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 Python (3.4.3) (judge verdict: Wrong Answer)

from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import defaultdict, Counter
from bisect import bisect

setrecursionlimit(10**6)

def read():
  return int(input())

def reads():
  return [int(x) for x in input().split()]

N = read()

if N == 1 or N % 2 == 0:
  print("No")
  exit()

assert N >= 3
print("Yes")

print(1, 2)
print(2, 3)
print(3, N+1)
print(N+1, N+2)
print(N+2, N+3)

for i in range(4, N, 2):
  print(1, i)
  print(i, i+1)
  
  print(1, N + i+1)
  print(N + i+1, N + i)