Problem Statement

Imagine you have a set of building blocks numbered $1$ to N$.$ You want to arrange them in a line, but with a special twist:

The arrangement must be "balanced," meaning you can split it into two halves such that the sum of the numbers in the first half equals the sum of the numbers in the second half.

You want to find the arrangement with the smallest possible order. For example, if numbers are arranged in ascending order, it becomes harder to achieve balance.

Here's an example:

If N $5,$ you could arrange the blocks as $[2,3,1,4,5].$ Here, the first half $(2)+3+1)$ equals the second half $(4+5).$

But there's a smaller order possible: $[1,2,4,3,5].$ In this case, the first half $(1+2+4)$ still equals the second half $(3+5).$

Can you find the arrangement with the smallest possible order for any given number of blocks N$?$

Input Format

The first line of input contains one integers N

Output Format

For each input, output a line containing N integers pl$,$p$2$pN seprated by space the lexicographically smallest balanced permutation.

Constraints