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 Ruby (2.3.3) (judge verdict: Runtime Error)

import java.util.*;
import java.io.*;

class Main {
	public static void main(String... args) {
		int M = 1_000_000_007;
		String S = IN.next();
		
		long a   = 0;
		long ab  = 0;
		long abc = 0;
		long t   = 1;

		for (int i = 0; i < S.length(); i++) {
			switch (S.charAt(i)) {
				case 'A':
					a = (a + t) % M;
					break;
				case 'B':
					ab = (ab + a) % M;
					break;
				case 'C':
					abc = (abc + ab) % M;
					break;
				default:
					abc = (abc * 3 + ab) % M;
					ab  = (ab * 3 + a) % M;
					a   = (a * 3 + t) % M;
					t   = (t * 3) % M;
			}
			puts(Arrays.toString(new long[] {a, ab, abc, t}));
		}
		puts(abc);
		flush();
	}
	static final Scanner IN = new Scanner(System.in);
	static final PrintWriter OUT = new PrintWriter(System.out);
	static <T> void puts(T arg) { OUT.println(arg); }
	static void flush() { OUT.flush(); }
}