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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace 課題1
{
    class Program
    {
        static void Main(string[] args)
		{
			
			string str = Console.ReadLine();

			string[] strArray = new string[str.Length];

			//1文字目の文字を取得する
			char c1 = str[0];
			//あ

			//forを使って1文字ずつ列挙する
			for (int num = 0; num < str.Length; num++)
			{
				strArray[num] = str[num].ToString();
			}

			int intCount = 0;

			int n = str.Length;
			int k = 3;
			var nums = Enumerable.Range(1, n).ToArray();
			var combinations = Combination.Enumerate(nums, k, withRepetition: false);

			foreach (var elem in combinations)
			{
				if(strArray[elem[0]-1]=="A"|| strArray[elem[0]-1] == "?")
				{
					if (strArray[elem[1]-1] == "B" || strArray[elem[1]-1] == "?")
					{
						if (strArray[elem[2]-1] == "C" || strArray[elem[2]-1] == "?")
						{

							string myStr = "?";

							// 1文字の文字列をchar型へ（その1）
							//
							char c = myStr[0];

							int intCountNUm = CountChar(str, c);

							if (intCountNUm == 0)
							{
								intCount++;
							}
							else
							{
								intCount = intCount + intCountNUm;
							}
						}
					}
				}
			}

			double gggg = Math.Pow(10, 9)+7;

			Console.WriteLine(double.Parse(intCount.ToString())%gggg);
		}

		public static int CountChar(string s, char c)
		{
			return s.Length - s.Replace(c.ToString(), "").Length;
		}



	}

	public static class Combination
	{
		public static IEnumerable<T[]> Enumerate<T>(IEnumerable<T> items, int k, bool withRepetition)
		{
			if (k == 1)
			{
				foreach (var item in items)
					yield return new T[] { item };
				yield break;
			}
			foreach (var item in items)
			{
				var leftside = new T[] { item };

				// item よりも前のものを除く （順列と組み合わせの違い)
				// 重複を許さないので、unusedから item そのものも取り除く
				var unused = withRepetition ? items : items.SkipWhile(e => !e.Equals(item)).Skip(1).ToList();

				foreach (var rightside in Enumerate(unused, k - 1, withRepetition))
				{
					yield return leftside.Concat(rightside).ToArray();
				}
			}
		}
	}



}