CSES - 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