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.util.regex.*;
import java.math.BigInteger;
import java.math.BigDecimal;

public class Codeforces{
	
	static class MyScanner{
		BufferedReader br;
		StringTokenizer st;
		
		MyScanner(FileReader fileReader){
			br = new BufferedReader(fileReader);
		}
		
		MyScanner(){
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String nn(){
			while(st == null || !st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		int ni(){
			return Integer.parseInt(nn());
		}
		
		long nl(){
			return Long.parseLong(nn());
		}
		
		double nd(){
			return Double.parseDouble(nn());
		}
	}
	
	private static PrintWriter out;
	
	private static int convertStringToInt(String s){
		return Integer.parseInt(s);
	}
	
	public static void main(String[] args) throws FileNotFoundException{
		
		
		// Input from file
		// File inputFile = new File("input.txt");
		// File outputFile = new File("output.txt");
		// FileReader fileReader = new FileReader(inputFile);
		// Here it ends
			
		MyScanner sc = new MyScanner();
		
		out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
		// out = new PrintWriter(new PrintStream(outputFile)); // Output to file
		
		int n = sc.ni();
		
		if(n <= 2){
			out.println("No");
		}else{
			out.println("Yes");
			int left = 0, right = 0;
			
			ArrayList<Integer> l = new ArrayList<>();
			ArrayList<Integer> r = new ArrayList<>();
			for(int i = 1; i <= n; i += 2){
				left++;
				l.add(i);
			}
			
			for(int i = 2; i <= n; i += 2){
				right++;
				r.add(i);
			}
			
			out.print(right + " ");
			for(Integer i: r) out.print(i + " ");
			out.println();
			out.print(left + " ");
			for(Integer i: l) out.print(i + " ");
		}
		
		out.close();
	}
}