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:
//https://github.com/EgorKulikov/yaal/tree/master/lib/main/net/egork
        
import java.util.*;
import java.io.*;
public class Main{
    static PrintWriter out;
    static InputReader in;
    public static void main(String args[]){
        out = new PrintWriter(System.out);
        in = new InputReader();
        new Main();
        out.flush(); out.close();
    }   
    Main(){
        solve();
    }
    long modInverse(long a, long m)
    {
        long m0 = m;
        long y = 0, x = m - 1;
 
        if (m == 1)
            return 0;
 
        while (a > 1) {
            // q is quotient
            if(m == 0)return -1;
            long q = a / m;
 
            long t = m;
 
            // m is remainder now, process
            // same as Euclid's algo
            m = a % m;
            a = t;
            t = y;
 
            // Update x and y
            y = x - q * y;
            x = t;
        }
 
        // Make x positive
        if (x < 0)
            x += m0;
 
        return (x % m0 + m0) % m0;
    }
    int gcd(int x, int y){
    	if(x % y == 0)return y;
    	return gcd(y, x % y);
    }
    void solve(){
    	int n = in.nextInt();
    	ArrayList<Integer> al = new ArrayList<>();
    	ArrayList<Integer> al1 = new ArrayList<>();
    	for(int i = 1; i <= n - 1; i++){
    		if(i != 1 && gcd(n, i) != 1)continue;
    		if((long)i * i % n == 1){
    			int x = (int)modInverse(i, n);
    			// System.out.println(i + " " + x);
    			if(i != x && x != -1)al1.add(i);
    		}
    		else al.add(i);
    	}
    	for(int i = 0; i < 4 * (al1.size() / 4); i++){
    		al.add(al1.get(i));
    	}
    	Collections.sort(al);
    	if(al.size() == 0 || al.get(0) != 1)al.add(1);
    	Collections.sort(al);
    	out.println(al.size());
    	for(int x : al)out.print(x + " ");
    }
    public static class InputReader{
        BufferedReader br;
        StringTokenizer st;
        InputReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
        public String next(){
            while(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){}
            }
            return st.nextToken();
        }
    }
}