Problem: 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


5


Output


3
1 2 3 

Input


8


Output


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].

Solution (in JAVA):

Solution:
/*
bts songs to dance to:
ON
 */
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import static java.lang.System.out;
import java.util.*;
import java.io.*;
import java.math.*;

public class x1514C
{
    public static void main(String hi[]) throws Exception
    {
        BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(infile.readLine());
        int N = Integer.parseInt(st.nextToken());
        ArrayList<Integer> ls = new ArrayList<Integer>();
        int cnt = 0;
        long mod = 1L;
        for(int v=1; v < N; v++)
            if(gcd(v, N) == 1)
            {
                cnt++;
                ls.add(v);
                mod = (mod*v)%N;
            }
        if(mod > 1)
            cnt--;
        System.out.println(cnt);
        StringBuilder sb = new StringBuilder();
        for(int x: ls)
            if(x != mod || x == 1)
                sb.append(x+" ");
        System.out.println(sb);
    }
    public static long gcd(long a, long b)
    {
        if(a > b)
        {
            long t = a;
            a = b;
            b = t;
        }
        if(a == 0L)
            return b;
        return gcd(b%a, a);
    }
}
/*
split into N is even or odd case?
N is even:
    product of all numbers MUST be odd
N is odd:
    product of all numbers MUST be even
NECESSARY CONDITION: gcd(v, N) == 1

 */