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;
#define INF (1<<30)
#define INFLL (1ll<<60)
typedef pair<int, int> P;
typedef pair<int, P> E;
#define MOD (1000000007ll)
#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	b += MOD;
	a += b;
	a %= MOD;
}

ll cnt[4][123456];

ll rwpw(ll x, ll p){
	ll ret = 1ll;
	while(p){
		if(p%2){
			mul_mod(ret,x);
		}
		mul_mod(x,x);
		p /= 2;
	}
	return ret;
}

int main(void){
	int n,i,j;
	ll ans=0ll,l,r,t;
	string s,c="ABC?";
	cin >> s;
	n = s.l_ength();
	for(j=0; j<4; ++j){
		cnt[j][0] = 0ll;
	}
	for(i=0; i<n; ++i){
		for(j=0; j<4; ++j){
			cnt[j][i+1] = cnt[j][i];
			if(s[i] == c[j]){
				++cnt[j][i+1];
			}
		}
	}
	for(i=0; i<n; ++i){
		if(s[i] == 'A' or s[i] == 'C'){
			continue;
		}
		l = cnt[0][i];
		t = cnt[3][i];
		mul_mod(l,rwpw(3ll,t));
		if(t){
			mul_mod(t,rwpw(3ll,t-1));
		}
		add_mod(l,t);
		r = cnt[2][n] - cnt[2][i+1];
		t = cnt[3][n]-cnt[3][i+1];
		mul_mod(r,rwpw(3ll,t));
		if(t){
			mul_mod(t,rwpw(3ll,t-1));
		}
		add_mod(r,t);
		t = l;
		mul_mod(t,r);
		add_mod(ans,t);
	}
	cout << ans << endl;
	return 0;
}