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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<algorithm>
#include<fstream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<cctype>
#include<cmath>
#include<vector>
#include<climits>
#include<queue>

using namespace std;

int main()
{
    long long i,j;
    char S[100005];
    //string S;
    //cin >> S;
    scanf("%s",S);
    long long  a=strlen(S);
    long long N = a, MOD = 1000000007;
    long long dp[100010][4] = {};
    for(i = N; i >= 0; --i)
    {
        for(j = 3; j >= 0; --j)
        {
            if(i == N)
            {
                dp[i][j] = (j == 3 ? 1 : 0);
            }
            else
            {
                dp[i][j] = dp[i+1][j] * (S[i] == '?' ? 3: 1);
                if(j < 3 && (S[i] == '?' || S[i] == "ABC"[j]))
                {
                    dp[i][j] += dp[i+1][j+1];
                }
                dp[i][j] %= MOD;
            }
        }
    }
    cout << dp[0][0] << endl;
}