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Contest: Task: Related: TaskD TaskF

Score : $1300$ points

Problem Statement

There is a string $s$ consisting of a and b. Snuke can perform the following two kinds of operation any number of times in any order:

  • Choose an occurrence of aa as a substring, and replace it with b.
  • Choose an occurrence of bb as a substring, and replace it with a.

How many strings $s$ can be obtained by this sequence of operations? Find the count modulo $10^9 + 7$.

Constraints

  • $1 \leq |s| \leq 10^5$
  • $s$ consists of a and b.

Input

Input is given from Standard Input in the following format:

$s$

Output

Print the number of strings $s$ that can be obtained, modulo $10^9 + 7$.

Sample Input 1

aaaa

Sample Output 1

6

Six strings can be obtained:

  • aaaa
  • aab
  • aba
  • baa
  • bb
  • a

Sample Input 2

aabb

Sample Output 2

5

Five strings can be obtained:

  • aabb
  • aaa
  • bbb
  • ab
  • ba

Sample Input 3

ababababa

Sample Output 3

1

Snuke cannot perform any operation.

Sample Input 4

babbabaaba

Sample Output 4

35