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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
function Main(input) {
    let cin = new Inputer(input);
    let S = cin.getStr();
    let N = S.length;
    const ABC = "ABC";
    const MOD = 1e9 + 7;
    let dp = new Array(N + 1).fill(0).map(() => new Array(3 + 1).fill(0));
    for (let i = N; i >= 0; --i) {
        for (let j = 3; j >= 0; --j) {
            if (i == N) {
                dp[i][j] = (j == 3 ? 1 : 0);
            } else {
                dp[i][j] = dp[i + 1][j] * (S[i] == '?' ? 3 : 1);
                if (j < 3 && (S[i] == '?' || S[i] == ABC[j])) {
                    dp[i][j] += dp[i + 1][j + 1];
                }
                dp[i][j] %= MOD;
            }
        }
    }
    console.log(dp[0][0]);
}
class Inputer{constructor(t){this.cnt=0,this.items=t.split(/\n|\s/)}getInt(){return this.items[this.cnt++]-0}getIntArray(t){let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getInt();return r}getStr(){return this.items[this.cnt++]}getStrArray(t){let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getStr();return r}}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));