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: Accepted)


//20190820
//https://atcoder.jp/contests/abc104/tasks/abc104_d
import java.util.Scanner;

class Main {
    static final long mod = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String s = sc.next();
        int len = s.length();
        long[][] dp = new long[len][4];

        // 初期化処理
        if (s.charAt(0) == 'A') {
            dp[0][0] = 1;
            dp[0][1] = 1;
        } else if (s.charAt(0) == '?') {
            dp[0][0] = 3;
            dp[0][1] = 1;
        } else {
            dp[0][0] = 1;
        }
        for (int i = 1; i < len; i++) {
            char c = s.charAt(i);
            for (int j = 0; j < 4; j++) {
                // コピーする
                dp[i][j] = dp[i - 1][j];
                dp[i][j] %= mod;
            }
            // 追加する
            if (c == 'A') {
                dp[i][1] += dp[i - 1][0];

            } else if (c == 'B') {
                dp[i][2] += dp[i - 1][1];

            } else if (c == 'C') {
                dp[i][3] += dp[i - 1][2];

            } else if (c == '?') {
                for (int k = 0; k < 4; k++) {
                    dp[i][k] *= 3;
                    dp[i][k] %= mod;
                }
                dp[i][1] += dp[i - 1][0];
                dp[i][2] += dp[i - 1][1];
                dp[i][3] += dp[i - 1][2];
            }
            for (int j = 0; j < 4; j++) {
                dp[i][j] %= mod;
            }
        }

        System.out.println(dp[len - 1][3]);
        sc.close();
    }
}