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
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

n = ni()

two_power = [pow(2, i) for i in range(30)]

# 2べき判定
if n in two_power:
    print("No")

# 1とNまでつなげる
else:
    edges = []
    for i in range(2, (n+1) - (n+1)%2):
        edges.append((1, i))

# 2からNまでとN+2から2Nまでつなげる (偶数ならN-1まで)
    for i in range(2, (n+1) - (n+1)%2):
        if i % 2:
            edges.append((i, n + i - 1))
        else:
            edges.append((i, n + i + 1))

# N+2とN+1つなげる
    edges.append((n+1, n+2))

# 偶数なら最上位ビットにNを、それ以外+1に2Nをつなげる
    if n%2 == 0:
        edges.append((1 << (n.bit_length() - 1), n))
        edges.append((n - (1 << (n.bit_length()) - 1) + 1, 2*n))

    print("Yes")
    for edge in edges:
        print(*edge)