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:
import sys
input = sys.stdin.readline

N = int(input())

# if power of 2
n = N.bit_length()
if N == 1 << (n-1):
    print('No')
    exit()

def solve(N):
    graph = []
    for n in range(2,N,2):
        graph.append((n,n+1))
        graph.append((n+1,1))
        graph.append((1,N+n))
        graph.append((N+n,N+n+1))
    graph.append((N+1,2))
    if N&1:
        return graph
    L = N.bit_length()
    n = 1 << (L-1)
    m = N ^ n ^ 1
    # n even, m odd
    graph.append((N,m))
    graph.append((n+N,N+N))
    return graph


graph = solve(N)

print('Yes')
for a,b in graph:
    print(a,b)