowers[i - 1], 3);
        }

        int result = 0;
        Map<String, Integer> subToCount = new HashMap<>();
        subToCount.put("", 1);
        for (char ch : S.toCharArray()) {
            Map<String, Integer> nextSubToCount = new HashMap<>();

            for (String sub : subToCount.keySet()) {
                if (sub.length() <= 2) {
                    nextSubToCount.put(sub, nextSubToCount.getOrDefault(sub, 0) + subToCount.get(sub));

                    String nextSub = String.format("%s%c", sub, ch);
                    nextSubToCount.put(nextSub, nextSubToCount.getOrDefault(nextSub, 0) + subToCount.get(sub));
                }
            }

            for (String nextSub : nextSubToCount.keySet()) {
                if (nextSub.length() == 3) {
                    result = addMod(result,
                            computeABCNumber(threePowers, wildCount, nextSub, nextSubToCount.get(nextSub)));
                }
            }

            subToCount = nextSubToCount;
        }

        return result;
    }

    static int addMod(int x, int y) {
        return (x + y) % MODULUS;
    }

    static int multiplyMod(int x, int y) {
        return (int) ((long) x * y % MODULUS);
    }

    static int computeABCNumber(int[] threePowers, int wildCount, String sub, int count) {
        for (int i = 0; i < sub.length(); ++i) {
            if (sub.charAt(i) != '?' && sub.charAt(i) != TARGET.charAt(i)) {
                return 0;
            }
        }

        return multiplyMod(count, threePowers[wildCount - (int) sub.chars().filter(ch -> ch == '?').count()]);
    }
}