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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
power = [2**i-1 for i in range(2,14) ]
m = 0
for p in power:
  if n % p == 0:
    m = p
    d = n // p
    break
if m == 0:
  print("No")
elif d == 1:
  print("Yes")
  for i in range(2*n-1):
    print(" ".join([str(i+1),str(i+2)]))
else:
  print("Yes")
  for k in range(d): 
    for i in range(m-1):
      print(" ".join([str(k*m+i+1),str(k*m+i+2)]))
      print(" ".join([str(k*m+i+1+n),str(k*m+i+2+n)]))
    print(" ".join([str(k*m+m),str(k*m+n+1)]))
    if k != d-1:
      print(" ".join([str(k*m+1),str(k*m+m+1)]))