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: Accepted)

use std::io::*;
use std::str::FromStr;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n = read::<usize>();
    solve(n);
}

fn solve(n: usize) {
    if n.count_ones() == 1 {
        println!("No");
        return;
    }
    let max_bit = n.next_power_of_two() / 2;
    let mut anss: Vec<(usize, usize)> = vec![];
    for i in 1..max_bit - 1 {
        anss.push((i, i + 1));
    }
    for i in 1..max_bit - 1 {
        let prev = if i == 1 { n + 1 } else { n + (i ^ 1) };
        let next = n + ((i + 1) ^ 1);
        anss.push((prev, next));
    }
    anss.push((1, max_bit));
    anss.push((1, max_bit + 1));
    anss.push((n + 1, n + max_bit));
    anss.push((n + 1, n + 1 + max_bit));
    anss.push((max_bit, n + 1 + max_bit));
    for i in (max_bit + 2)..n + 1 {
        let prev = max_bit ^ (i % 2) ^ (i % 4 / 2);
        anss.push((prev, i));
        let next = (i - max_bit) / 2 * 2;
        anss.push((next, i + n));
    }
    println!("Yes");
    for ans in anss.iter() {
        println!("{} {}", ans.0, ans.1);
    }
}