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: Wrong Answer)

#include <iostream>
#include<map>
#include <algorithm>
#include <vector>
#include <string>
#include <utility>
#include <queue>
#define INF 1e9+7
#define rep(i,n) for(int i=0;i<n;i++)
#define NO cout<<"NO"<<endl;
#define YES cout << "YES"<<endl;
#define No cout << "No"<<endl;
#define Yes cout << "Yes"<<endl;
#define all(a) a.begin(),a.end()
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;


//(int)'a'は97 (int)'A'は65 (int)'1'は49
//おまじない

const int maxn = 100000;

int main() {

	string s;
	ll ans = 0;
	ll mod = INF;
	ll sc = 0, sq = 0;
	ll la = 0, lc = 0, lq = 0;

	cin >> s;

	rep(i, s.size()) {
		if (s[i] == 'C')sc++;
		if (s[i] == '?')sq++;
	}

	ll qk = 1;

	for (int i = 0; i < sq; i++) {
		qk = qk * 3;
	}


	rep(i, s.size()) {
		ll rc = sc - lc;
		ll rq = sq - lq;
		if (s[i] == 'B') {
			//ABC
			ans += (la * rc)*qk;
			//AB?
			ans += (la * rq)*(qk / 3);
			//?BC
			ans += (lq * rc) *(qk / 3);
			//?B?
			ans += (lq* rq)*(qk / 9);

		}
		else if (s[i] == '?') {
			rq--;
			//A?C
			ans += (la * rc)*(qk / 3);
			//??C
			ans += (lq * rc)*(qk / 9);
			//A??
			ans += (la * rq)*(qk / 9);
			//???
			ans += (lq * rq)*(qk / 27);
			lq++;
		}
		else if (s[i] == 'A') {
			la++;
		}
		else if (s[i] == 'C') {
			lc++;
		}
		ans = ans % mod;
	}

	cout << ans << endl;

	return 0;
}