Counting Reorders

• Time limit: 1.00 s
• Memory limit: 512 MB

Calculate the number of ways you can reorder the characters of a string so that no two adjacent characters are the same.

For example, the answer for aabc is $6$, because the possible orders are abac, abca, acab, acba, baca, and caba.

Input

The only input line has a string that consists of $n$ characters between a–z.

Output

Print an integer: the answer modulo $10^9+7$.

Constraints

• $1 \le n \le 5000$
  

Example

Input:
aabc

Output:
6