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 <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <set>
#include <cstdint>
#include <cstdio>
#include <cstring>
#include <utility>
#include <queue>

using namespace std;
typedef long long signed int ll;

constexpr int inf = INT32_MAX / 2;
constexpr int mod = 1000000007;
constexpr int maxn = 100000;

class djikstra {
private:
	ll* d = nullptr;
	map<int, map<int, ll>> p;
	int sz = 0;
public:
	void add_path(int from, int to, ll cost) {
		p[from][to] = cost;
	}
	void compute(int from,int nodes) {
		sz = nodes;
		if (d != nullptr) delete d;
		d = new ll[nodes];
		auto cmp = [this](int a, int b) {return d[a] > d[b]; };
		priority_queue <ll, vector<ll>, decltype(cmp)> q(cmp);
		for (int i = 0; i < nodes; i++) d[i] = INT64_MAX / 2;
		d[from] = 0;
		q.push(from);
		while (!q.empty()) {
			for (auto& e : p[q.top()]) {
				if (d[e.first] > d[q.top()] + e.second) {
					d[e.first] = d[q.top()] + e.second;
					q.push(e.first);
				}
			}
			q.pop();
		}
	}
	ll operator[](int node) {
		if (node >= sz) return INT64_MAX/2;
		return d[node];
	}
};

string s;
ll abc[maxn + 1], bc[maxn + 1], c[maxn + 1], q[maxn + 1];

ll dpow3[maxn + 1];
ll mpow3(ll power) {
	if (power == 0) return 1;
	if (dpow3[power] == 0) dpow3[power] = (3 * mpow3(power - 1)) % mod;
	return dpow3[power];
}

int main() {
	cin >> s;
	for (int i = s.length() - 1; i >= 0; i--) q[i] = q[i + 1] + (s[i] == '?' ? 1 : 0);
	for (int i = s.length() - 1; i >= 0; i--) c[i] = ((c[i + 1] * (s[i] == '?' ? 3 : 1)) + (s[i] == '?' || s[i] == 'C' ? mpow3(q[i + 1]) : 0)) % mod;
	for (int i = s.length() - 2; i >= 0; i--) bc[i] = ((bc[i + 1] * (s[i] == '?' ? 3 : 1)) + (s[i] == '?' || s[i] == 'B' ? c[i + 1] : 0)) % mod;
	for (int i = s.length() - 3; i >= 0; i--) abc[i] = ((abc[i + 1] * (s[i] == '?' ? 3 : 1)) + (s[i] == '?' || s[i] == 'A' ? bc[i + 1] : 0)) % mod;
	std::cout << abc[0] << endl;
}