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 "fmt"
const mod int64 = 1000000007
func main() {
  var s string
  var n int
  var m int64 = 0
  r := map[string]int64{}
  l := map[string]int64{}
  fmt.Scan(&s)
  n = len(s)
  for i:=0;i<n;i++ {
    r[s[i:i+1]]++
  }
  for i:=0;i<n;i++ {
    r[s[i:i+1]]--
    if s[i:i+1] == "B" || s[i:i+1] == "?" {
      m += l["A"]*r["C"]*pow(3,l["?"])*pow(3,r["?"])
      m %= mod
      m += l["?"]*r["C"]*pow(3,l["?"]-1)*pow(3,r["?"])
      m %= mod
      m += l["A"]*r["?"]*pow(3,l["?"])*pow(3,r["?"]-1)
      m %= mod
      m += l["?"]*r["?"]*pow(3,l["?"]-1)*pow(3,r["?"]-1)
      m %= mod
    }
    l[s[i:i+1]]++
  }
  fmt.Println(m)
}
func pow(base int64,power int64) int64 {
  if base == 1 { return 1 }
  if power < 0 { return 0 }
  if power == 0 { return 1 }
  if power%2 == 0 {
    var h int64 = pow(base,power/2)
    return (h*h)%mod
  } else {
    return (base*pow(base,power-1))%mod
  }
}