Problem: 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.

Examples

Input

3


Output

Yes
1 2
2 3
3 4
4 5
5 6


Input

1


Output

No

Solution (in PYTHON3):

Solution:
N = int(input())
def judge(N):
  if N <= 2:
    print('No')
    return
  for k in range(2, 18):
    if 2 ** k > N + 1:
       break
  K = 2 ** (k - 1) - 1
  if N - K == 1:
    print('No')
    return
  print('Yes')
  if N % 2:
    for i in range(1, K):
      print('{} {}'.format(i, i + 1))
      print('{} {}'.format(i + N, i + 1 + N))
    print('{} {}'.format(K, N + 1))
    if K < N:
      for i in range(K + 1, N + 1):
        print('{} {}'.format(i, 1 if i % 2 else i + 1))
        print('{} {}'.format(i + N, 1 if i % 2 == 0 else i - 1 + N))
  else:
    for i in range(K + 1, N):
      print('{} {}'.format(i, 1 if i % 2 else i + 1))
      print('{} {}'.format(i + N, 1 if i % 2 == 0 else i - 1 + N))
    m = N ^ (K + 1)
    print('{} {}'.format(N, m + N))
    print('{} {}'.format(m + N, K + 1))
    print('{} {}'.format(K + 1, 2 * N))
    P = [i for i in range(2, K + 1)]
    P.pop(P.index(m))
    print('{} {}'.format(2 * N - 1, P[0]))
    for i, p in enumerate(P[:-1]):
      print('{} {}'.format(p, P[i + 1]))
      print('{} {}'.format(p + N, P[i + 1] + N))
    print('{} {}'.format(P[-1], m))
    print('{} {}'.format(P[-1] + N, m + N))
    print('{} {}'.format(K + 1, N + 1))
judge(N)