Problem: Find out if it is possible to partition the first n positive integers into two non-empty disjoint sets S_1 and S_2 such that:

gcd(sum(S_1), sum(S_2)) > 1 

Here sum(S) denotes the sum of all elements present in set S and gcd means the[greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor).

Every integer number from 1 to n should be present in exactly one of S_1 or S_2.

Input

The only line of the input contains a single integer n (1 ≤ n ≤ 45 000)

Output

If such partition doesn't exist, print "No" (quotes for clarity).

Otherwise, print "Yes" (quotes for clarity), followed by two lines, describing S_1 and S_2 respectively.

Each set description starts with the set size, followed by the elements of the set in any order. Each set must be non-empty.

If there are multiple possible partitions — print any of them.

Examples

Input

1


Output

No

Input

3


Output

Yes
1 2
2 1 3 

Note

In the first example, there is no way to partition a single number into two non-empty sets, hence the answer is "No".

In the second example, the sums of the sets are 2 and 4 respectively. The gcd(2, 4) = 2 > 1, hence that is one of the possible answers.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        new Main().solve();
    }

    void solve() {
        int n = ni();
        if (n <= 2) {
            System.out.println("No");
            return;
        }
        int k = n % 2 == 0 ? n / 2 : (n + 1) / 2;
        System.out.println("Yes");
        System.out.println("1 " + k);
        System.out.print((n - 1));
        for (int i = 1; i <= n; i++) {
            if (i != k) {
                System.out.print(" " + i);

            }
        }
    }


    class Pair {
        int c;
        int pl;

        public Pair(int c, int pl) {
            this.c = c;
            this.pl = pl;
        }
    }


    static final int mod = 1000000007;
    static StringBuilder ans = new StringBuilder();
    static Reader in = new Reader();
    static final double eps = 1e-9;

    //////////////////////////////////
    //input functions/////////////////
    static int ni() {
        return Integer.parseInt(in.next());
    }

    static long nl() {
        return Long.parseLong(in.next());
    }

    static String ns() {
        return in.next();
    }

    static double nd() {
        return Double.parseDouble(in.next());
    }

    static int[] nia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    static int[] pnia(int n) {
        int a[] = new int[n + 1];
        for (int i = 1; i <= n; i++) a[i] = ni();
        return a;
    }

    static long[] nla(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    static String[] nsa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) a[i] = ns();
        return a;
    }

    static double[] nda(int n) {
        double a[] = new double[n];
        for (int i = 0; i < n; i++) a[i] = nd();
        return a;
    }

    //////output functions////////////////
    static void pr(Object a) {
        ans.append(a + "\n");
    }

    static void pr() {
        ans.append("\n");
    }

    static void p(Object a) {
        ans.append(a);
    }

    static void pra(int[] a) {
        for (int i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(long[] a) {
        for (long i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(String[] a) {
        for (String i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void pra(double[] a) {
        for (double i : a) ans.append(i + " ");
        ans.append("\n");
    }

    static void sop(Object a) {
        System.out.println(a);
    }

    static void flush() {
        System.out.print(ans);
        ans = new StringBuilder();
    }

    static void exit() {
        System.out.print(ans);
        System.exit(0);
    }

    static int min(int... a) {
        int min = a[0];
        for (int i : a) min = Math.min(min, i);
        return min;
    }

    static int max(int... a) {
        int max = a[0];
        for (int i : a) max = Math.max(max, i);
        return max;
    }

    static int gcd(int... a) {
        int gcd = a[0];
        for (int i : a) gcd = gcd(gcd, i);
        return gcd;
    }

    static long min(long... a) {
        long min = a[0];
        for (long i : a) min = Math.min(min, i);
        return min;
    }

    static long max(long... a) {
        long max = a[0];
        for (long i : a) max = Math.max(max, i);
        return max;
    }

    static long gcd(long... a) {
        long gcd = a[0];
        for (long i : a) gcd = gcd(gcd, i);
        return gcd;
    }

    static String pr(String a, long b) {
        String c = "";
        while (b > 0) {
            if (b % 2 == 1) c = c.concat(a);
            a = a.concat(a);
            b >>= 1;
        }
        return c;
    }

    static long powm(long a, long b, long m) {
        long an = 1;
        long c = a;
        while (b > 0) {
            if (b % 2 == 1) an = (an * c) % m;
            c = (c * c) % m;
            b >>= 1;
        }
        return an;
    }

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

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

    static class Reader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public Reader() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

}