You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.

For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.

<image>

Input

The first and the only line contain one integer n (1 ≤ n ≤ 10^5).

Output

If there is no solution, output "NO" in the first line. 

If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.

Examples

Input


3


Output


YES
1 4 5 2 3 6 

Input


4


Output


NO

Note

Example from the statement is shown for the first example. 

It can be proved that there is no solution in the second example.
import java.util.ArrayList;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Random;
import java.io.PrintWriter;
/*
    Solution Created: 22:47:59 11/09/2019
    Custom Competitive programming helper.
*/
public class Main {
	public static void solve(Reader in, Writer out) {
		int n = in.nextInt();
		if(n%2==0) {
			out.println("NO");
			return;
		}
		out.println("YES");
		int[] a = new int[2*n];
		int cur = 1;
		for(int i = 0; i<n; i++) {
			if(i%2==0) {
				a[i] = cur;
				a[i+n] = cur+1;
			}else {
				a[i] = cur+1;
				a[i+n] = cur;
			}
			cur+=2;
		}
		for(int i = 0; i<2*n; i++) out.print(a[i]+" ");
	}
	public static void main(String[] args) {
		Reader in = new Reader();
		Writer out = new Writer();
		solve(in, out);
		out.exit();
	}

static class Graph {
	private ArrayList<Integer> con[];
	private boolean[] visited;

	public Graph(int n) {
		con = new ArrayList[n];
		for (int i = 0; i < n; ++i)
			con[i] = new ArrayList();
		visited = new boolean[n];
	}

	public void reset() {
		Arrays.fill(visited, false);
	}

	public void addEdge(int v, int w) {
		con[v].add(w);
	}

	public void dfs(int cur) {
		visited[cur] = true;
		for (Integer v : con[cur]) {
			if (!visited[v]) {
				dfs(v);
			}
		}
	}

	public void bfs(int cur) {
		Queue<Integer> q = new LinkedList<>();
		q.add(cur);
		visited[cur] = true;
		while (!q.isEmpty()) {
			cur = q.poll();
			for (Integer v : con[cur]) {
				if (!visited[v]) {
					visited[v] = true;
					q.add(v);
				}
			}
		}
	}
}

static class Reader {
	static BufferedReader br;
	static StringTokenizer st;
	private int charIdx = 0;
	private String s;

	public Reader() {
		this.br = new BufferedReader(new InputStreamReader(System.in));
	}

	public int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

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

	public char nextChar() {
		if (s == null || charIdx >= s.length()) {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			s = st.nextToken();
			charIdx = 0;
		}
		return s.charAt(charIdx++);
	}

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

	public char[] nca() {
		return next().toCharArray();
	}

	public String[] nS(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public int nextInt() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Integer.parseInt(st.nextToken());
	}

	public double nextDouble() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Double.parseDouble(st.nextToken());
	}

	public Long nextLong() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Long.parseLong(st.nextToken());
	}

	public String next() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return st.nextToken();
	}

	public static void readLine() {
		try {
			st = new StringTokenizer(br.readLine());
		} catch (Exception e) {
		}
	}
}

static class Sort {
	static Random random = new Random();
	public static void sortArray(int[] s) {
        shuffle(s);
        Arrays.sort(s);
    }
	public static void sortArray(long[] s) {
        shuffle(s);
        Arrays.sort(s);
    }
	public static void sortArray(String[] s) {
        shuffle(s);
        Arrays.sort(s);
    }
	public static void sortArray(char[] s) {
        shuffle(s);
        Arrays.sort(s);
    }
    private static void shuffle(int[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            int t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }
    private static void shuffle(long[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            long t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }
    private static void shuffle(String[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            String t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }
    private static void shuffle(char[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            char t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }
}

static class Util{
	    static boolean isPrime(int n) { 
	        if (n <= 1) return false; 
	        if (n <= 3) return true; 
	        if (n % 2 == 0 || n % 3 == 0) return false; 
	        for (int i = 5; i * i <= n; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	        return true; 
	    }
		public static int upperBound(long[] a, long v) {
			int l=0, h=a.length-1, ans = -1;
			while(l<h) {
				int mid = (l+h)/2;
				if(a[mid]<=v) {
					ans = mid;
					l = mid+1;
				}else h = mid-1;
			}
			return ans;
		}
		public static int lowerBound(long[] a, long v) {
			int l=0, h=a.length-1, ans = -1;
			while(l<h) {
				int mid = (l+h)/2;
				if(v<=a[mid]) {
					ans = mid;
					h = mid-1;
				}else l = mid-1;
			}
			return ans;
		}
	    public static boolean[] getSieve(int n) {
	        boolean[] isPrime = new boolean[n+1];
	        for (int i = 2; i <= n; i++) isPrime[i] = true;
	        for (int i = 2; i*i <= n; i++) if (isPrime[i]) 
	                for (int j = i; i*j <= n; j++) isPrime[i*j] = false;
	        return isPrime;
	    }
	    public static int gcd(int a, int b) { 
	        if (a == 0) 
	            return b; 
	        return gcd(b%a, a); 
	    }
		public static long modAdd(long a, long b, long mod) {
			return (a%mod+b%mod)%mod;
		}
		public static long modMul(long a, long b, long mod) {
			return ((a%mod)*(b%mod))%mod;
		}
		public static void dbg(Object... o) { 
			System.out.println(Arrays.deepToString(o)); 
		}
	}

static class Writer {
	private PrintWriter pw;
	public Writer(){
		pw = new PrintWriter(System.out);
	}
	
	public void printArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	public void printlnArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	public void printArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	public void printlnArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	public void print(Object o) {
		pw.print(o.toString());
	}
	public void println(Object o) {
		pw.println(o.toString());
	}
	public void println() {
		pw.println();
	}
	public void flush() {
		pw.flush();
	}
	public void exit() {
		pw.close();
	}
}
}
