Problem: An undirected graph is called k-regular, if the degrees of all its vertices are equal k. An edge of a connected graph is called a bridge, if after removing it the graph is being split into two connected components.

Build a connected undirected k-regular graph containing at least one bridge, or else state that such graph doesn't exist.

Input

The single line of the input contains integer k (1 ≤ k ≤ 100) — the required degree of the vertices of the regular graph.

Output

Print "NO" (without quotes), if such graph doesn't exist. 

Otherwise, print "YES" in the first line and the description of any suitable graph in the next lines.

The description of the made graph must start with numbers n and m — the number of vertices and edges respectively. 

Each of the next m lines must contain two integers, a and b (1 ≤ a, b ≤ n, a ≠ b), that mean that there is an edge connecting the vertices a and b. A graph shouldn't contain multiple edges and edges that lead from a vertex to itself. A graph must be connected, the degrees of all vertices of the graph must be equal k. At least one edge of the graph must be a bridge. You can print the edges of the graph in any order. You can print the ends of each edge in any order.

The constructed graph must contain at most 106 vertices and 106 edges (it is guaranteed that if at least one graph that meets the requirements exists, then there also exists the graph with at most 106 vertices and at most 106 edges). 

Examples

Input

1


Output

YES
2 1
1 2

Note

In the sample from the statement there is a suitable graph consisting of two vertices, connected by a single edge.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;


public class Main {

	static class Task {
		
		int NN = 200005;
		int MOD = 1000000007;;
		int INF = 2000000000;
		long INFINITY = 2000000000000000000L;
		
		class Pair {
			Integer from , to;
			
			public Pair(int a, int b) {
				this.from = a;
				this.to = b;
			}
		}
		
		List<String> s = new ArrayList<>();
		
		void test(int k, int cnt, PrintWriter out) {
			boolean [][] g = new boolean[1002][1002];
			int n = 0;
			if(s.size() != cnt) {
				out.println("Number edges expected: "+(cnt) + " found: "+s.size());
			}
			for(String ss: s) {
				int u = Integer.parseInt(ss.split(" ")[0]);
				int v = Integer.parseInt(ss.split(" ")[1]);
				g[u][v] = true;
				g[v][u] = true;
				n = Math.max(n, Math.max(u, v));
			}
			boolean ok = true;
			for(int i=1;i<=n;++i) {
				int deg = 0;
				for(int j=1;j<=n;++j) {
					if(g[i][j])
						++deg;
				}
				if(deg != k) {
					ok = false;
					out.println("oops at " + i + " with deg = " + deg);
				}
			}
			if(ok) {
				out.println("All OK");
			}
		}
		
		public void solve(InputReader in, PrintWriter out) {
			int k = in.nextInt();
			if(k%2 == 0) {
				out.println("NO");
				return;
			}
			out.println("YES");
			int nodes = 2 * ((k/2)*(2*(k/2+1)) + 1);
			out.print(nodes);
			int edges = (nodes * k/2);
			out.println(" " + edges);
			build(1, k);
			build(1 + nodes/2, k);
			s.add(1 + " " + (1 + nodes/2));
			//test(k, edges, out);
			for(String ss: s) {
				int u = Integer.parseInt(ss.split(" ")[0]);
				int v = Integer.parseInt(ss.split(" ")[1]);
				out.println(u + " " + v);
			}
		}
		
		void build(int start, int k) {
			for(int i=1;i<k;++i) {
				s.add((start) + " " + (start + i));
			}
			int row = k / 2 + 1;
			int col = k/2;
			for(int j=1;j<=col;++j) {
				for(int i=1;i<=row;++i) {
					for(int jj=i+1;jj<=row;++jj ) {
						s.add(getNum(i, j, 1, k, start) + " " + getNum(jj, j, 1, k, start));
						s.add(getNum(i, j, 1, k, start) + " " + getNum(jj, j, 2, k, start));
						s.add(getNum(i, j, 2, k, start) + " " + getNum(jj, j, 1, k, start));
						s.add(getNum(i, j, 2, k, start) + " " + getNum(jj, j, 2, k, start));
					}
					if(i > 1) {
						s.add(getNum(i, j, 1, k, start) + " " + getNum(i, j, 2, k, start));
					}
				}
			}
		}
		
		int getNum(int row, int col, int type, int k, int start) {
			return start + (row - 1) * (k - 1) + (col-1)*2 + type;
		}
		
	}
	
	static void prepareIO(boolean isFileIO) {
		//long t1 = System.currentTimeMillis();
		Task solver = new Task();
		// Standard IO
		if(!isFileIO) {
			InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solver.solve(in, out);
	        //out.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        out.close();
		}
        // File IO
		else {
			String IPfilePath = System.getProperty("user.home") + "/Downloads/ip.in";
	        String OPfilePath = System.getProperty("user.home") + "/Downloads/op.out";
	        InputReader fin = new InputReader(IPfilePath);
	        PrintWriter fout = null;
	        try {
				fout = new PrintWriter(new File(OPfilePath));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
	        solver.solve(fin, fout);
	        //fout.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        fout.close();
		}
	}
	
	public static void main(String[] args) {
        prepareIO(false);
	}
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        
        public InputReader(String filePath) {
        	File file = new File(filePath);
            try {
				reader = new BufferedReader(new FileReader(file));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            tokenizer = null;
        }
        
        public String nextLine() {
        	String str = "";
        	try {
				str = reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        	return str;
        }
        
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
    }

}