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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;


namespace SolutionCS
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            if ((N - 3) % 4 == 0)
            {
                Console.WriteLine("Yes");
                for (int i = 0; i < N * 2 - 1; i++)
                {
                    Console.WriteLine("{0} {1}", i + 1, i + 2);
                }

                return;
            }

            if ( N >= 5 && (N - 3) % 4 == 2) { 

                Console.WriteLine("Yes");

                for (int i = 0; i < N - 3; i++)
                {
                    Console.WriteLine("{0} {1}", i + 1, i + 2);
                    Console.WriteLine("{0} {1}", N + i + 1, N + i + 2);
                }

                Console.WriteLine("{0} {1}", N - 2, N + 1);

                Console.WriteLine("1 {0}", N);
                Console.WriteLine("{0} {1}", N, N - 1);

                Console.WriteLine("{0} {1}", N + 1, N * 2 - 1);
                Console.WriteLine("{0} {1}", N * 2 - 1, N * 2);
                return;
            }

            if (N >= 5 && (N - 3) % 4 == 3)
            {

                Console.WriteLine("Yes");

                for (int i = 0; i < N - 4; i++)
                {
                    Console.WriteLine("{0} {1}", i + 1, i + 2);
                    Console.WriteLine("{0} {1}", N + i + 1, N + i + 2);
                }

                Console.WriteLine("{0} {1}", N - 3, N + 1);

                Console.WriteLine("1 {0}", N - 1);
                Console.WriteLine("1 {0}", N);
                Console.WriteLine("{0} {1}", N - 1, N - 2);

                Console.WriteLine("{0} {1}", N + 1, N * 2 - 2);
                Console.WriteLine("{0} {1}", N * 2 - 2, N * 2 - 1);
                Console.WriteLine("{0} {1}", N * 2 - 2, N * 2);
                return;
            }

            Console.WriteLine("No");
        }
    }
}