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;
#define mod 1000000007
long long dp[100010][4];
int main()
{
    string s,a="ABC";
    while(cin>>s)
    {
        memset(dp,0,sizeof(dp));
        dp[s.size()][3]=1;
        for(int i=s.size()-1;i>=0;i--)
           for(int j=3;j>=0;j--)
           {
               dp[i][j]=dp[i+1][j]*(s[i]=='?'?3:1);
               if(j<3&&(s[i]=='?'||s[i]==a[j]))
               dp[i][j]+=dp[i+1][j+1];
               dp[i][j]=dp[i][j]%mod;
           }
        cout<<dp[0][0]<<endl;
    }
    return 0;
}
