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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.ABC_104
{
    class D
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            string s = Console.ReadLine();

            var dp = new long[s.Length + 1, 4];//文字数、いくつマークしたか?
            var keys = new char[3] { 'A', 'B', 'C' };
            int mask = 1000000000 + 7;
            for (int i = s.Length; i >= 0; i--)
            {
                for (int j = 0; j <= 3; j++)
                {
                    if (i == s.Length)//最後まで見た
                    {
                        dp[i, j] = j == 3 ? 1 : 0;
                    }
                    else
                    {
                        if (j == 3)
                        {
                            dp[i, j] = dp[i + 1, j];
                            dp[i, j] *= s[i] == '?' ? 3 : 1;
                            dp[i, j] %= mask;
                        }
                        else
                        {
                            int m1 = s[i] == '?' ? 3 : 1;
                            int m2 = s[i] == '?' || s[i] == keys[j] ? 1 : 0;
                            dp[i, j] = m1 * dp[i + 1, j] + m2 * dp[i + 1, j + 1];
                            dp[i, j] %= mask;
                        }
                    }
                }
            }
            /*for(int i = 0; i < dp.GetLength(0); i++)
            {
                string str = "";
                for(int j = 0; j < dp.GetLength(1); j++)
                {
                    str += dp[i, j].ToString() + " ";
                }
                Console.WriteLine(str);
            }*/
            Console.WriteLine(dp[0, 0]);
        }
    }
}