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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

void addedge(int u, int v) {
	cout<<u<<' '<<v<<'\n';
}

int main() {
	//35c
	int n;
	cin>>n;
	int k = 0;
	while ((1<<k) < n) k ++;
	if ((1<<k) == n) {
		cout<<"No";
		return 0;
	}
	k --;
	cout<<"Yes"<<'\n';
	addedge(3 + n, 1 + n);
	for (int i = 3; i <= n; i += 2) {
		addedge(1, i);
		addedge(i, i - 1 + n);
		addedge(1, i - 1);
		addedge(i - 1, i + n);
	}
	if (n % 2 == 0) {
		int x = (1<<k);
		int y = n ^ 1 ^ x;
		assert(y < n);
		addedge(n, x);
		addedge(n<<1, y);
	}
}