Contest Duration: - (local time) (100 minutes) Back to Home
D - Redistribution /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq S \leq 2000
• 入力はすべて整数

### 入力

S


### 入力例 1

7


### 出力例 1

3


### 入力例 2

2


### 出力例 2

0


### 入力例 3

1729


### 出力例 3

294867501


Score : 400 points

### 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.

### Constraints

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

### Input

Input is given from Standard Input in the following format:

S


### 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