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.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {

    static int MAX_N = 100010;

    public static void main(String[] args) throws IOException {

	initReader(System.in);

	solve();

	printWriter.flush();
    }

    /***********************************************************************************************/

    static boolean[] a = new boolean[MAX_N];

    public static void solve() throws IOException {
	int n = nextInt();

	long pre = 1;
	for (int i = 1; i < n; i++) {
	    if (gcd(i, n) == 1) {
		a[i] = true;
		pre = (pre * i) % n;
	    }
	}

	if (pre % n != 1) {
	    a[(int) pre] = false;
	}

	int cnt = 0;
	for (int i = 1; i < n; i++) {
	    if (a[i]) {
		cnt++;
	    }
	}

	printWriter.println(cnt);
	for (int i = 1; i < n; i++) {
	    if (a[i]) {
		printWriter.print(i + " ");
	    }
	}
    }

    public static void init() {

    }

    public static int gcd(int a, int b) {
	return b == 0 ? a : gcd(b, a % b);
    }

    /***********************************************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static PrintWriter printWriter;

    static void initReader(InputStream input) {
	reader = new BufferedReader(new InputStreamReader(input));
	tokenizer = new StringTokenizer("");
	printWriter = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    }

    static boolean hasNext() {
	try {
	    while (!tokenizer.hasMoreTokens()) {
		tokenizer = new StringTokenizer(reader.readLine());
	    }
	} catch (Exception e) {
	    return false;
	    // TODO: handle exception
	}
	return true;
    }

    static String next() throws IOException {
	while (!tokenizer.hasMoreTokens()) {
	    tokenizer = new StringTokenizer(reader.readLine());
	}
	return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
	try {
	    return reader.readLine();
	} catch (Exception e) {
	    return null;
	    // TODO: handle exception
	}
    }

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

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

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

    static char nextChar() throws IOException {
	return next().charAt(0);
    }

}

class Node implements Comparable {
    int x, y, t;

    Node(int x, int y, int t) {
	this.x = x;
	this.y = y;
	this.t = t;

    }

    @Override
    public int compareTo(Object o) {
	// TODO Auto-generated method stub

	Node rhs = (Node) o;

	return this.t - rhs.t;
    }
}