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;
const int N=100005;
int n,nn;
int main()
{
	scanf("%d",&n);for(nn=1;nn<n;nn<<=1);
	if(nn==n){puts("No");return 0;}else puts("Yes");
	int a[6]={1,n+2,3,n+1,2,n+3};
	for(int i=1;i<6;i++)printf("%d %d\n",a[i-1],a[i]);
	for(int i=4;i<n;i+=2)
	{
		printf("%d %d\n",i,1);printf("%d %d\n",i,n+i+1);
		printf("%d %d\n",i+1,1);printf("%d %d\n",i+1,n+i);
	}
	if(~n&1)
	{
		for(int i=2;i<n;i++)if((n^i^1)<n)
		{
			printf("%d %d\n",n,i);
			printf("%d %d\n",n+n,n^i^1);
			return 0;
		}
	}
	return 0;
}