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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DWeLoveABC solver = new DWeLoveABC();
        solver.solve(1, in, out);
        out.close();
    }

    static class DWeLoveABC {
        public void solve(int testNumber, Scanner in, PrintWriter out) {

            String s = in.next();
            ModInt[] mi = new ModInt[4];
            Arrays.fill(mi, new ModInt(0));

            mi[0] = new ModInt(1);

            if (s.charAt(0) == 'A') {
                mi[1] = new ModInt(1);
            }

            if (s.charAt(0) == '?') {
                mi[0] = new ModInt(3);
                mi[1] = new ModInt(1);
            }

            for (int i = 1; i < s.length(); i++) {
                char c = s.charAt(i);

                if (c == '?') {
                    mi[3] = mi[3].mul(3).add(mi[2]);
                    mi[2] = mi[2].mul(3).add(mi[1]);
                    mi[1] = mi[1].mul(3).add(mi[0]);
                    mi[0] = mi[0].mul(3);
                }
                if (c == 'C') {
                    mi[3] = mi[3].add(mi[2]);
                }
                if (c == 'B') {
                    mi[2] = mi[2].add(mi[1]);
                }
                if (c == 'A') {
                    mi[1] = mi[1].add(mi[0]);
                }
            }


            out.println(mi[3].getVal());

        }

    }

    static class ModInt {
        long val;
        int MOD = (int) 1e9 + 7;

        public ModInt(long i) {
            this.val = (i + MOD) % MOD;
        }

        public ModInt mul(long l) {
            return new ModInt(this.val * l);
        }

        public ModInt add(ModInt m) {
            return new ModInt(this.val + m.getVal());
        }

        public long getVal() {
            return val;
        }

        public String toString() {
            return "ModInt{" +
                    "val=" + val +
                    ", MOD=" + MOD +
                    '}';
        }

    }
}