You are given an integer ~N~. You want to break it down into three integers ~a~, ~b~, and ~c~ such that ~a+b+c=N~ and maximizes: $$\displaystyle abc + bc + ab + ac $$

Print out the maximum such value of ~abc + bc + ab + ac~ given ~N~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 5 \times 10^6)~.

Output Specification

Output the maximum such value of ~abc + bc + ab + ac~.

Subtasks

Subtask 1 [20%]

~N \le 1~ ~000~

Subtask 2 [80%]

No further constraints.

Sample Input

4

Sample Output

7

Explanation for Sample

One possible solution would be ~a = 1, b = 2, c = 1~.