Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

3

Sample Output 1

Yes
1 2
2 3
3 4
4 5
5 6

The sample output represents the following graph:

Sample Input 2

1

Sample Output 2

No

There is no tree satisfying the condition.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define FOR(i,a,b) for (int i=a;i<=b;++i)
#define FORD(i,a,b) for (int i=a;i>=b;--i)
using namespace std;
typedef long long LL;
typedef pair<int,int> pa;
typedef vector<int> vec;
void getint(int &v){
    char ch,fu=0;
    for(ch='*'; (ch<'0'||ch>'9')&&ch!='-'; ch=getchar());
    if(ch=='-') fu=1, ch=getchar();
    for(v=0; ch>='0'&&ch<='9'; ch=getchar()) v=v*10+ch-'0';
    if(fu) v=-v;
}
int n,h[500010];
int lowbit(int x){
	return x&-x;
}
int main(){
	cin>>n;
	if  (lowbit(n)==n) return puts("No"),0;
	puts("Yes");
	printf("1 2\n");
	printf("2 3\n");
	printf("3 %d\n",n+1);
	printf("%d %d\n",n+1,n+2);
	printf("%d %d\n",n+2,n+3);
	h[2]=2;
	h[3]=3;
	for (int i=4;i<n;i+=2){
		printf("%d %d\n",i,i+1);
		printf("%d %d\n",i+1,1);
		printf("%d %d\n",n+1,n+i);
		printf("%d %d\n",n+i,n+i+1);
		h[i]=n+i;
		h[i+1]=i+1;
	}
	if (n%2==0){
		printf("%d %d\n",n,h[n-lowbit(n)]);
		printf("%d %d\n",n+n,h[lowbit(n)^1]);
	}
	return 0;
}