Bracket Sequences I

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

Your task is to calculate the number of valid bracket sequences of length $n$. For example, when $n=6$, there are $5$ sequences:

• ()()()
  
• ()(())
  
• (())()
  
• ((()))
  
• (()())
  

Input

The only input line has an integer $n$.

Output

Print the number of sequences modulo $10^9+7$.

Constraints

• $1 \le n \le 10^6$
  

Example

Input:
6

Output:
5