Problem Statement

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.

Input

Input is given from Standard Input in the following format:
S

Output

Print the answer.

Constraints

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

Sample Input 1

7

Sample Output 1

3

3 sequences satisfy the condition: {3,4}, {4,3} and {7}.

Sample Input 2

2

Sample Output 2

0

There are no sequences that satisfy the condition.

Sample Input 3

1729

Sample Output 3

294867501

见题面 Input 部分

见题面 Output 部分