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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.stream.Collectors;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long n = in.nextLong();
            LinkedList<BigInteger> bigIntegers = new LinkedList<>();
            BigInteger bigInteger = BigInteger.valueOf(1);
            for (long i = 1; i < n; i++) {
                if (BigInteger.valueOf(n).gcd(BigInteger.valueOf(i)).equals(BigInteger.ONE)) {
                    bigInteger = bigInteger.multiply(BigInteger.valueOf(i));
                    bigInteger = bigInteger.mod(BigInteger.valueOf(n));
                    bigIntegers.add(BigInteger.valueOf(i));
                }
            }
            if (BigInteger.valueOf(bigInteger.longValue()).equals(BigInteger.ONE)) {
                int bs  = bigIntegers.size();
                out.println(bs);
                for (BigInteger integer : bigIntegers) {
                    out.print(integer + " ");
                }
            } else {
                bigIntegers.remove(bigInteger);
                int bs  = bigIntegers.size();
                out.println(bs);
                for (BigInteger integer : bigIntegers) {
                    out.print(integer + " ");
                }
            }
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}