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 <algorithm>
#include <iostream>
#include <vector>
#include <map>
#include <cstdio>
#include <string>
#include <cmath>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define repr(i, n) for (int i = (n) - 1; i >= 0; i--)
#define FOR(i,i0,n) for(int (i)=(i0);(i)<(n);(i)++)
#define rn return
typedef std::pair<int,int> P;
using namespace std;
using ll = long long;




int main(){
    string S;
    cin >> S;
    int N = S.size();
    int MOD = 1000000007;
    
    long long dp[100010][4] = {};
    
    dp[0][0] = 1LL;
    FOR(i,1,N+1){
        
        if (S[i-1] == '?'){
            dp[i][1] = dp[i-1][1]*3LL + dp[i-1][0];
            dp[i][2] = dp[i-1][2]*3LL+ dp[i-1][1];
            dp[i][3] = dp[i-1][3]*3LL+ dp[i-1][2];
            dp[i][0] = dp[i-1][0]*3LL;
        }
        if (S[i-1] == 'A'){
            dp[i][0] = dp[i-1][0];
            dp[i][1] = dp[i-1][1]+ dp[i-1][0];
            dp[i][2] = dp[i-1][2];
            dp[i][3] = dp[i-1][3];
        }
        if (S[i-1] == 'B'){
            dp[i][0] = dp[i-1][0];
            dp[i][1] = dp[i-1][1];
            dp[i][2] = dp[i-1][2]+ dp[i-1][1] ;
            dp[i][3] = dp[i-1][3];
        }
        if (S[i-1] == 'C'){
            dp[i][0] = dp[i-1][0];
            dp[i][1] = dp[i-1][1];
            dp[i][2] = dp[i-1][2];
            dp[i][3] = dp[i-1][3]+ dp[i-1][2];
        }
        rep(j,4) dp[i][j] %= MOD;
    }
    cout << dp[N][3]%MOD << endl;
    rn 0;
}