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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
import static java.lang.Math.*;
import java.util.concurrent.ThreadLocalRandom;

public class Sol implements Runnable {

    long mod = (long)1e9 + 7;

    void solve(InputReader in, PrintWriter w) {

        long n = in.nextLong();
        long sum = (n * (n + 1L)) / 2L;

        for(long i=2;i<n;i++) {
            if(sum % i == 0) {
                w.println("Yes");
                w.println("1 "+i);
                w.print((n - 1)+" ");
                for(long j=1;j<=n;j++) if(j != i) w.print(j+" ");
                return;
            }
        }

        w.println("No");
    }

    // ************* Code ends here ***************

    void init() throws Exception {
        //Scanner in;
        InputReader in;
        PrintWriter w;
        boolean online = false;

        String common_in_fileName = "\\in";
        String common_out_fileName = "\\out";
        int test_files = 0;

        for (int file_no = 0; file_no <= test_files; file_no++) {

            String x = "" + file_no;
            if (x.length() == 1) x = "0" + x;

            String in_fileName = common_in_fileName + "" + x;
            String out_fileName = common_out_fileName + "" + x;

            if (online) {
                //in = new Scanner(new File(in_fileName + ".txt"));
                in = new InputReader(new FileInputStream(new File(in_fileName + ".txt")));
                w = new PrintWriter(new FileWriter(out_fileName + ".txt"));
            } else {
                //in = new Scanner(System.in);
                in = new InputReader(System.in);
                w = new PrintWriter(System.out);
            }

            solve(in, w);
            w.close();
        }
    }

    public void run() {
        try {
            init();
        } catch (Exception e) {
            System.out.println(e);
            e.printStackTrace();
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Sol(), "Sol", 1 << 28).start();
    }

    static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public String nextLine() {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c)) {
                c = read();
            }

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    if (c < '0' || c > '9') {
                        throw new InputMismatchException();
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(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;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {

            public boolean isSpaceChar(int ch);
        }
    }
}