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<bits/stdc++.h>
#define mod 1000000007
using namespace std;
char s[100000];
long long n, f[4][100000]; // 0 ? 1 A 2 AB 3 ABC

int main(){
    scanf("%s", s + 1);
    n = strlen(s + 1);
    f[0][0] = 1;
    for (int i = 1; i <= n; i++){
        for (int j = 0; j <= 3; j++){
            f[j][i] = f[j][i-1];
            if (s[i] == '?') f[j][i] = (f[j][i]*3)% mod;
            if (j > 0 && (s[i] == '?' || s[i] - 'A' + 1 == j)){
                f[j][i] = (f[j][i] + f[j-1][i-1])% mod;
            }
        }
    }
    cout << f[3][n];
}
