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: \[ abc + bc + ab + ac \]

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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