Product 1 Modulo N

time limit per test: 1 second

memory limit per test: 256 megabytes

Articles

Now you get Baby Ehab’s first words: “Given an integer $n$ , find the longest subsequence of $1,2,…,n−1$ 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 $n$ ( $2≤n≤10^5$ ).

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.

Examples

input

output

1
2

3
1 2 3

input

output

1
2

4
1 3 5 7

Note

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 $[1,2,3]$ .

Tutorial

若 $gcd(x, n) \neq 1$ ，那么不存在一个数 $y$ 使得 $xy \equiv 1 \ (mod \ n)$ ，所以这 $k$ 个数中必不包括与 $n$ 不互质的数，而所有与 $n$ 互质的数的乘积 $B$ 满足 $B \equiv 1 \ (mod \ n)$ 或者 $B \equiv -1 \ (mod \ n)$ 。

Code

#include <bits/stdc++.h>

using namespace std;

const int maxn = 1e6+1;
int a[maxn], tot;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    long long ans = 1;
    for(int i = 1; i < n; ++ i) {
        if (__gcd(i, n) == 1) {
            a[++tot] = i;
            ans = ans * i % n;
        }
    }
    if (ans != 1) tot --;
    cout << tot << "\n";
    for(int i = 1; i <= tot; ++ i) {
        cout << a[i] << " \n"[i==tot];
    }
    return 0;
}