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 (Clang 3.8.0) (judge verdict: Accepted)

//
//  main.cpp
//

#include <algorithm>
#include <array>
#include <assert.h>
#include <iomanip>
#include <iostream>
#include <limits>
#include <math.h>
#include <memory>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <vector>

using namespace std;

using ll = int64_t;
using ull = uint64_t;

template<typename T>
vector<T> make_vec_nd(T init, ll size) {
    return vector<T>(size, init);
}
template<typename T, typename... Args>
auto make_vec_nd(T init, ll size, Args... rest) {
    auto inner = make_vec_nd(init, rest...);
    return vector<decltype(inner)>(size, inner);
}

#define rep(i,a,b) for(ll i=(a);i<(b);i++)
#define rrep(i,a,b) for(ll i=(a)-1;i>=(b);i--)

struct Mod {
    static ll BASE;
    ll value = 0;
    static ll residue(ll value) { return (value % BASE + BASE) % BASE; }
    Mod()
    : value(0) {}
    Mod(ll value)
    : value(residue(value)) {}
    Mod operator+(const Mod& rhs) const { return Mod(value + rhs.value); }
    void operator+=(const Mod& rhs) { *this = *this + rhs; }
    Mod operator-(const Mod& rhs) const { return Mod(value - rhs.value); }
    void operator-=(const Mod& rhs) { *this = *this - rhs; }
    Mod operator*(const Mod& rhs) const { return Mod(value * rhs.value); }
    void operator*=(const Mod& rhs) { *this = *this * rhs; }
    Mod operator/(const Mod& rhs) const { return *this * rhs.inv(); }
    void operator/=(const Mod& rhs) { *this = *this / rhs; }
    Mod inv() const {
        if (value == 0) {
            assert(false);
            throw "[Mod::inv] div by zero";
        }
        ll ans, sub;
        ll d = Mod::gcd_with_coef(value, BASE, ans, sub);
        if (d != 1) {
            assert(false);
            throw "[Mod::inv] not invertible";
        }
        return ans;
    }
    static ll gcd_with_coef(ll x, ll y, ll& out_cx, ll& out_cy) {
        if (x < 0) {
            ll d = gcd_with_coef(-x, y, out_cx, out_cy);
            out_cx *= -1;
            return d;
        }
        if (y < 0) {
            ll d = gcd_with_coef(x, -y, out_cx, out_cy);
            out_cy *= -1;
            return d;
        }
        if (x > y) {
            return gcd_with_coef(y, x, out_cy, out_cx);
        }
        if (x == 0) {
            out_cx = 0;
            out_cy = 1;
            return y;
        }
        ll q = y / x;
        ll r = y % x;
        ll d = gcd_with_coef(r, x, out_cy, out_cx);
        out_cx -= q * out_cy;
        return d;
    }
};
ll Mod::BASE = 1000000007;

int main() {
    string s;
    cin >> s;
    auto a_cnt = make_vec_nd(Mod(0), s.size()+1);
    auto ab_cnt = make_vec_nd(Mod(0), s.size()+1);
    auto abc_cnt = make_vec_nd(Mod(0), s.size()+1);
    Mod hatena_cnt_pow = 1;
    rep(n,1,s.size()+1) {
        if (s[n-1] == 'A' || s[n-1] == '?') {
            a_cnt[n] += a_cnt[n-1] + hatena_cnt_pow;
            ab_cnt[n] += ab_cnt[n-1];
            abc_cnt[n] += abc_cnt[n-1];
        }
        if (s[n-1] == 'B' || s[n-1] == '?') {
            a_cnt[n] += a_cnt[n-1];
            ab_cnt[n] += ab_cnt[n-1] + a_cnt[n-1];
            abc_cnt[n] += abc_cnt[n-1];
        }
        if (s[n-1] == 'C' || s[n-1] == '?') {
            a_cnt[n] += a_cnt[n-1];
            ab_cnt[n] += ab_cnt[n-1];
            abc_cnt[n] += abc_cnt[n-1] + ab_cnt[n-1];
        }
        if (s[n-1] == '?') {
            hatena_cnt_pow *= 3;
        }
    }
    cout << abc_cnt[s.size()].value << endl;
}