Prefix Product Sequence

题意翻译

题目描述 是否存在一个长度为$n$的排列，使得其前缀积在$mod\,n$意义下两两不同？ 输入 一行一个正整数$n(1 \leq n \leq 10^5)$ 输出 如果存在，输出一行$YES$，接下来$n$行每行一个数表示这个排列；如果不存在，输出一行$NO$

题目描述

Consider a sequence $ \[a_{1},a_{2},... ,a_{n}\] $ . Define its prefix product sequence . Now given $ n $ , find a permutation of $ \[1,2,...,n\] $ , such that its prefix product sequence is a permutation of $ \[0,1,...,n-1\] $ .

输入输出格式

输入格式

The only input line contains an integer $ n $ ( $ 1<=n<=10^{5} $ ).

输出格式

Consider a sequence $ \[a_{1},a_{2},... ,a_{n}\] $ . Define its prefix product sequence . Now given $ n $ , find a permutation of $ \[1,2,...,n\] $ , such that its prefix product sequence is a permutation of $ \[0,1,...,n-1\] $ .

输入输出样例

输入样例 #1

7

输出样例 #1

YES
1
4
3
6
5
2
7

输入样例 #2

6

输出样例 #2

NO

说明

For the second sample, there are no valid sequences.