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:
//import kotlin.reflect.jvm.internal.impl.load.kotlin.JvmType;

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/*
@author kalZor
 */
public class TaskC {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        int testCount = 1;
//        testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class Solver {
        public int gcd(int a,int b){
            if(a==0) return b;
            else return gcd(b%a,a);
        }
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            ArrayList<Integer> a = new ArrayList<>();
            a.add(1);
            long prd = 1;
            for(int i=2;i<n;i++){
                if(gcd(i,n)==1){
                    prd = (prd*i)%n;
                    a.add(i);
                }
            }
            if(prd!=1){
                out.println(a.size()-1);
                for(int x:a){
                    if(x!=prd) out.print(x+" ");
                }
                out.println();
                return;
            }
            out.println(a.size());
            for(int x:a) out.print(x+" ");
            out.println();
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader(InputStream stream){
            br = new BufferedReader(new
                InputStreamReader(stream));
        }

        public String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt(){
            return Integer.parseInt(next());
        }

        public long nextLong(){
            return Long.parseLong(next());
        }

        public double nextDouble(){
            return Double.parseDouble(next());
        }

        public String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }
            catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }

        public int[] nextArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
                return a;
        }
    }
}