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.util.stream.IntStream;
import java.util.Scanner;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author valeesi
 */
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);
        CProduct1ModuloN solver = new CProduct1ModuloN();
        solver.solve(1, in, out);
        out.close();
    }

    static class CProduct1ModuloN {
        private static int gcdThing(int a, int b) {
            BigInteger b1 = BigInteger.valueOf(a);
            BigInteger b2 = BigInteger.valueOf(b);
            BigInteger gcd = b1.gcd(b2);
            return gcd.intValue();
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int total = 0;
            int[] arr = IntStream.range(1, n).toArray();
            long result = 1;
            for (int i = 1; i < n; i++) {
                if (gcdThing(i, n) != 1) {
                    arr[i - 1] = -1;
                } else {
                    result = (result * i) % n;
                    total++;
                }
            }

            if (result != 1) {
                arr[(int) result - 1] = -1;
                total--;
            }

            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < arr.length; i++) {
                if (arr[i] != -1) {
                    sb.append(arr[i] + " ");
                }
            }
            out.println(total);
            out.println(sb.toString());
        }

    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            scanner = new Scanner(reader);
            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 int nextInt() {
            return Integer.parseInt(next());
        }

    }
}