A12818 | Almost Equal

You are given integer $n$ . You have to arrange numbers from $1$ to $2n$ , using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every $n$ consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard $2n$ numbers differ not more than by $1$ .

For example, choose $n = 3$ . On the left you can see an example of a valid arrangement: $1 + 4 + 5 = 10$ , $4 + 5 + 2 = 11$ , $5 + 2 + 3 = 10$ , $2 + 3 + 6 = 11$ , $3 + 6 + 1 = 10$ , $6 + 1 + 4 = 11$ , any two numbers differ by at most $1$ . On the right you can see an invalid arrangement: for example, $5 + 1 + 6 = 12$ , and $3 + 2 + 4 = 9$ , $9$ and $12$ differ more than by $1$ .


The first and the only line contain one integer $n$ ( $1 \le n \le 10^5$ ).

If there is no solution, output "NO" in the first line.

If there is a solution, output "YES" in the first line. In the second line output $2n$ numbers — numbers from $1$ to $2n$ in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.