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.util.*;
import java.io.*;
public class C {
    static class Reader{
        private BufferedReader reader;
        private StringTokenizer tokenizer;
        Reader(InputStream input)
        {
            this.reader = new BufferedReader(new InputStreamReader(input));
            this.tokenizer = new StringTokenizer("");
        }
        public String next() throws IOException {
            while(!tokenizer.hasMoreTokens())
            {
                tokenizer = new StringTokenizer(reader.readLine());
            }   
            return tokenizer.nextToken();
        }
        public int nextInt() throws IOException
        {
            return Integer.parseInt(next());
        }
        public double nextDouble() throws IOException
        {
            return Double.parseDouble(next());
        }
        public long nextLong() throws IOException
        {
            return Long.parseLong(next());
        }
    }
    static class solution
    {
        public int GCD(int a, int b)
        {
            
            while(a!=b && a>0 && b>0)
            {
                int min = Math.min(a,b);
                int max = Math.max(a, b);
                a = max%min;
                b = min;
            }
            if(a==0)return b;
            if(b==0)return a;
            if(a==b)return a;
            return b;
        }
        public boolean isPerfectSquare(int n)
        {
            int i = (int)Math.floor(Math.sqrt(n));
            // for (int i = 1; i * i <= n; i++) {
     
            //     if ((n % i == 0) && (n / i == i)) {
            //         return true;
            //     }
            // }
            if(i*i==n)return true;
            return false;
        }
        public boolean isPrime(int n)
        {
            for(int i=2;i<=Math.sqrt(n);i++)
            {
                if(n%i==0)return false;
            }
            return true;
        }
        public String solve(int N)
        {
            StringBuffer sb = new StringBuffer();
            int length = 0;
            long prod = 1;
            for(int i=1;i<=N-2;i++){
                if(GCD(i,N)==1)
                {
                    sb.append(i+" ");
                    prod = (prod*i)%N;
                    length++;
                }
            }
            if(prod==N-1)
            {
                sb.append(N-1);
                length++;
            }
            return length+"\n"+sb.toString();

        }

    }
    public static void main(String[] args) throws IOException{
        Reader scan = new Reader(System.in);
        
        BufferedOutputStream b = new BufferedOutputStream(System.out);
       // int a = scan.nextInt();
        int N = scan.nextInt();
        solution sol = new solution();
        // System.out.println(sol.GCD(a, N));
        String ans = sol.solve(N);
        
        b.write((ans).getBytes());
        b.flush();
        
    }
    
}