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>

using namespace std;

const int R = 1e9 + 7; string s; int n, p; long long dp[ 2 ][ 4 ];

int main()
{
    ios_base::sync_with_stdio( false ), cin.tie( nullptr ), cout.tie( nullptr ), cin >> s, n = s.size(), dp[ 0 ][ 3 ] = 1;

    for( int i = n, j = n - 1, q = 1; i > 0; i = j--, p = q, q = 1 - p )
        for( int k = 4, l = 3; k > 0; k = l-- )
        {
            auto &x = dp[ q ][ l ];  x = dp[ p ][ l ]; auto &y = s[ j ];

            if ( y == '?' )
                x *= 3, x %= R;

            if( k < 4 and ( y == '?' or ( y - 'A' ) == l ) )
                x += dp[ p ][ k ], x %= R;
        }

    cout << dp[ p ][ 0 ];
}