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;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		String s = in.next();
		long div = 1000000007;
		int n = s.length();
		int[] a = new int[n];
		boolean[] b = new boolean[n];
		int[] c = new int[n];
		int[] q = new int[n];
		char ch = s.charAt(0);
		if(ch=='A') a[0]++;
		else if(ch=='B') b[0] = true;
		else if(ch=='C') c[0]++;
		else q[0]++;
		for(int i=1;i<n;i++) {
			ch = s.charAt(i);
			a[i] = a[i-1];
			c[i] = c[i-1];
			q[i] = q[i-1];
			if(ch=='A') a[i]++;
			else if(ch=='B') b[i] = true;
			else if(ch=='C') c[i]++;
			else {
				b[i] = true;
				q[i]++;
			}
		}
		long[] threePow = new long[n];
		threePow[0] = 0;
		threePow[1] = 1;
		for(int i=2;i<n;i++) {
			threePow[i] = (threePow[i-1]*3)%div;
		}
		
		long ans = 0;
		for(int i=1;i<n-1;i++) {
			if(b[i]) {
				ans += (((threePow[q[i-1]+1]*a[i-1]%div+threePow[q[i-1]]*q[i-1]%div)%div) * (threePow[q[n-1]-q[i]+1]*(c[n-1]-c[i])%div+threePow[q[n-1]-q[i]]*(q[n-1]-q[i])%div)%div)%div;
			}
			if(ans>=div) ans %= div;
		}
		
		System.out.println(ans);
		in.close();
	}

}