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.*;
import java.util.*;
import java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;
 
public class part implements Runnable
{
    static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
 
        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()
        {
            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);
        }
    }
    
    public static void main(String args[]) throws Exception
    {
        new Thread(null, new part(),"part",1<<26).start();
    }
    /*class Wand {
        int ind;
        int val;
        Wand(int a, int b) {
            ind = a;
            val = b;
        }
    }*/ //(This statement shows how to make our own class)
    
    //to count no of 1 in binary form::
    long count_one (int n){
            long count=0;
            while(n>0)
            {
               n = n&(n-1);
               count++;
            }
            return count;
       }
    //To Find most significant setbit of a number::
    int Last_set_bit(int n){
        return (int)(Math.log(n)/Math.log(2));
    }   
    //power mod::
    static long powmod(long x, long n, long m) {
        if (n == 0) return 1;

        else if (n % 2 == 0) return powmod(((x % m) * (x % m)) % m, n / 2, m);

        else if (n % 2 == 1) return (((x % m) * powmod(((x % m) * (x % m)) % m, (n - 1) / 2, m)) % m);

        else return 0;
    }
    //binary expo::
    static long binaryexpo(long x, long n){
        if(n==0) return 1;
        if(n%2==0) return binaryexpo(x*x,n);
        else return x*binaryexpo(x*x,(n-1)%2);
    }
    //GCD od 2 nos::
    public static long gcd(long a, long b) {
        if(b==0) return a;
        return gcd(b%a,a);
    }
    //GCD of Array::
    public static long gcd(long[] input) {
        long result = input[0];
 
        for (int i = 1; i < input.length; i++) {
            result = gcd(result, input[i]);
        }
 
        return result;
    }
    //LCM of 2 nos::
    public static long lcm(long a, long b) {
        return a * (b / gcd(a, b));
    }
    //LCM of Array::
    public static long lcm(long[] input) {
        long result = input[0];
 
        for (int i = 1; i < input.length; i++) {
            result = lcm(result, input[i]);
        }
 
        return result;
    }
    //BINARY TREE::
    public class Node{
        int data;
        Node left,right;
        Node(int data){
            this.data = data;
            left = right = null;
        }

        public void insert(int value){
            if(value<=data){
                if(left==null) left = new Node(value);
                else left.insert(value);
            }
            else{
                if(right==null) right = new Node(value);
                else right.insert(value);
            }
        }  

        public boolean contains(int value){
           if(value==data) return true;
            else if(value<data){
                if(left==null) return false;
                else return left.contains(value);
            }
            else{
                if(right==null) return false;
                else return right.contains(value);
            }
        }
    }
    //FOR FINDING HEIGHT OF A TREE::
    public int maxht(Node root){
        if(root == null) return 0;
        else{
            int ld = maxht(root.left);
            int rd = maxht(root.right);
            
            if(ld>rd) return ld+1;
            else return rd+1;
        }
    }
    //Graph::
    public class graph{
        ArrayList<Integer> a;
        int d;
        boolean b;

        void graph(){
            this.d = 0;
            this.b = false;
        }
    }
    //Code starts right here... 
    public void run()
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        /*write your code here*/
        /*take input through sc.nextInt and all and output through w.print & w.println*/
        int n = sc.nextInt();
        if(n==1||n==2) w.println("No");
        else{
            w.println("Yes");
            if(n%2!=0){
                w.print((n/2)+" ");
                for(int c=2;c<=n;c+=2) w.print(c+" ");
                w.println();
                w.print(((n/2)+1)+" ");
                for(int c=1;c<=n;c+=2) w.print(c+" ");    
            }
            else{
                w.print((n/2)+" ");
                for(int c=2;c<=n;c+=2) w.print(c+" ");
                w.println();
                w.print(((n/2))+" ");
                for(int c=1;c<=n;c+=2) w.print(c+" ");       
            }
        }

        w.close();
    }
    
}