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)


import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;

import java.util.*;

public class Main {
    long MOD = (long) 1e9 + 7;

    InputStream in;
    OutputStream out;

    public Main() {
        this(System.in, System.out);
    }

    public Main(InputStream in, OutputStream out) {
        this.in = in;
        this.out = out;
    }

    void run() {
        Scanner sc = new Scanner(this.in);
        PrintWriter out = new PrintWriter(this.out);

        // write your code
        String s = sc.next();

        int l = s.length();
        int[] a = new int[l + 1], ax = new int[l + 1];
        int[] c = new int[l + 1], cx = new int[l + 1];
        long[] pow2 = new long[l + 1], pow3 = new long[l + 1];
        pow2[0] = 1;
        pow3[0] = 1;

        for (int i = 0; i < l; i++) {
            a[i + 1] += a[i];
            ax[i + 1] += ax[i];
            c[l - i - 1] += c[l - i];
            cx[l - i - 1] += cx[l - i];
            pow2[i + 1] = pow2[i] * 2 % MOD;
            pow3[i + 1] = pow3[i] * 3 % MOD;

            switch (s.charAt(i)) {
                case 'A':
                    a[i + 1]++;
                    break;
                case '?':
                    ax[i + 1]++;
            }
            switch (s.charAt(l - i - 1)) {
                case 'C':
                    c[l - i - 1]++;
                    break;
                case '?':
                    cx[l - i - 1]++;
            }
        }

//        debug(a, ax);
//        debug(c, cx);

        long ans = 0;
        for (int i = 1; i < l - 1; i++) {
            if (s.charAt(i) == 'B' || s.charAt(i) == '?') {
                long cnt = 0;
                long x1 = 1L * a[i] * c[i + 1] % MOD * pow3[ax[i]] % MOD * pow3[cx[i + 1]] % MOD;
                long x2 = (cx[i + 1] > 0) ? 1L * a[i] * cx[i + 1] % MOD * pow3[ax[i]] % MOD * pow3[cx[i + 1] - 1] % MOD : 0;
                long x3 = (ax[i] > 0) ? 1L * ax[i] * c[i + 1] % MOD * pow3[ax[i] - 1] % MOD * pow3[cx[i + 1]] % MOD : 0;
                long x4 = (ax[i] > 0 && cx[i + 1] > 0) ? 1L * ax[i] * cx[i + 1] % MOD * pow3[ax[i] - 1] % MOD * pow3[cx[i + 1] - 1] % MOD : 0;
//                debug(x1, x2, x3, x4);
                ans = (ans + x1 + x2 + x3 + x4) % MOD;
            }
        }

        out.println(ans);

        out.flush();
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}