A. Almost Equaltime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.  InputThe first and the only line contain one integer n (1 \le n \le 10^5).OutputIf 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.ExamplesInput
3
Output
YES
1 4 5 2 3 6 Input
4
Output
NONoteExample from the statement is shown for the first example. It can be proved that there is no solution in the second example.
3

YES 1 4 5 2 3 6 
['constructive algorithms', 'greedy', 'math', '*1200']