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: Wrong Answer)

using System;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

namespace ABC104_D___We_Love_ABC別解
{
    class Program
    {
        static void Main(string[] args)
        {
            var S = Console.ReadLine();
            var accumA = new int[S.Length + 1];
            var accumC = new int[S.Length + 1];
            var accumQ = new int[S.Length + 1];
            for (int i = 0; i < S.Length; i++)
            {
                accumA[i + 1] = accumA[i] + (S[i] == 'A' ? 1 : 0);
                accumC[i + 1] = accumC[i] + (S[i] == 'C' ? 1 : 0);
                accumQ[i + 1] = accumQ[i] + (S[i] == '?' ? 1 : 0);
            }
            var totalA = accumA[S.Length];
            var totalC = accumC[S.Length];
            var totalQ = accumQ[S.Length];
            ModInt power3Q = 1;
            for (int i = 0; i < totalQ; i++) power3Q *= 3;
            ModInt power3Qminus1 = power3Q / 3;
            ModInt power3Qminus2 = power3Qminus1 / 3;
            ModInt power3Qminus3 = power3Qminus2 / 3;

            ModInt result = 0;
            for (int i = 1; i < S.Length; i++)
            {
                if (S[i - 1] == 'B')
                {
                    result += accumA[i - 1] * (totalC - accumC[i]) * power3Q;
                    result += accumA[i - 1] * (totalQ - accumQ[i]) * power3Qminus1;
                    result += accumQ[i - 1] * (totalC - accumC[i]) * power3Qminus1;
                    result += accumQ[i - 1] * (totalQ - accumQ[i]) * power3Qminus2;
                }
                if (S[i - 1] == '?')
                {
                    result += accumA[i - 1] * (totalC - accumC[i]) * power3Qminus1;
                    result += accumA[i - 1] * (totalQ - accumQ[i]) * power3Qminus2;
                    result += accumQ[i - 1] * (totalC - accumC[i]) * power3Qminus2;
                    result += accumQ[i - 1] * (totalQ - accumQ[i]) * power3Qminus3;
                }
            }
            Console.WriteLine(result.ToString());
        }
    }
    //パクリ元　https://atcoder.jp/contests/arc067/submissions/5337727
    struct ModInt
    {
        const int MOD = 1000000007;
        long Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator long(ModInt modInt) => modInt.Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator ModInt(long val) => new ModInt(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, ModInt b)
        {
            long res = a.Data + b.Data;
            return new ModInt() { Data = res >= MOD ? res - MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, long b) => a.Data + b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, ModInt b)
        {
            long res = a.Data - b.Data;
            return new ModInt() { Data = res < 0 ? res + MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, long b) => a.Data - b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator /(ModInt a, ModInt b) => a.Data * GetInverse(b);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => Data.ToString();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long GetInverse(long a)
        {
            long div;
            long p = MOD;
            long x1 = 1, y1 = 0, x2 = 0, y2 = 1;
            while (true)
            {
                if (p == 1) return x2;
                div = a / p;
                x1 -= x2 * div;
                y1 -= y2 * div;
                a %= p;
                if (a == 1) return x1;
                div = p / a;
                x2 -= x1 * div;
                y2 -= y1 * div;
                p %= a;
            }
        }
    }
}