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.*;
public class main {
class FastScanner{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st=new StringTokenizer("");
String next() {
while(!st.hasMoreTokens()) {
try {
st=new StringTokenizer(br.readLine());
}
catch(IOException e) {
e.printStackTrace();
}
}
return st.nextToken();
}
int nextInt() {
return Integer.parseInt(next());
}
long nextLong() {
return Long.parseLong(next());
}
String nextLine() {
String str = "";
try {
str = br.readLine();
} catch (IOException e) {
e.printStackTrace();
}
return str;
}}
static boolean check(int n){
    return Math.ceil(Math.sqrt(n))==Math.floor(Math.sqrt(n));
}
static long power(long a,long b,long mod){
 long ans=1;
 while(b!=0){
 if((b&1)==1){
 ans=(ans*a)%mod;
 }
 a=(a*a)%mod;
 b>>=1;
 }
 return ans;
}

// 2 5
//     
static long gcd(long a,long b){
  if(a==0){
    return b;
  }
  return gcd(b%a,a);
} 

 static boolean bl[]=new boolean[2000];

    public static void main(String[] args) {
 FastScanner scan=new main().new FastScanner();
 int t=scan.nextInt();
 
ArrayList<Long>A=new ArrayList<>();
A.add(1l);
long mul=1l;
for(int i=2;i<t;++i){
  if(gcd(i,t)==1){
    A.add((long)i);
    mul=(mul*i)%t;
  }
}
//System.out.println(mul);
if(mul!=1){
  A.remove(new Long(mul%t));
}
{
  System.out.println(A.size());
  for(int i=0;i<A.size();++i){
System.out.print(A.get(i)+" ");
  }
}
    }}