Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

A??C

Sample Output 1

8

In this case, Q = 2, and we can make 3^Q = 9 strings by by replacing each occurrence of ? with A, B or C. The ABC number of each of these strings is as follows:

AAAC: 0

AABC: 2

AACC: 0

ABAC: 1

ABBC: 2

ABCC: 2

ACAC: 0

ACBC: 1

ACCC: 0

The sum of these is 0 + 2 + 0 + 1 + 2 + 2 + 0 + 1 + 0 = 8, so we print 8 modulo 10^9 + 7, that is, 8.

Sample Input 2

ABCBC

Sample Output 2

3

When Q = 0, we print the ABC number of S itself, modulo 10^9 + 7. This string is the same as the one given as an example in the problem statement, and its ABC number is 3.

Sample Input 3

????C?????B??????A???????

Sample Output 3

979596887

In this case, the sum of the ABC numbers of all the 3^Q strings is 2291979612924, and we should print this number modulo 10^9 + 7, that is, 979596887.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)
const ll mo=1000000007;
ll ans=0;

int main()
{
string s;
cin >> s;
ll len=(int)(s.length());
ll dp[len][4]={};
if(s[0]=='A'){dp[0][0]=1;dp[0][1]=1;}
else if(s[0]=='?'){dp[0][0]=3;dp[0][1]=1;}
else {dp[0][0]=1;}
string abc="ABCZ";
rep(i,len-1)rep(j,4){
    if(s[i+1]=='?'){
        dp[i+1][j]+=3*dp[i][j];
        dp[i+1][j]=dp[i+1][j]%mo;
        if(j!=3){dp[i+1][j+1]+=dp[i][j];dp[i+1][j+1]=dp[i+1][j+1]%mo;}
        }
    else if(s[i+1]==abc[j]){
        dp[i+1][j]+=dp[i][j];
        dp[i+1][j]=dp[i+1][j]%mo;
        dp[i+1][j+1]+=dp[i][j];
        dp[i+1][j+1]=dp[i+1][j+1]%mo;
    }
    else {
        dp[i+1][j]+=dp[i][j];
        dp[i+1][j]=dp[i+1][j]%mo;
    }
}
/* for (int i = 0; i < 4; ++i){
for (int j = 0; j < 4; ++j) {
    cout << dp[i][j] << " ";
}cout  << endl;} */

cout << dp[len-1][3] << endl;
return 0;
}