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.*;
import java.math.*;

public class Main {
	static PrintWriter pw = new PrintWriter(System.out);

	public static void main(String[] args) throws IOException, InterruptedException {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<Integer> arrl = new ArrayList<>();
		long ans = 1;
		for (int i = 1; i < n - 1; i++) {
			if (gcd(i, n) == 1) {
				ans = (ans * i) % n;
				arrl.add(i);
			}
		}
//		pw.println(ans);
		if ((ans * (n - 1)) % n == 1) {
			arrl.add(n - 1);
		}
		pw.println(arrl.size());
		for (int k : arrl) {
			pw.print(k + " ");
		}
		pw.close();
	}
	
	static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;

		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int compareTo(tuble other) {
			if (this.x == other.x) {
				if (this.y == other.y)
					return this.z - other.z;
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}

	public static class pair implements Comparable<pair> {
		int x;
		int y;

		public pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x == x && p.y == y;
			}
			return false;
		}

		public int hashCode() {
			return new Integer(x).hashCode() * 31 + new Integer(y).hashCode();
		}

		public int compareTo(pair other) {
			if (this.x == other.x) {
				return Long.compare(this.y, other.y);
			}
			return Long.compare(this.x, other.x);
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

}