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;

namespace Atcoder_program_test_Csharp
{
    using System;
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');//2つ以上のスペース区切り入力の取得
            int N = int.Parse(str[0]);  //数値で受け取りたい場合は変換する
            int counter = 1;
            int output = 1;
            if (N >= 2)
            {
                Console.WriteLine("Yes");
                for (; ; )
                {
                    Console.Write(output + " ");
                    Console.WriteLine(output + 1);
                    if (counter == N * 2 - 1)
                    {
                        break;
                    }
                    else
                    {
                        counter = counter + 1;
                    }
                    output = output + 1;
                }
            }
            else Console.WriteLine("No");
        }
    }
}