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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * @author Peter Li
 * @version 04/19/2021
 */
public class C {
    private final static int[] list = new int[100000];
    
    private static int gcd(int a, int b) {
        if (a < b) {
            return gcd(b, a);
        }
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }
    
    private static int solve() {
        int good = 0;
        long prod = 1;
        for (int i = 1; i < index; i++) {
            prod = (prod * list[i]) % n;
            if (prod == 1) {
                good = i;
            }
        }
        System.out.println(good + 1);
        return good;
    }
    
    private static int n, index;
    
    public static void main(String[] args) throws IOException {
        n = ni();
        index = 0;
        for (int i = 1; i <= n; i++) {
            if (gcd(n, i) == 1) {
                list[index++] = i;
            }
        }
        // System.out.println(Arrays.toString(list));
        int good = solve();
        for (int i = 0; i <= good; i++) {
            System.out.print(list[i] + " ");
        }
    }
    
    private static final String DELIMINATOR = " \n\r\f\t";
    private final static BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1 << 15);
    private static StringTokenizer st = new StringTokenizer("", DELIMINATOR);
    
    private static boolean hasNext() {
        makeStringTokenizerReady();
        return st.hasMoreTokens();
    }
    
    private static void makeStringTokenizerReady() {
        while (!st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine(), DELIMINATOR);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
    
    private static String ns() {
        makeStringTokenizerReady();
        return st.nextToken();
    }
    
    private static long nl() {
        return Long.parseLong(ns());
    }
    
    private static int ni() {
        return (int) nl();
    }
    
    private static double nd() {
        return Double.parseDouble(ns());
    }
    
    private static int[] na(int n) {
        int[] ans = new int[n];
        for (int i = 0; i < n; i++) {
            ans[i] = ni();
        }
        return ans;
    }
    
    private static String[] nsa(int n) {
        String[] ans = new String[n];
        for (int i = 0; i < n; i++) {
            ans[i] = ns();
        }
        return ans;
    }
}