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 Ruby (2.3.3) (judge verdict: Accepted)

n = gets.to_i
ok = true
20.times do |i|
    ok = false if (1<<i) == n
end
if !ok
    puts "No"
    exit
end
a = []
2.times do |i|
    a << [i+1,i+2]
end
a << [3,1+n]
a << [n+1,n+2]
a << [n+3,n+2]
i = 4
((n-3)/2).times do
    a << [i,i+1]
    a << [i+1,1+n]
    a << [1+n,i+n]
    a << [i+n,i+1+n]
    i += 2
end
if n%2 == 0
    (1..n).each do |i|
        if (n^(2*i)^1) < n
            a << [n,i*2+n]
            a << [2*n,n^(2*i)^1]
            break
        end
    end
end
puts "Yes"
a.size.times do |i|
    puts "#{a[i][0]} #{a[i][1]}"
end