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: Wrong Answer)

n=gets.to_i
d=1<<(n.bit_length-1)
if d==n
puts "No"
else
if d*2-1==n
(1...n*2).map{|i|puts "#{i} #{i+1}"}
else
d-=1
(1...d).map{|i|puts "#{i} #{i+1}"}
puts "#{d} #{n+1}"
(n+1...n+d).map{|i|puts "#{i} #{i+1}"}
d+=1

if n>d
puts "#{d} 1"
puts "#{d+1} 1"
puts "#{n+d} #{d+1}"
puts "#{n+d+1} #{d}"
(d+2..n).map{|i|
puts "#{i} #{i-d}"
puts "#{n+i} #{i-1}"
}
end
end
end