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 <vector>
#include <string>

using namespace std;

const int mod = 1000000007;

int main() {
  string s; cin >> s;
  // dp[i][x] := i文字までみたとき,
  // dp[i][0]: Aが何個あるか?
  // dp[i][1]: ABが何個あるか?
  // dp[i][2]: ABCが何個あるか?
  vector<vector<long long>> dp(s.length()+10, vector<long long>(3, 0));
  // mul: 現時点で文字列として考えられる種類. "?" が出現するたび3倍される
  long long mul = 1;
  for (int i = 0; i < s.length(); i++) {
    if (s[i] == 'A') {
      dp[i+1][0] = dp[i][0] + mul;
      dp[i+1][1] = dp[i][1];
      dp[i+1][2] = dp[i][2];
    }
    if (s[i] == 'B') {
      dp[i+1][0] = dp[i][0];
      dp[i+1][1] = dp[i][1] + dp[i][0];
      dp[i+1][2] = dp[i][2];
    }
    if (s[i] == 'C') {
      dp[i+1][0] = dp[i][0];
      dp[i+1][1] = dp[i][1];
      dp[i+1][2] = dp[i][2] + dp[i][1];
    }
    if (s[i] == '?') {
      // ?のときは, 3つの構成可能文字列に分岐するので, 3倍する
      dp[i+1][0] = dp[i][0] * 3 + mul;
      dp[i+1][1] = dp[i][1] * 3 + dp[i][0];
      dp[i+1][2] = dp[i][2] * 3 + dp[i][1];
      mul = (mul * 3) % mod;
    }
    dp[i+1][0] %= mod;
    dp[i+1][1] %= mod;
    dp[i+1][2] %= mod;
  }
  cout << dp[s.length()][2] << endl;
  return 0;
}