#D4222. Redistribution
Redistribution
Redistribution
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
inputFormat
outputFormat
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
样例
73