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 <bits/stdc++.h>
using namespace std;
const int N = (int) 1e5+5;

int n;
void ngk(){
    cin >> n;
    
    if (n < 3 || n % 2 == 0) {
        cout << "No";
        return;
    }
    else {
        cout << "Yes" << '\n';
        cout << 1 << ' ' << 2 << '\n';
        cout << 2 << ' ' << 3 << '\n';
        cout << 3 << ' ' << n+1 << '\n';
        cout << n+1 << ' ' << n+2 << '\n';
        cout << n+2 << ' ' << n+3 << '\n';
        for(int i=4;i<=n;i+=2){
            cout << i << ' ' << i+1 << '\n';
            cout << i+1 << ' ' << 1 << '\n';
            cout << 1 << ' ' << i+n << '\n';
            cout << i+n << ' ' << i+n+1 << '\n';
        }
    }
    
} 

int main(){
    #ifdef NGKCP
        freopen("input.txt","r",stdin);
    #endif
    iostream::sync_with_stdio(0);
    ngk();
}
/*
    Array limits;
    Corner cases;
*/