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: Accepted)

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#define ll long long
int main(void) {
   ll dp[100000+100][4]={0};
   ll MOD = 1000000007LL;
   char *S = (char *)malloc(100100 * sizeof(char));
   scanf("%s", S); 
   int n = strlen(S);
   int k;
   dp[0][3] = 1;
   for (int i = 0; i < n; i++) {
      if (S[i]=='?') {
        k = 3;
      } else {
        k = 1;
      }
      for (int j = 0; j < k; j++) {
        dp[i+1][0] += dp[i][0]; 
        dp[i+1][1] += dp[i][1];
        dp[i+1][2] += dp[i][2]; 
        dp[i+1][3] += dp[i][3]; 
      }
      if (S[i] == 'A') {
        dp[i+1][0] += dp[i][3];
      } else if (S[i] == 'B') {
        dp[i+1][1] += dp[i][0]; 
      } else if (S[i] == 'C') {
        dp[i+1][2] += dp[i][1];
      } else {
        dp[i+1][0] += dp[i][3];
        dp[i+1][1] += dp[i][0];
        dp[i+1][2] += dp[i][1];
      }
      for (int l = 0; l < 4; l++) {
        if (dp[i+1][l]>MOD) {
           dp[i+1][l] %= MOD;
        }
      }
   }
   printf("%lld\n",dp[n][2]%MOD);
   return 0;
}