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 prt(int x,int y) {
	printf("%d %d\n",x,y);
}
int main() {
	int n,m=1;
	scanf("%d",&n);
	while(m<n) m<<=1;
	if(m==n) printf("No\n");
	else {
		printf("Yes\n");
		prt(1,2),prt(2,3),prt(3,n+1),prt(n+1,n+2),prt(n+2,n+3);
		for(int i=4;i<n;i+=2) {
			prt(1,i),prt(1,i+1);
			prt(i,i+1+n),prt(i+1,i+n);
		}
		if(n%2==0) {
			for(int i=2;i<n;i++) {
				if((n^i^1)<n) {
					prt(i,n);
					prt(n^i^1,2*n);
					break;
				}
			}
		}
	}
	return 0;
}