시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 512 MB 0 0 0 0.000%

문제

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.

입력

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

출력

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.

예제 입력 1

4

예제 출력 1

YES
3 0 2 1

예제 입력 2

3

예제 출력 2

NO

예제 입력 3

1

예제 출력 3

YES
0