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.*;

public class Main {

    void run() throws IOException {
        int n = nextInt();
        boolean[] used = new boolean[n];
        int ans = 0;
        long now = 1;
        for (int i = 1; i < n; i++) {
            if (gcd(i, n) == 1) {
                ans++;
                now *= i;
                now %= n;
                used[i] = true;
            }
        }
        if (now != 1) ans--;
        else now = 0;
        out.println(ans);
        for (int i = 1; i < n; i++) if (used[i] && i != now) out.print(i + " ");
    }

    int gcd(int a, int b) {
        while (a % b != 0) {
            int h = a % b;
            a = b;
            b = h;
        }
        return b;
    }


    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);
    StringTokenizer in = new StringTokenizer("");


    // pairs
    class pil implements Comparable<pil> {
        int first;
        long second;

        pil(int f, long s) {
            this.first = f;
            this.second = s;
        }

        public int compareTo(pil o) {
            if (first != o.first) return Integer.compare(first, o.first);
            return Long.compare(second, o.second);
        }
    }

    class pii implements Comparable<pii> {
        int fi;
        int se;

        pii(int f, int s) {
            se = s;
            fi = f;
        }

        public int compareTo(pii o) {
            if (fi != o.fi) return Integer.compare(fi, o.fi);
            return Integer.compare(se, o.se);
        }
    }

    class vert {
        int to;
        int iter;
        int idx;
        int ed;

        vert(int s, int f, int zz, int gg) {
            to = s;
            iter = f;
            idx = zz;
            ed = gg;
        }
    }


    class pll implements Comparable<pll> {
        long first;
        long second;

        pll(long f, long s) {
            this.first = f;
            this.second = s;
        }

        public int compareTo(pll o) {
            if (first != o.first) return Long.compare(first, o.first);
            return Long.compare(second, o.second);
        }
    }

    class pli implements Comparable<pli> {
        long first;
        int second;

        pli(long f, int s) {
            this.first = f;
            this.second = s;
        }

        public int compareTo(pli o) {
            if (first != o.first) return Long.compare(first, o.first);
            return Integer.compare(second, o.second);
        }
    }

    boolean hasNext() throws IOException {
        if (in.hasMoreTokens()) return true;
        String s;
        while ((s = br.readLine()) != null) {
            in = new StringTokenizer(s);
            if (in.hasMoreTokens()) return true;
        }
        return false;
    }

    String nextToken() throws IOException {
        while (!in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static void main(String[] args) throws IOException {
        Main m = new Main();
        m.run();
        m.out.close();
    }
}