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.math.*;
import java.util.*;
import java.io.*;



public class main
{
  static Map<String,Integer> map=new HashMap<>();
    public static void main(String[] args)
    {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
         final int mod=1000000007;
        int test_case =1;
                    StringBuilder sb=new StringBuilder();
      for(int t1=0;t1<test_case;t1++)
      {
          int n=in.nextInt();
          List<Integer>  ls=new ArrayList();
          ls.add(1);
          long mul=1;
          for(int i=2;i<n-1;i++)
          {
              if(GCD(i,n)==1)
              {
                  ls.add(i);
                  mul*=i;
                  mul%=n;
   //              System.out.println(i+"  "+mul+" "+mul%n);
              }
          }
          
       //   System.out.println(mul+" "+mul%n);
          if(n>2){
          
      //        System.out.println((mul*(n-1))%n);
              
          if((mul*(n-1))%n==1)
          {
              ls.add(n-1);
           //   System.out.println(n-1);
          }
          }
        System.out.println(ls.size());          
            for(int i:ls)
            {
                System.out.print(i+" ");
            }
          
          

      }
    
 
 
        pw.flush();
        pw.close();
    }
    
    
    static int factorial(int n,int mod)
    {
        long res = 1;
        for (int i=2; i<=n; i++)
            res=((res%mod)*(i%mod))%mod;
        return (int)res;
    }
    


    
    static int length(long l)
    {
        int c=0;
        while(l>0)
        {
            c++;
            l/=2;
        }
        
        return c;
    }

    
    static int CeilIndex(int A[], int l, int r, int key) 
    { 
        while (r - l > 1) { 
            int m = l + (r - l) / 2; 
            if (A[m] <= key) 
                r = m; 
            else
                l = m; 
        } 
  
        return r; 
    } 
    static int LongestIncreasingSubsequenceLength(int A[], int size) 
    { 
        // Add boundary case, when array size is one 
  
        int[] tailTable = new int[size]; 
        int len; // always points empty slot 
  
        tailTable[0] = A[0]; 
        len = 1; 
        for (int i = 1; i < size; i++) { 
            if (A[i] > tailTable[0]) 
 
                tailTable[0] = A[i]; 
  
            else if (A[i] <= tailTable[len - 1]) 
 
                tailTable[len++] = A[i]; 
  
            else
 
                tailTable[CeilIndex(tailTable, -1, len - 1, A[i])] = A[i]; 
        } 
  
        return len; 
    }
    
 
    
    static int[] next(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] next=new int[n];
 
        for (int i = n-1; i >= 0; i--) { 
 
            while (!S.empty() && arr[S.peek()] <= arr[i]) { 
                S.pop(); 
 
            } 
            if (S.empty()) { 
                next[i]=-1;
            } 
            else 
            { 
 
                next[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        return next;
    }
    static int[] back(int arr[], int n) { 
 
        Stack<Integer> S = new Stack<>(); 
  
        int[] back=new int[n];
 
        for (int i = 0; i < n; i++) { 
 
            while (!S.empty() && arr[S.peek()] < arr[i]) { 
                S.pop(); 
            } 
            if (S.empty()) { 
                back[i]=-1;
            } 
            else 
            { 
                back[i]=S.peek(); 
            } 
            S.push(i); 
        } 
        
        return back;
    }
 
    
    
 
    static class InputReader
    {
 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
 
        public int snext()
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars)
            {
                curChar = 0;
                try
                {
                    snumChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n)
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextInt();
            }
            return a;
        }
        public long[] nextlongArray(int n)
        {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
            {
                a[i] = nextLong();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c))
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine()
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c)
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
 
    public static long mod = 1000000007;
    public static int d;
    public static int p;
    public static int q;
 
    public static int[] suffle(int[] a,Random gen)
    {
        int n = a.length;
        for(int i=0;i<n;i++)
        {
            int ind = gen.nextInt(n-i)+i;
            int temp = a[ind];
            a[ind] = a[i];
            a[i] = temp;
        }
        return a;
    }
 
    public static void swap(int a, int b){
        int temp = a;
        a = b;
        b = temp;
    }
 
    public static HashSet<Integer> primeFactorization(int n)
    {
        HashSet<Integer> a =new HashSet<Integer>();
        for(int i=2;i*i<=n;i++)
        {
            while(n%i==0)
            {
                a.add(i);
                n/=i;
            }
        }
        if(n!=1)
            a.add(n);
        return a;
    }
 
    public static void sieve(boolean[] isPrime,int n)
    {
        for(int i=1;i<n;i++)
            isPrime[i] = true;
 
        isPrime[0] = false;
        isPrime[1] = false;
 
        for(int i=2;i*i<n;i++)
        {
            if(isPrime[i] == true)
            {
                for(int j=(2*i);j<n;j+=i)
                    isPrime[j] = false;
            }
        }
    }
 
    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==0)
            return a;
        else
            return GCD(b,a%b);
    }
 
    public static void extendedEuclid(int A,int B)
    {
        if(B==0)
        {
            d = A;
            p = 1 ;
            q = 0;
        }
        else
        {
            extendedEuclid(B, A%B);
            int temp = p;
            p = q;
            q = temp - (A/B)*q;
        }
    }
 
    public static long LCM(long a,long b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int LCM(int a,int b)
    {
        return (a*b)/GCD(a,b);
    }
 
    public static int binaryExponentiation(int x,int n)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
    int binarySearch(int arr[], int l, int r, int x) 
    { 
        if (r >= l) { 
            int mid = l + (r - l) / 2; 
  
 
            if (arr[mid] == x) 
                return mid; 
  
 
            if (arr[mid] > x) 
                return binarySearch(arr, l, mid - 1, x); 
  
 
            return binarySearch(arr, mid + 1, r, x); 
        } 
  
 
        return -1; 
    } 
  
 
    public static long binaryExponentiation(long x,long n)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=result * x;
            x=x*x;
            n=n/2;
        }
        return result;
    }
 
    public static int modularExponentiation(int x,int n,int M)
    {
        int result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static long modularExponentiation(long x,long n,long M)
    {
        long result=1;
        while(n>0)
        {
            if(n % 2 ==1)
                result=(result * x)%M;
            x=(x*x)%M;
            n=n/2;
        }
        return result;
    }
 
    public static int modInverse(int A,int M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    public static long modInverse(long A,long M)
    {
        return modularExponentiation(A,M-2,M);
    }
 
    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;
    }
    static class Pair
    {
        long  x;
        int  y;
    }
 
    static class pair implements Comparable<pair>
    {
        Integer x, y;
        pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
 
        public int compareTo(pair o) {
            int result = x.compareTo(o.x);
            if(result==0)
                result = y.compareTo(o.y);
 
            return result;
        }
 
        public String toString()
        {
            return x+" "+y;
        }
 
        public boolean equals(Object o)
        {
            if (o instanceof pair)
            {
                pair p = (pair)o;
                return (Math.abs(p.x-x)==0 && Math.abs(p.y-y)==0);
            }
            return false;
        }
 
        public int hashCode()
        {
            return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    }
}