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 Rust (1.15.1) (judge verdict: Wrong Answer)

pub fn read<T: std::str::FromStr>() -> T {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).ok();
        s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
        read::<String>()
                .split_whitespace()
                .map(|e| e.parse().ok().unwrap())
                .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
        (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: u32) -> Vec<T> {
        (0..n).map(|_| read()).collect()
}

fn main() {
        let n: u32 = read();
        let mut tmp = n + 1;
        if n == 1 {
                println!("No");
        } else {
                while tmp > 1 {
                        if tmp % 2 > 0 {
                                break;
                        }
                        tmp /= 2;
                }
                if tmp == 1 {
                        println!("Yes");
                        for i in 1..2 * n {
                                println!("{} {}", i, i + 1);
                        }
                } else {
                        println!("No");
                }
        }
}