Your task is to calculate the number of ways an integer $n$ can be represented as a sum of three distinct positive integers.

For example, if $n=9$, there are $3$ solutions:

• $1+2+6=9$
• $1+3+5=9$
• $2+3+4=9$

Input

The only input line has an integer $n$.

Output

Print one line: the number of solutions.

Example

Input:

9

Output:

3

Grading

In each test $1 \le n \le 1000$. You will get $100$ points for the task if your program gives the correct answer in each test.