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.

Examples

Input

A??C


Output

8


Input

ABCBC


Output

3


Input

????C?????B??????A???????


Output

979596887
#include <iostream>
#include <string>
#define ll long long
using namespace std;

const int MOD = 1000000007;

int main() {
  string S;
  cin >> S;

  int len = S.size();
  ll a = 0, ab = 0, abc = 0, all_s = 1;

  for (int i = 0; i < len; i++) {
    if (S[i] == 'A')
      a = (a + all_s) % MOD;
    else if (S[i] == 'B')
      ab = (ab + a) % MOD;
    else if (S[i] == 'C')
      abc = (abc + ab) % MOD;
    else if (S[i] == '?') {
      abc   = (abc * 3 + ab) % MOD;
      ab    = (ab * 3 + a) % MOD;
      a     = (a * 3 + all_s) % MOD;
      all_s = (all_s * 3) % MOD;
    }
  }
  cout << abc << endl;
}