A Maximization Problem

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 64M

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Problem type

You are given an integer N. You want to break it down into three non-negative 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.


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