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