Given is an integer S. Find how many sequences there are whose terms are all integers greater than or equal to 3, and whose sum is equal to S. The answer can be very large, so output it modulo 10^9 + 7.

Constraints

• $1 \leq S \leq 2000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer.

Examples

Input

7

Output

3

Input

2

Output

0

Input

1729

Output

294867501

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