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.util.Scanner;

class Main{


	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);			//文字の入力

		String S = sc.next();
		long mod = 1000000007L;
		String ABC = "ABC";
		long[][] dp = new long[S.length()][4];


		if(S.charAt(0) == '?'){					//初期値
			dp[0][0] = 3;
		}else{
			dp[0][0] = 1;
		}

		if(S.charAt(0) == 'A' || S.charAt(0) == '?'){
			dp[0][1] = 1;
		}


		for(int i = 1;i < S.length();i++){
			for(int j = 0;j < 4;j++){

				if(j == 0){
					if(S.charAt(i) == 'A' ||S.charAt(i) == 'B'||S.charAt(i) == 'C'){
						dp[i][0] = dp[i-1][0];
					}else{
						dp[i][0] = dp[i-1][0]*3L;
					}
					
					dp[i][j] %=mod;


				}else{

					long x = (S.charAt(i) == '?' ? 3L : 1L);				//?だったら３、他は１
					long y =( (S.charAt(i) == ABC.charAt(j-1)|| S.charAt(i) == '?') ? 1L :0L);

					dp[i][j] = (dp[i-1][j] * x) + (dp[i-1][j-1]*y); 
				dp[i][j] %=mod;
				}
			}


		}

		System.out.println(dp[S.length()-1][3] );
	}

}