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.*;
public class Main
{
	public static void main(String[] args) throws Exception
	{
		// int t = ni();
		int t = 1;
		while(t-->0) {
			int n = ni();
			if(n <= 2){
				sopln("No");
				exit();
			}
			else{
				sopln("Yes");
				int count = 0;
				int count1 = 0;
				for(int i=1;i<=n;i+=2){
					count++;
					ans.append(i+" ");
				}
				for(int i=2;i<=n;i+=2){
					count1++;
					ans1.append(i+" ");
				}
				sopln(count + " "+ ans);
				sopln(count1 + " "+ ans1);
			}
		}
		// sop(ans);
	}
	static final long mod=1000000007l;
    static StringBuilder ans=new StringBuilder();
    static StringBuilder ans1=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.print(a);}
	static void sopln(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());}
    }
 
}