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 Java7 (OpenJDK 1.7.0) (judge verdict: Runtime Error)

import java.util.*;

public class Main{
	
	static final int r = 1000000007;
	static long dp[][];
	
	public static long solve(int p, int j, String s){
		long ans = 0;
		String abc = "ABC";
		if(dp[p][j] != 0)return dp[p][j];
		if(p == s.length()){
			if(j < 3)return dp[p][j] = 0 % r;
			return dp[p][j] = 1 % r;
		}	
		long m1 = 1, m2 = 0;
		if(s.charAt(p) == '?')m1 = 3;
		if(j == 3)
			return dp[p][j] = (m1 * solve(p + 1, j, s)) % r;
		if(m1 == 3)m2 = 1;
		else if(s.charAt(p) == abc.charAt(j))m2 = 1;
		return dp[p][j] = ((m1 * solve(p + 1, j, s))% r) + ((m2 * solve(p + 1, j + 1, s)) % r);
	}	
	
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		String s = sc.next();
		dp = new long[s.length()][3];
		sc.close();
		long ans = solve(0, 0, s);	
		System.out.println(ans);
	}
}