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>
long long t1[100005],t2[100005],t3[100005],t4[100005];
int main(){
	char s[100005];
	int i,j,k,l,m,n;
	
	scanf("%s",s);
	t1[0]=t2[0]=t3[0]=0;
	t4[0]=1;
	if(s[0]=='A'){
	t1[0]=1;	} 
	if(s[0]=='?'){t1[0]=1;t4[0]=3;} 
	l=strlen(s);

	for(i=1;i<l;i++){
	t1[i]=t1[i-1];
	t2[i]=t2[i-1];
	t3[i]=t3[i-1];
	t4[i]=t4[i-1];
	if(s[i]=='A')t1[i]+=t4[i-1];
	if(s[i]=='B')t2[i]+=t1[i-1];
	if(s[i]=='C')t3[i]+=t2[i-1];
	if(s[i]=='?'){
	t1[i]=t1[i-1]*3+t4[i]; 
t2[i]=t2[i-1]*3+t1[i-1];
t3[i]=t3[i-1]*3+t2[i-1];	
	t4[i]*=3;
}
		t1[i]%=1000000007;
		t2[i]%=1000000007;
		t3[i]%=1000000007;
		t4[i]%=1000000007;
	}
	printf("%lld",t3[l-1]);
	 return 0;
}