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

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

The only input line has an integer $n$ .

• $1 \le n \le 10^6$

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