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 (7.3.0) (judge verdict: Wrong Answer)

N=int(input())
if (N&-N)==N:
  print('No')
  exit()
print('Yes')
M=str(bin(N))[2:]
M=1<<(len(M)-1)
P=[]
B=False
if set(str(bin(N))[2:])==set('1'):
  N+=2
  M=str(bin(N))[2:]
  M=1<<(len(M)-1)
  B=True
  N-=2
for i in range(M-2):
  P.append([i+1,i+2])
P.append([M-1,N+1])
for i in range(M-2):
  P.append([N+1+i,N+2+i])
if B:
  for i in range(len(P)):
    print(*P[i])
  exit()
for i in range(1,((N-M+3)>>1)):
  P.append([1,M+(i<<1)-2])
  P.append([M+(i<<1)-2,M+(i<<1)-1])
  P.append([1,N+M+(i<<1)-1])
  P.append([N+M+(i<<1)-1,N+M+(i<<1)-2])
if len(P)!=(N<<1)-1:
  X=(N-M)^(N-M-1)
  P.append([N,N-M])
  for i in range(len(P)):
    if P[i][0]==N-M-1:
      if X^(P[i][1]%N)==N:
        P.append([N<<1,P[i][1]])
        break
    if P[i][1]==N-M-1:
      if X^(P[i][0]%N)==N:
        P.append([N<<1,P[i][0]])
        break
for i in range(len(P)):
  print(*P[i])