Almost Equal
题意翻译
### Problem C Almost Equal
题意:给出一个数字n,由1,2,3,...,2*n按一定顺序组成一个圆环,求出一种顺序使得以下成立:
将圆环上的每n个连续数字累加起来得到一个和,将这个和写在黑板上,写完2n个和以后,使得黑板上任意两个和的差小于等于1。
举例:
当n=3的情况:
![mlxmTI.png](https://s2.ax1x.com/2019/08/19/mlxmTI.png)
在左图中,1+4+5=10,4+5+2=11,5+2+3=10,2+3+6=11,3+6+1=10,6+1+4=11
|11-10|<=1,满足题意。
在右图中,1+5+6=12,3+2+4=9, |12-9|>=3,不满足题意。
输入:一个正整数n,(1<=n<=100000)
输出:如果没有解决方案,输出“NO”
如果有解决方案,输出“YES”,下一行输出2n个正整数,表示满足题意的任意一种顺序
题目描述
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 $ .
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1205A/9cba5ca83f08157cd471ad2c4144ebafdf1f05ac.png)
输入输出格式
输入格式
The first and the only line contain one integer $ n $ ( $ 1 \le n \le 10^5 $ ).
输出格式
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.
输入输出样例
输入样例 #1
3
输出样例 #1
YES
1 4 5 2 3 6
输入样例 #2
4
输出样例 #2
NO
说明
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.