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.BigInteger;
import java.text.*;
public class Main {
    static long mod = 1000_000_007;
    static long mod1 = 998244353;
    static boolean fileIO = false;
    static boolean memory = true;
    static FastScanner f;
    static PrintWriter pw;
    static double eps = (double)1e-6;
    static long oo = Long.MAX_VALUE;
 
    // N = 1 or N = max ?
    // longs vs. ints ?
    // max / min ?

    public static void solve() throws Exception {

        int n = f.ni();

        if (n <= 4) {
            pn(1);
            pn(1);
            return;
        }

        if (isPrime(n)) {
            pn(n - 2);
            for (int i = 1; i + 2 <= n; ++i) {
                p(i + " ");
            }
            return;
        }

        ArrayList<Integer> ans = new ArrayList<>();
        ans.add(1);
        long m = 1;

        for (int i = 2; i < n; ++i) {
            if (gcd(i , n) > 1) continue;
            ans.add(i);
            m *= i;
            m %= n;
        }

        if (m != 1) ans.remove(ans.size() - 1);
        pn(ans.size());
        for (Integer x : ans) p(x + " ");

    }    
 
    public static void main(String[] args)throws Exception {
        if(memory) new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();System.exit(1);}}}, "", 1 << 28).start();
        else new Main().run();
    }
        
/******************************END OF MAIN PROGRAM*******************************************/
    void run()throws Exception {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            f = new FastScanner("");
            pw = new PrintWriter(System.out);
        }
        else {
            f = new FastScanner();
            pw = new PrintWriter(System.out);
        }
        //
        int t = 1;
        int tt = 1;
 
        while(t --> 0) {
            //p("Case #" + (tt++) + ": ");
            //fw.write("\n");
            solve();
        }
        
        pw.flush(); 
        pw.close(); 
    }
 
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner(String str) throws Exception {
            try {
                br = new BufferedReader(new FileReader("!a.txt"));
            }
            catch (Exception e) {
                e.printStackTrace();
            }
        }
 
        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public String next()throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        public int ni() throws IOException {return Integer.parseInt(next());}
 
        public long nl() throws IOException {return Long.parseLong(next());}
 
        public String nextLine() throws IOException {return br.readLine();}
 
        public double nd() throws IOException {return Double.parseDouble(next());}
    }
 
    public static void pn(Object... o) {for(int i = 0; i < o.length; ++i) pw.print(o[i] + (i + 1 < o.length ? " ": "\n"));}
    public static void p(Object... o) {for(int i = 0; i < o.length; ++i) pw.print(o[i] + (i + 1 < o.length ? " " : ""));}
    public static void pni(Object... o) {for(Object obj : o) pw.print(obj + " "); pw.println(); pw.flush();}
    public static int gcd(int a,int b){if(b==0)return a;else{return gcd(b,a%b);}}
    public static long gcd(long a,long b){if(b==0l)return a;else{return gcd(b,a%b);}}
    public static long lcm(long a,long b){return (a*b/gcd(a,b));}
    public static long pow(long a,long b){long res=1;while(b>0){if((b&1)==1)res=res*a;b>>=1;a=a*a;}return res;}
    public static int pow(int a,int b){int res=1;while(b>0){if((b&1)==1)res=res*a;b>>=1;a=a*a;}return res;}
    public static long mpow(long a,long b, long m){long res=1;while(b>0){if((b&1)==1)res=((res%m)*(a%m))%m;b>>=1;a=((a%m)*(a%m))%m;}return res;}
    public static long mul(long a , long b , long mod){return ((a%mod)*(b%mod)%mod);}
    public static long adp(long a , long b){return ((a%mod)+(b%mod)%mod);}
    public static int dig(long a){int cnt=0;while(a>0){a/=10;++cnt;}return Math.max(1,cnt);}
    public static int dig(int a){int cnt=0;while(a>0){a/=10;++cnt;}return Math.max(1,cnt);}
    public static boolean isPrime(long n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(long i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    public static boolean isPrime(int n){if(n<=1)return false;if(n<=3)return true;if(n%2==0||n%3==0)return false;for(int i=5;i*i<=n;i=i+6)if(n%i==0||n%(i+2)==0)return false;return true;}
    public static TreeSet<Long> factors(long n){TreeSet<Long> hs=new TreeSet<Long>();for(long i=1;i<=(long)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    public static HashSet<Integer> factors(int n){HashSet<Integer> hs=new HashSet<Integer>();for(int i=1;i<=(int)Math.sqrt(n);i++){if(n%i==0){hs.add(i);hs.add(n/i);}}return hs;}
    public static TreeSet<Long> pf(long n){TreeSet<Long> ff=factors(n);TreeSet<Long> ans=new TreeSet<Long>();for(Long i:ff)if(isPrime(i))ans.add(i);return ans;}
    public static HashSet<Integer> pf(int n){HashSet<Integer> ff=factors(n);HashSet<Integer> ans=new HashSet<Integer>();for(Integer i:ff)if(isPrime(i))ans.add(i);return ans;}
    public static int gnv(char c){return Character.getNumericValue(c);}
    public static void sort(int[] a){ArrayList<Integer> l=new ArrayList<>();for(int i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    public static void sort(long[] a){ArrayList<Long> l=new ArrayList<>();for(long i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;++i)a[i]=l.get(i);}
    public static void sort(ArrayList<Integer> a){Collections.sort(a);}
}