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.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class ABC
	{
		static readonly int mod = 1000000007;  // 10^9+7

		static void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });


			string s = Console.ReadLine();
			//int n = int.Parse(Console.ReadLine());
			//long n = long.Parse(Console.ReadLine());
			//int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] vs = Console.ReadLine().Split().Select(long.Parse).ToArray();
			char[] c = new char[] { '?', 'A', 'B', 'C' };
			long[,] dp = new long[s.Length + 1, 4];
			dp[0, 0] = 1;
			for (int i = 1; i <= s.Length; i++) {
				dp[i, 0] = (s[i - 1] == '?' ? 3 : 1) * dp[i - 1, 0] % mod;
				for (int j = 1; j < 4; j++) {
					dp[i, j] = ((s[i - 1] == '?' || s[i - 1] == c[j] ? 1 : 0) * dp[i - 1, j - 1] + (s[i - 1] == '?' ? 3 : 1) * dp[i - 1, j]) % mod;
				}
			}
			//for (int j = 0; j < dp.GetLength(1); j++) {
			//	for (int i = 0; i < dp.GetLength(0); i++) {
			//		System.Diagnostics.Debug.Write($"{dp[i, j]} ");
			//	}
			//	System.Diagnostics.Debug.WriteLine($"");
			//}
			Console.WriteLine(dp[s.Length,3]);


			Console.Out.Flush();
		}
	}
}