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>

using namespace std;

int main() {
    char c;
    
    long long int ca = 0, cab = 0, cabc = 0;
    long long int q3 = 1;
    int z = 1e9 + 7;
    while (cin >> c) {
        if (c == 'A') {
            ca = (ca + q3) % z;
        } else if (c == 'B') {
            cab = (cab + ca) % z;
        } else if (c == 'C') {
            cabc = (cabc + cab) % z;
        } else if (c == '?') {
            cabc = (cabc * 3 + cab) % z;
            cab = (cab * 3 + ca) % z;
            ca = (ca * 3 + q3) % z;
            q3 = q3 * 3 % z;
        }
    }

    cout << cabc << endl;

    return 0;
}