Beautiful Permutation

A permutation $a\_0, a\_1, \ldots, a\_{n - 1}$ of $0, 1, \ldots, n - 1$ is said to be beautiful if the sequence $b\_0, \ldots, b\_{n - 1}$ defined as $b\_i = |a\_i - i|$ is also a permutation of $0, \ldots, n - 1$. 

Given $n$, construct a beautiful permutation of $n$ elements or determine that it does not exist.

The first line contains a single integer $n$ ($1 \leq n \leq 10^6$): the size of the permutation.

If there is no beautiful permutation of $n$ elements, output a single line with the word "NO".

Otherwise, on the first line, print "YES", and on the second line, print $n$ space-separated integers $a\_0, \ldots, a\_{n-1}$: the beautiful permutation. If there are multiple beautiful permutations, print any one of them.