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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Out.Flush();
            Read();
        }
        static void Solve()
        {
            var S = ReadLine();
            var N = S.Length;
            var A = 'A';
            var B = 'B';
            var C = 'C';
            var Q = '?';
            var right = new Dictionary<char, long>() { { A, 0 }, { B, 0 }, { C, 0 }, { Q, 0 } };
            var left = new Dictionary<char, long>() { { A, 0 }, { B, 0 }, { C, 0 }, { Q, 0 } };
            foreach (var s in S.Skip(2))
                ++right[s];
            ++left[S[0]];
            var ans = 0L;
            var preClc = new long[N];
            for(var i=0;i<N;++i)
            {

            }
            var cmb = new Combination(N, Mod);
            for (var i = 1; i < N - 1; ++i)
            {
                if (S[i] == B || S[i] == Q)
                {
                    var lAnum = left[A];
                    var rCnum = right[C];
                    var lQnum = left[Q];
                    var rQnum = right[Q];

                    var lQsum = 0L;
                    for (var lq = 0; lq <= lQnum; ++lq)
                    {
                        var num = cmb.nCk((int)lQnum, lq) * modpow(2, lQnum - lq, Mod) % Mod;
                        var t = (lAnum + lq) * num % Mod;
                        lQsum = (lQsum + t) % Mod;
                    }
                    var rQSum = 0L;
                    for (var rq = 0; rq <= rQnum; ++rq)
                    {
                        var num = cmb.nCk((int)rQnum, rq) * modpow(2, rQnum - rq, Mod) % Mod;
                        var t = (rCnum + rq) * num % Mod;
                        rQSum = (rQSum + t) % Mod;
                    }
                    ans = (ans + lQsum * rQSum % Mod) % Mod;

                }
                --right[S[i + 1]];
                ++left[S[i]];
            }
            WriteLine(ans);
        }


        static long modpow(long a, long n, long mod)
        {
            var res = 1L;
            while (0 < n)
            {
                if (n % 2 != 0) res = res * a % mod;
                a = a * a % mod;
                n >>= 1;
            }
            return res;
        }
        public class Combination
        {
            readonly long mod;
            readonly long[] fac, finv, inv;
            public Combination(long n, long mod = 1000000007)
            {
                long max = n + 1;
                this.mod = mod;
                fac = new long[max];
                finv = new long[max];
                inv = new long[max];
                fac[0] = fac[1] = 1;
                finv[0] = finv[1] = 1;
                inv[1] = 1;
                for (int i = 2; i < max; ++i)
                {
                    fac[i] = fac[i - 1] * i % mod;
                    inv[i] = mod - inv[mod % i] * (mod / i) % mod;
                    finv[i] = finv[i - 1] * inv[i] % mod;
                }
            }
            public long nCk(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 | k < 0) return 0;
                return fac[n] * (finv[k] * finv[n - k] % mod) % mod;
            }
        }

    }
}