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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

import static java.lang.System.in;
import static java.lang.System.out;

public class Main{
    final static int INF=Integer.MAX_VALUE;
    final static int nINF=Integer.MIN_VALUE;
    final static long MOD=1000000007;

    public static void main(String[] args){
        FastReader fr=new FastReader();
        int tc=1;
        while(tc-->0){
            int n=fr.nextInt();
            ArrayList<Integer>al=new ArrayList<>();
            long mult=1;
            for (int i=1;i<=n;i++){
                if(gcd(i,n)==1){
                    al.add(i);
                    mult=(mult*i)%n;
                }
            }

            int tr=-1;
            if(mult>1){
                tr=(int)mult;
            }

            if(tr==-1){
                out.println(al.size());
            }
            else {
                out.println(al.size()-1);
            }

            StringBuilder sb=new StringBuilder();
            for (int here:al){
                if (here!=tr){
                    sb.append(here+" ");
                }
            }
            sb.deleteCharAt(sb.length()-1);
            out.println(sb);
        }
    }

    ///////////////////////////////////////////////////////////

    static int[] fillInt(int n,FastReader fr){
        int ret[]=new int[n];
        for(int i=0;i<n;i++){
            ret[i]=fr.nextInt();
        }
        return ret;
    }

    static long[] fillLong(int n,FastReader fr){
        long ret[]=new long[n];
        for(int i=0;i<n;i++){
            ret[i]=fr.nextInt();
        }
        return ret;
    }

    static int max(int a,int b){
        return Math.max(a,b);
    }

    static long max(long a,long b){
        return Math.max(a,b);
    }

    static int min(int a,int b){
        return Math.min(a,b);
    }

    static long min(long a,long b){
        return Math.min(a,b);
    }

    static int modDivide(int a,int b){
        return (int) (a*Math.pow(b,MOD-2)%MOD);
    }

    static int gcd(int a,int b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }

    static long gcd(long a,long b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }

    static int lcm(int a,int b){
        return (a*b)/gcd(a,b);
    }

    static int longestProperPrefixSuffix(String str){
        // KMP
        int n=str.length();
        int st[]=new int[n];
        int len=0,c=1;
        while(c<n){
            if(str.charAt(len)==str.charAt(c)){
                len++;
                st[c]=len;
                c++;
            }else{
                if(len>0){
                    len=st[len-1];
                }else{
                    st[c]=0;
                    c++;
                }
            }
        }
//        out.println(Arrays.toString(st));
        return st[n-1];
    }

    static int lowerBound(int a[],int val){
        int ret=Arrays.binarySearch(a,val);
        if(ret<0){
            return -1;
        }else{
            while(ret>0 && a[ret-1]==val){
                ret--;
            }
            return ret;
        }
    }

    static int upperBound(int a[],int val){
        int ret=Arrays.binarySearch(a,val);
        if(ret<0){
            return -1;
        }else{
            while(ret<a.length-1 && a[ret+1]==val){
                ret++;
            }
            return ret;
        }
    }

    static class FastReader{
        BufferedReader br;
        StringTokenizer st;

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

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

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

        byte nextByte(){
            return Byte.parseByte(next());
        }

        Float nextFloat(){
            return Float.parseFloat(next());
        }

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

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

        short nextShort(){
            return Short.parseShort(next());
        }

        Boolean nextbol(){
            return Boolean.parseBoolean(next());
        }

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