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: Wrong Answer)

#include <iostream> // cin, cout, cerr, clog
#include <algorithm> // minmax, sort, swap
#include <numeric> // iota, accumulate, inner_product
#include <cstdio> // printf, scanf
#include <climits> // INT_MIN, LLONG_MIN
#include <cmath> // long, trig, pow
#include <string> // string, stoi, to_string
#include <vector> // vector
#include <queue> // queue, priority_queue
#include <deque> // deque
#include <stack> // stack
#include <map> // key-value pairs sorted by keys
#include <set> // set
#include <unordered_map> // hashed by keys
#include <unordered_set> // hashed by keys
#include <iomanip> // cout<<setprecision(n)
#include <functional> // std::function<void(int)>

#define rep(i,n) for(int i = 0; i < n; i++)
#define ENDL "\n"
#define print(i) std::cout << (i) << "\n"

#define int long long // at least int64 > 9*10^18
#define all(v) v.begin(), v.end()

signed main() {
	int n;
	std::cin >> n;
	for(int i=1;i<1000000;i*=2) {
		if(n==i-1) {
			print("Yes");
			for(int j=1;j<=2*n-1;j++) {
				std::cout << j << ' ' << j+1 << ENDL;
			}
			return 0;
		}
	}
	std::cout << "No" << ENDL;
	return 0;
}