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 <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <iomanip>
#include <array>
#include <numeric>
#include <regex>
#include <bitset>
#include <deque>

using namespace std;
typedef long long ll;
typedef pair<int, int> p_ii;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)

const int INF = 1e9;
const double PI = acos(-1.0);
const ll MOD = 1e9 + 7;


int main() {
	
	string S;
	cin >> S;

	vector<ll> dp(100010, -1), a(100010,-1), ab(100010,-1), sum(100010,-1);
	dp[0] = 0; a[0] = 0; ab[0] = 0; sum[0] = 1;

	rep(i, S.size()) {
		dp[i + 1] = dp[i]; a[i + 1] = a[i]; ab[i + 1] = ab[i]; sum[i + 1] = sum[i];
		if (S[i] == '?') {
			a[i + 1] += (sum[i] + 2 * a[i]) % MOD;
			ab[i + 1] += (a[i] + 2 * ab[i]) % MOD;
			dp[i + 1] += (ab[i] + 2 * dp[i]) % MOD;

			sum[i + 1] = sum[i] * 3;
		}
		else {
			if (S[i] == 'A') {
				a[i + 1] += sum[i] % MOD;
			}
			else if (S[i] == 'B') {
				ab[i + 1] += a[i] % MOD;
			}
			else if (S[i] == 'C') {
				dp[i + 1] += ab[i] % MOD;
			}
		}
	}

	cout << dp[S.size()]%MOD << endl;

	return 0;
}