Problem:
Score : 700 points

Problem Statement

You are given an integer N. Determine if there exists a tree with 2N vertices numbered 1 to 2N satisfying the following condition, and show one such tree if the answer is yes.

Assume that, for each integer i between 1 and N (inclusive), Vertex i and N+i have the weight i. Then, for each integer i between 1 and N, the bitwise XOR of the weights of the vertices on the path between Vertex i and N+i (including themselves) is i.

Constraints

N is an integer.

1 \leq N \leq 10^{5}

Input

Input is given from Standard Input in the following format:

N

Output

If there exists a tree satisfying the condition in the statement, print Yes; otherwise, print No.
Then, if such a tree exists, print the 2N-1 edges of such a tree in the subsequent 2N-1 lines, in the following format:

a_{1} b_{1}
\vdots
a_{2N-1} b_{2N-1}

Here each pair (a_i, b_i) means that there is an edge connecting Vertex a_i and b_i. The edges may be printed in any order.

Sample Input 1

3

Sample Output 1

Yes
1 2
2 3
3 4
4 5
5 6

The sample output represents the following graph:

Sample Input 2

1

Sample Output 2

No

There is no tree satisfying the condition.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.lang.reflect.Array;
import java.util.*;
import java.util.Map.Entry;
import java.util.function.Function;
import java.util.stream.Collectors;

@SuppressWarnings("unused")
public class Main {
	FastScanner in = new FastScanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	final int MOD = (int)1e9+7;
	void printlnYN(boolean b){out.println((b ? "Yes" : "No"));}
	
	
	
	//System.out.println();はつかわない！！
	void solve() throws Exception{
		int N = in.nextInt();
		int e = 1;
		while(e < N) e *= 2;
		if(N == e * 2){
			printlnYN(false);
		}else{
			printlnYN(true);
			
			if(N+1 == e){
				for(int i = 0; i < 2*N-1; i++){
					out.println((i+1) + " " + (i+2));
				}
			}else{
				int r = (N ^ e);
				for(int i = 0; i < N; i++){
					out.println((i+1) + " " + (i+2));
				}
				out.println((N+1) + " " + (r));
				out.println((r) + " " + (N+2));
				for(int i = N+1; i < 2*N+1; i++){
					if((i+2) == r) out.println((i+1) + " " + (i+3));
					else if((i+1) == r) continue;
					else out.println((i+1) + " " + (i+2));
				}
			}
		}
	}
	
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		solve();
		out.flush();
	}
	
	class FastScanner {
		Reader input;

		FastScanner() {this(System.in);}
		FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}
		
		int nextInt() {return (int) nextLong();}

		long nextLong() {
			try {
				int sign = 1;
				int b = input.read();
				while ((b < '0' || '9' < b) && b != '-' && b != '+') {
					b = input.read();
				}
				if (b == '-') {
					sign = -1;
					b = input.read();
				} else if (b == '+') {
					b = input.read();
				}
				long ret = b - '0';
				while (true) {
					b = input.read();
					if (b < '0' || '9' < b) return ret * sign;
					ret *= 10;
					ret += b - '0';
				}
			} catch (IOException e) {
				e.printStackTrace();
				return -1;
			}
		}

		double nextDouble() {
			try {
				double sign = 1;
				int b = input.read();
				while ((b < '0' || '9' < b) && b != '-' && b != '+') {
					b = input.read();
				}
				if (b == '-') {
					sign = -1;
					b = input.read();
				} else if (b == '+') {
					b = input.read();
				}
				double ret = b - '0';
				while (true) {
					b = input.read();
					if (b < '0' || '9' < b) break;
					ret *= 10;
					ret += b - '0';
				}
				if (b != '.') return sign * ret;
				double div = 1;
				b = input.read();
				while ('0' <= b && b <= '9') {
					ret *= 10;
					ret += b - '0';
					div *= 10;
					b = input.read();
				}
				return sign * ret / div;
			} catch (IOException e) {
				e.printStackTrace();
				return Double.NaN;
			}
		}

		char nextChar() {
			try {
				int b = input.read();
				while (Character.isWhitespace(b)) {
					b = input.read();
				}
				return (char) b;
			} catch (IOException e) {
				e.printStackTrace();
				return 0;
			}
		}

		String nextStr() {
			try {
				StringBuilder sb = new StringBuilder();
				int b = input.read();
				while (Character.isWhitespace(b)) {
					b = input.read();
				}
				while (b != -1 && !Character.isWhitespace(b)) {
					sb.append((char) b);
					b = input.read();
				}
				return sb.toString();
			} catch (IOException e) {
				e.printStackTrace();
				return "";
			}
		}
		
		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}
 
		public int[] nextIntArrayDec(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}
 
		public int[] nextIntArray1Index(int n) {
			int[] res = new int[n + 1];
			for (int i = 0; i < n; i++) {
				res[i + 1] = nextInt();
			}
			return res;
		}
 
		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}
 
		public long[] nextLongArrayDec(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}
 
		public long[] nextLongArray1Index(int n) {
			long[] res = new long[n + 1];
			for (int i = 0; i < n; i++) {
				res[i + 1] = nextLong();
			}
			return res;
		}
 
		public double[] nextDoubleArray(int n) {
			double[] res = new double[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}
	}
}
/* end Main */