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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public  class Solution
{   
    static int mod=1000000007;
    static FastReader sc=new FastReader();
    public static long gcd(long a,long b)
    {
        if(b==0)return a;
        else
        {
            return(gcd(b,a%b));
        }
    }
    public static long multiply(long a,long b)
    {
        return((a%mod * b%mod)%mod);
    }
	public static void main (String[] args) throws java.lang.Exception
	{
	    StringBuilder sb=new StringBuilder();
		long n=sc.nextLong();
		long mul=1;
		int count=0;
		ArrayList<Long> al=new ArrayList<Long>();
		for(long i=1;i<n-1;++i)
		{
		    if(gcd(i,n)==1)
		    {
		        al.add(i);
		        ++count;
		        sb.append(i+" ");
		        mul=(mul*i)%n;
		    }
		}
		if((mul*(n-1))%n==1)
		{
		    ++count;
		    sb.append((n-1)+" ");
		}
		System.out.println(count);
		System.out.println(sb.toString());

    }
	
	static void printintarray(int[] arr)
{
	int n=arr.length;
	for(int i=0;i<n;++i)
	{
		System.out.print(arr[i]+" ");
	}
	System.out.println();
}
	static void printlongarray(long[] arr)
{
	int n=arr.length;
	for(int i=0;i<n;++i)
	{
		System.out.print(arr[i]+" ");
	}
	System.out.println();
}

	static int[] arrayintinput(int n)
	{
	    int arr[]=new int[n];
	    for(int i=0;i<n;++i)
	    {
	        arr[i]=sc.nextInt();
	    }
	    return arr;
	}
	static long[] arraylonginput(int n)
	{
	    long arr[]=new long[n];
	    for(int i=0;i<n;++i)
	    {
	        arr[i]=sc.nextLong();
	    }
	    return arr;
	}
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.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()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
 
}
//  System.out.println("Case #"+(y+1)+": "+ans);