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)

//
//  main.cpp
//
// g++ -std=c++14 main.cpp
//

//#include "main.hpp"
#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
#include <math.h>
using namespace std;
typedef long long ll;

int main(void){
    string s;
    cin >> s;
    
    ll abc[100010], a[100010], ab[100010], inf = 1e9 + 7, q = 1;
    abc[0] = ab[0] = a[0] = 0;
    
    for (int i = 0; i < s.size(); i++) {
        a[i + 1] = a[i];
        ab[i + 1] = ab[i];
        abc[i + 1] = abc[i];
        if (char(s[i]) == 'A') a[i + 1] = a[i] + q;
        if (char(s[i]) == 'B') ab[i + 1] = ab[i] + a[i];
        if (char(s[i]) == 'C') abc[i + 1] = abc[i] + ab[i];
        if (char(s[i]) == '?') {
            a[i + 1] = 3 * a[i] + q;
            ab[i + 1] = 3 * ab[i] + a[i];
            abc[i + 1] = 3 * abc[i] + ab[i];
            q = (3 * q) % inf;
        }
        a[i + 1] %= inf;
        ab[i + 1] %= inf;
        abc[i + 1] %= inf;
    }
    
    cout << abc[s.size()] << endl;
    
    //for (int i = 0; i <= s.size(); i++) cout << a[i] << " " << ab[i] << " " << abc[i] << endl;
    
    /*int cnt = 0;
    for (int i = 0; i < pow(3, 4); i++) {
        int ic = i;
        for (int j = 0; j < 4; j++) {
            if (ic % 3 == 0) cnt++;
            ic /= 3;
        }
    }
    cout << cnt << endl;*/
}

/*
g++ -std=c++14 main.cpp
*/