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.IO;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;


static class P
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        if (n < 3 || n % 2 != 1)
        {
            Solve(n);
            return;
        }
        List<Tuple<int, int>> res = new List<Tuple<int, int>>();
        res.Add(new Tuple<int, int>(1, 2));
        res.Add(new Tuple<int, int>(2, 3));
        res.Add(new Tuple<int, int>(3, 1 + n));
        res.Add(new Tuple<int, int>(1 + n, 2 + n));
        res.Add(new Tuple<int, int>(2 + n, 3 + n));
        for (int i = 4; i < n; i += 2)
        {
            res.Add(new Tuple<int, int>(i, i + 1));
            res.Add(new Tuple<int, int>(i + 1, 1));
            res.Add(new Tuple<int, int>(1, i + n));
            res.Add(new Tuple<int, int>(i + n, i + 1 + n));
        }
        Console.WriteLine("Yes");
        Console.WriteLine(string.Join("\n", res.Select(x => $"{x.Item1} {x.Item2}")));

    }

    static void Solve(int n)
    {
        var msb = 1;
        while (msb * 2 <= n) msb *= 2;
        if ((n & -n) == n)
        {
            throw new Exception();
        }
        List<Tuple<int, int>> res = new List<Tuple<int, int>>();
        for (int i = 1; i < msb - 1; i++)
        {
            res.Add(new Tuple<int, int>(i, i + 1));
            res.Add(new Tuple<int, int>(i + n, i + n + 1));
        }
        res[2] = new Tuple<int, int>(1, 3);
        res[3] = new Tuple<int, int>(1 + n, 3 + n);
        res.Add(new Tuple<int, int>(msb - 1, 2 + n));
        //2134...2134...
        for (int i = msb; i < n - 2; i += 2)
        {
            res.Add(new Tuple<int, int>(i, i + 1));
            res.Add(new Tuple<int, int>(i + 1, 1));
            res.Add(new Tuple<int, int>(1, i + n));
            res.Add(new Tuple<int, int>(i + n, i + 1 + n));
        }

        int lsb = (n & -n);
        if (lsb == 2)
        {
            res.Add(new Tuple<int, int>(n + n - 1, n + n));
            res.Add(new Tuple<int, int>(lsb - 1, n + n - 1));
            res.Add(new Tuple<int, int>(n, lsb));
            res.Add(new Tuple<int, int>(n - 1, n));
            res.Add(new Tuple<int, int>(n + n - 1, n - 2));
            res.Add(new Tuple<int, int>(1, n + n - 2));
        }
        else
        {
            res.Add(new Tuple<int, int>(n + n - 1, n + n));
            res.Add(new Tuple<int, int>(lsb - 1, n + n - 1));
            res.Add(new Tuple<int, int>(n, lsb));
            res.Add(new Tuple<int, int>(n - 1, n));
            res.Add(new Tuple<int, int>(n, n - 2));
            res.Add(new Tuple<int, int>(1, n + n - 2));
        }

        Console.WriteLine("Yes");
        Console.WriteLine(string.Join("\n", res.Select(x => $"{x.Item1} {x.Item2}")));
        //Console.WriteLine(string.Join("\n", res.Select(x => $"{S(x.Item1, n)} {S(x.Item2, n)}")));
    }

    static string S(int i, int n) => i <= n ? i.ToString() : $"{i - n}_";
}