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Description

Given a positive integer $n$, consider an $n \times n$ matrix $a$ where the element in the $i$-th row and $j$-th column is given by $a_{i,j} = (i-1) \times n + j$. Below is an example for $n = 4$:

$ \begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \\ \end{bmatrix} $

Your task is to select some numbers from the matrix such that:

• Exactly two numbers are chosen from each row.

• Exactly two numbers are chosen from each column.

You need to determine the minimum sum of the numbers that are selected.

Input Format

The first line contains a positive integer $n$, representing the size of the matrix.

$2 \leq n \leq 10^3$

Output Format

A single integer, representing the minimum sum of the numbers that are selected.

Sample Input #1

2

Sample Output #1

10

Sample Input #2

4

Sample Output #2

68