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 REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)
typedef signed long long ll;

using namespace std;

int main(){
	ll a,ab,abc,all,M,x;
	M=1000000007;
	a=0;
	ab=0;
	abc=0;
	all=1;
	
	string S;
	cin >> S;
	ll l=S.length();
	
	for( int i=0; i<l ; ++i){
		x=S[i];
		if (x=='A') a+=all;
		if (x=='B') ab+=a;
		if (x=='C') abc+=ab;
		
		if (x=='?') {
			abc=abc*3+ab;
			ab=ab*3+a;
			a= a*3+all;
			all*=3;
		}
		abc%=M;
		ab%=M;
		a%=M;
		all%=M;	
	}
	cout << abc%M << endl;
}

