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: Runtime Error)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{

	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
    int twoPowMemo = 1;
    bool answer = true;
    for(int i = 0; i < 26; i++)
    {
      if(n == twoPowMemo) answer = false;
      twoPowMemo *= 2;//2のk乗を先にメモ
    }

    if(!answer)
    {
      Console.WriteLine("No");
    }else
    {
      Console.WriteLine("Yes");

      int[][] answers = new int[2*n-1][];
      int answerCount = 0;
      for(int i = 0; i < 2*n-1; i++) answers[i] = new int[2];

      answers[answerCount][0] = n+1;
      answers[answerCount][1] = 2;
      answerCount++;

      for(int i = 0; i < (n-1)/2; i++)
      {
        answers[answerCount][0] = 2*(i+1);
        answers[answerCount][1] = 2*(i+1)+1;
        answerCount++;

        answers[answerCount][0] = 2*(i+1)+1;
        answers[answerCount][1] = 1;
        answerCount++;

        answers[answerCount][0] = 2*(i+1)+n;
        answers[answerCount][1] = 1;
        answerCount++;

        answers[answerCount][0] = 2*(i+1)+n;
        answers[answerCount][1] = 2*(i+1)+n+1;
        answerCount++;
      }

      if(n%2 == 0)
      {
        int digitMemo = 0;
        while(true)
        {
          digitMemo++;

          if((n & (1<<digitMemo)) != 0)
          {
            answers[answerCount][0] = n;
            answers[answerCount][1] = (n^(1<<digitMemo))+n;
            answerCount++;

            answers[answerCount][0] = 2*n;
            answers[answerCount][1] = (1<<digitMemo)+1;
            answerCount++;
          }
        }
      }

      var answerText = new StringBuilder();
      for(long i = 0; i < answers.Length; i++)
      {
        answerText.AppendLine(string.Join(" ", answers[i]));
      }
      Console.Write(answerText);
    }

	}
}