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:
/*
								"जय श्री कृष्णा"
*/
import java.util.*;
import java.io.*;

public class Product_1_modulo_name implements Runnable {

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		public FastReader(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				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());
		}

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] nextIntArray(int size) {
			int[] arr = new int[size];
			for (int i = 0; i < size; ++i)
				arr[i] = nextInt();
			return arr;
		}

		long[] nextLongArray(int size) {
			long[] arr = new long[size];
			for (int i = 0; i < size; ++i)
				arr[i] = nextLong();
			return arr;
		}

		double[] nextDoubleArray(int size) {
			double[] arr = new double[size];
			for (int i = 0; i < size; ++i)
				arr[i] = nextDouble();
			return arr;
		}
	}

	static int mod = (int) (1e9 + 7),N = (int) (1e5);
	static final PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	static final FastReader fr = new FastReader();
	// static final FastReader fr = new FastReader("/home/atish/Java_Text_editor/input.txt");
	// static  PrintWriter out;
	public static void main(String[] args) throws java.lang.Exception {
		// try {
		// 	out = new PrintWriter(new File("/home/atish/Java_Text_editor/output.txt"));
		// } catch (Exception e) {
		// 	e.printStackTrace();
		// }
		new Thread(null, new Product_1_modulo_name(), "Main", 1 << 26).start();
	}

	void solve() {		
		int n = fr.nextInt();
		List<Integer> al = new ArrayList<>();
		long pod = 1;
		for (int i = 1; i < n; i++) {
			if (CP.i_gcd(n, i) == 1) {
				pod = (pod * i) % n;
				al.add(i);
			} 
		}
		if (pod != 1) {
			al.remove(al.size() - 1);
		}
		out.print(al.size() + "\n");
		for (int x : al)
			out.print(x + " ");
		
	}
	@Override
	public void run() {
		long start = System.nanoTime(); // Program Start
		boolean testcase = false;
		int t = testcase ? fr.nextInt() : 1;
		while (t-- > 0) {
			solve();
			out.print("\n");
			out.flush();
		}
		long end = System.nanoTime(); // Program End
//		System.err.println("Time taken: " + (end - start) / 1000000 + " ms"); 
	}

	static class CP {

		static boolean isPrime(long n) {
			if (n <= 1)
				return false;
			if (n == 2 || n == 3)
				return true;
			if (n % 2 == 0 || n % 3 == 0)
				return false;
			for (int i = 5; i * i <= n; i += 6) {
				if (n % i == 0 || n % (i + 2) == 0)
					return false;
			}
			return true;
		}
		static List<Integer> sieve(int size) {
			ArrayList<Integer> pr=new ArrayList<Integer>();
			boolean prime[] = new boolean[size]; 
		    for(int i=2;i<prime.length;i++)  prime[i] = true; 
			for(int i=2; i*i< prime.length; i++) {
				if(prime[i]) {
					for(int j=i*i; j<prime.length; j+=i) {
						prime[j]=false;
					}
				}
			}
			for(int i=2; i<prime.length; i++) if(prime[i]) pr.add(i);
			return pr;
		}

		static long binary_Expo(long a, long b) { // calculating a^b
			long res = 1;
			while (b != 0) {
				if ((b & 1) == 1) {
					res *= a;
					--b;
				}
				a *= a;
				b /= 2;
			}
			return res;
		}

		static long Modular_Expo(long a, long b) {
			long res = 1;
			while (b != 0) {
				if ((b & 1) == 1) {
					res = (res * a) % mod;
					--b;
				}
				a = (a * a) % mod;
				b /= 2;
			}
			return res;
		}

		static int i_gcd(int a, int b) {// iterative way to calculate gcd.
			while (true) {
				if (b == 0)
					return a;
				int c = a;
				a = b;
				b = c % b;
			}
		}

		static long gcd(long a, long b) {// here b is the remainder
			if (b == 0)
				return a; //because each time b will divide a.
			return gcd(b, a % b);
		}

		static long ceil_div(long a, long b) { // a numerator b denominator
			return (a + b - 1) / b;
		}

		static int getIthBitFromInt(int bits, int i) {
			return (bits >> (i - 1)) & 1;
		}

		static int upper_Bound(int a[], int x) {//closest to the left+1
			int l = -1, r = a.length;
			while (l + 1 < r) {
				int m = (l + r) >>> 1;
				if (a[m] <= x)
					l = m;
				else
					r = m;
			}
			return l + 1;
		}

		static int lower_Bound(int a[], int x) {//closest to the right
			int l = -1, r = a.length;
			while (l + 1 < r) {
				int m = (l + r) >>> 1;
				if (a[m] >= x)
					r = m;
				else
					l = m;
			}
			return r;
		}

		static void sort(int a[]) {
			PriorityQueue<Integer> q = new PriorityQueue<>();
			for (int i = 0; i < a.length; i++)
				q.add(a[i]);
			for (int i = 0; i < a.length; i++)
				a[i] = q.poll();
		}

		static int getMax(int arr[], int n) {
			int mx = arr[0];
			for (int i = 1; i < n; i++)
				if (arr[i] > mx)
					mx = arr[i];
			return mx;
		}
	}

}