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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class Solution1514C {
  public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    Solver1514C solver = new Solver1514C();
    solver.solve(0, in, out);
    out.close();
  }

  static class Solver1514C {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      Set<Integer> set = new HashSet<>();
      List<Integer> factors = factors(n);
      long pd = 1L;
      for (int i = 1; i <= n - 1; i++) {
        if (hasF(i, factors)) {
          continue;
        }
        set.add(i);
        pd *= (long) i;
        pd %= (long) n;
      }
      if (pd > 1) {
        set.remove((int) pd);
      }
      List<Integer> res = new ArrayList<>(set);
      Collections.sort(res);

      out.println(res.size());
      for (int i = 0; i < res.size(); i++) {
        if (i > 0) {
          out.print(" ");
        }
        out.print(res.get(i));
      }
      out.println();
    }

    private boolean hasF(int n, List<Integer> factors) {
      for (int i = 0; i < factors.size(); i++) {
        if (n % factors.get(i) == 0) {
          return true;
        }
      }
      return false;
    }

    private List<Integer> factors(int n) {
      List<Integer> res = new ArrayList<>();
      int bnd = (int) Math.sqrt(n);
      for (int i = 2; i <= bnd; i++) {
        if (n % i == 0) {
          while (n % i == 0) {
            n /= i;
          }
          res.add(i);
        }
      }
      if (n != 1) {
        res.add(n);
      }
      return res;
    }
  }

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