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.Linq;
using System.Security.Policy;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public string S;
        public long[] B, C, BC, ABC, T;
        public void Run()
        {
            S = Console.ReadLine();
            int L = S.Length;

            B = new long[S.Length + 1];
            C = new long[S.Length + 1];
            BC = new long[S.Length + 1];
            ABC = new long[S.Length + 1];
            T = new long[S.Length + 1];

            B[L] = 0;
            C[L] = 0;
            BC[L] = 0;
            ABC[L] = 0;
            T[L] = 1;

            for (int i = L - 1; i >= 0; i--)
            {
                if (S[i] == 'A' || S[i] == '?')
                {
                    B[i] += B[i + 1];
                    C[i] += C[i + 1];
                    BC[i] += BC[i + 1];
                    ABC[i] += ABC[i + 1];
                    T[i] += T[i + 1];

                    ABC[i] += BC[i + 1];
                }

                if (S[i] == 'B' || S[i] == '?')
                {
                    B[i] += B[i + 1];
                    C[i] += C[i + 1];
                    BC[i] += BC[i + 1];
                    ABC[i] += ABC[i + 1];
                    T[i] += T[i + 1];

                    B[i] += T[i + 1];
                    BC[i] += C[i + 1];
                }

                if (S[i] == 'C' || S[i] == '?')
                {
                    B[i] += B[i + 1];
                    C[i] += C[i + 1];
                    BC[i] += BC[i + 1];
                    ABC[i] += ABC[i + 1];
                    T[i] += T[i + 1];

                    C[i] += T[i + 1];
                }

                B[i] %= 1000000007;
                C[i] %= 1000000007;
                BC[i] %= 1000000007;
                T[i] %= 1000000007;
                ABC[i] %= 1000000007;
            }

            Console.WriteLine(ABC[0]);
        }
    }

    // libs ----------
    

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}