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