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();
			int[,] countA = new int[s.Length, 2];
			int[,] countC = new int[s.Length, 2];
			int c1 = 0, c2 = 0;
			for (int i = 0; i < s.Length; i++) {
				if (s[i] == 'A') {
					c1++;
				}
				if (s[i] == '?') {
					c2++;
				}
				countA[i, 0] = c1;
				countA[i, 1] = c2;
			}
			c1 = 0;
			c2 = 0;
			for (int i = s.Length - 1; i >= 0; i--) {
				if (s[i] == 'C') {
					c1++;
				}
				if (s[i] == '?') {
					c2++;
				}
				countC[i, 0] = c1;
				countC[i, 1] = c2;
			}

			long ans = 0;
			for (int i = 1; i < s.Length - 1; i++) {
				if (s[i] == 'B' || s[i] == '?') {
					//  a*3^q + q*3^(q-1)
					long a, c, q;
					q = countA[i - 1, 1];
					a = (long)countA[i - 1, 0] * Power3((int)q) % mod;
					a += q * Power3((int)q - 1) % mod;

					q = countC[i + 1, 1];
					c = (long)countC[i + 1, 0] * Power3((int)q) % mod;
					c += q * Power3((int)q - 1) % mod;

					ans += a * c % mod;
					ans %= mod;
				}
			}
			Console.WriteLine(ans);


			Console.Out.Flush();
		}

		static List<int> _Power3 = new List<int>();
		static int Power3(int x)
		{
			if (x < 0) {
				return 0;
			}
			if (x < _Power3.Count) {
				return _Power3[x];
			}
			if (_Power3.Count == 0) {
				_Power3.Add(1);
			}
			int i = _Power3.Count;
			long result = _Power3[i - 1];
			while (i <= x) {
				result *= 3;
				result %= mod;
				_Power3.Add((int)result);
				i++;
			}
			return (int)result;
		}

	}
}