Bracket Sequences I

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