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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strings"
)

const MOD = 1000000007

func main() {
	fmt.Println(MOD)
	scanner := bufio.NewScanner(os.Stdin)
	var str string
	scanner.Scan()
	fmt.Sscanf(scanner.Text(), "%s", &str)
	chars := strings.Split(str, "")

	sizes := make([]int, len(chars)+1)
	a := make([]int, len(chars)+1)
	ab := make([]int, len(chars)+1)
	abc := make([]int, len(chars)+1)

	sizes[0] = 1
	a[0] = 0
	ab[0] = 0
	abc[0] = 0

	for i := 1; i < len(sizes); i++ {
		if chars[i-1] == "?" {
			sizes[i] = (3 * sizes[i-1]) % MOD
		} else {
			sizes[i] = sizes[i-1]
		}
	}

	for i := 1; i < len(a); i++ {
		switch chars[i-1] {
		case "?":
			a[i] = (3*a[i-1]%MOD + sizes[i-1]) % MOD
		case "A":
			a[i] = (a[i-1] + sizes[i-1]) % MOD
		default:
			a[i] = a[i-1]
		}
	}

	for i := 1; i < len(ab); i++ {
		switch chars[i-1] {
		case "?":
			ab[i] = (3*ab[i-1]%MOD + a[i-1]) % MOD
		case "B":
			ab[i] = (ab[i-1] + a[i-1]) % MOD
		default:
			ab[i] = ab[i-1]
		}
	}

	for i := 1; i < len(abc); i++ {
		switch chars[i-1] {
		case "?":
			abc[i] = (3*abc[i-1]%MOD + ab[i-1]) % MOD
		case "C":
			abc[i] = (abc[i-1] + ab[i-1]) % MOD
		default:
			abc[i] = abc[i-1]
		}
	}

	/*
		fmt.Println(sizes)
		fmt.Println(a)
		fmt.Println(ab)
		fmt.Println(abc)
	*/

	fmt.Println(abc[len(chars)])
}