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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>

#define NEW(p,n){p=malloc((n)*sizeof(p[0]));if(p==NULL){printf("not enough memory\n");exit(1);};}
//pの型の変数n個の要素分のメモリを確保し、そのアドレスをpに代入するマクロ

#define MAX(a, b) ((a) > (b) ? (a) : (b))
#define MIN(a, b) ((a) < (b) ? (a) : (b))

#define MOD 1000000007

//S[0]から始まる文字列の長さを求める関数
int string_len(char* str){
    int len=0;
    while(str[len]!=0){
        len++;
    }
    return len;
}

int main(void){
    char S[100001];
    scanf("%s",S);

    //数列Sの長さ
    int N=string_len(S);

    long dp[N+1][3];
    dp[N][2]=1;
    dp[N][1]=0;
    dp[N][0]=0;
    for(int i=N-1;i>=0;i--){
        //dp[2]について
        if(S[i]=='?') dp[i][2]=(3*dp[i+1][2])%MOD;
        else dp[i][2]=dp[i+1][2];

        //dp[1]について
        if(S[i]=='?') dp[i][1]=(3*dp[i+1][1]+dp[i+1][2])%MOD;
        else if(S[i]=='B') dp[i][1]=(dp[i+1][1]+dp[i+1][2])%MOD;
        else dp[i][1]=dp[i+1][1];

        //dp[0]について
        if(S[i]=='?') dp[i][0]=(3*dp[i+1][0]+dp[i+1][1])%MOD;
        else if(S[i]=='A') dp[i][0]=(dp[i+1][0]+dp[i+1][1])%MOD;
        else dp[i][0]=dp[i+1][0];
    }

    printf("%ld\n",dp[0][0]);

    return 0;
}