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.IO;
using System.Text;

namespace AGC35
{
    class Program3
    {
        static void Main()
        {
            var N = int.Parse(Console.ReadLine());

            if (IsPowerOfTwo(N))
            {
                Console.WriteLine("No");
                return;
            }

            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Console.WriteLine("Yes");
            var p = GetPowerOfTwo(N);
            var twoP = (int)Math.Pow(2, p);
            for (int i = 1; i < (twoP - 1) * 2; i++)
                Console.WriteLine(i + " " + (i + 1));

            Console.WriteLine(((twoP + 1) * 2) + " " + (twoP) * 2);
            Console.WriteLine((twoP) * 2 + " 1");
            Console.WriteLine("1 " + (twoP + 1));
            Console.WriteLine((twoP + 1) + " " + (twoP));
            for (int i = twoP + 2; i <= N; i++)
            {
                Console.WriteLine((i - twoP) + " " + i);
                Console.WriteLine((i * 2) + " " + (i - 1));
            }

            Console.Out.Flush();
        }

        static bool IsPowerOfTwo(int num)
        {
            if (num <= 0)
                return false;
            return (num & (num - 1)) == 0;
        }

        static int GetPowerOfTwo(int num)
        {
            var p = 0;
            while (num <= 1)
            {
                num >>= 1;
                p++;
            }

            return p;
        }
    }
}