CF1514C · Product 1 Modulo N

• 难度：1600
• 标签：greedy、number theory
• 链接：https://codeforces.com/problemset/problem/1514/C
• 时间限制：1 second　内存限制：256 megabytes
• 出现位置：假期自习包/A-数学基础(快速幂/筛法/gcd/组合数取模)

英文原题面

Statement

Now you get Baby Ehab's first words: "Given an integer $n$, find the longest subsequence of $[1,2, \ldots, n-1]$ whose product is $1$ modulo $n$." Please solve the problem. A sequence $b$ is a subsequence of an array $a$ if $b$ can be obtained from $a$ by deleting some (possibly all) elements. The product of an empty subsequence is equal to $1$.

Input

The only line contains the integer $n$ ($2 \le n \le 10^5$).

Output

The first line should contain a single integer, the length of the longest subsequence. The second line should contain the elements of the subsequence, in increasing order. If there are multiple solutions, you can print any.

样例

样例 1

输入：

5

输出：

3
1 2 3 

样例 2

输入：

8

输出：

4
1 3 5 7 

样例解释（英文原文）

In the first example, the product of the elements is $6$ which is congruent to $1$ modulo $5$. The only longer subsequence is $[1,2,3,4]$. Its product is $24$ which is congruent to $4$ modulo $5$. Hence, the answer is $[1,2,3]$.