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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn get_pair(i: usize, n: usize) -> usize {
    if i <= n {
        i + n
    } else {
        i - n
    }
}

fn main() {
    let n = read::<usize>();
    let mut index = 1;
    while n >= index {
        if n == index {
            println!("No");
            return;
        }
        index *= 2;
    }
    println!("Yes");

    let mut max_full_bit = 1;
    while n >= 2 * max_full_bit - 1 {
        max_full_bit *= 2;
    }
    max_full_bit -= 1;

    let mut pairs = vec![];
    for i in 1..3 {
        pairs.push((i, i + 1));
    }
    pairs.push((1, get_pair(3, n)));
    for i in 1..3 {
        pairs.push((get_pair(i, n), get_pair(i + 1, n)));
    }

    if n % 2 == 1 {
        for i in 4..n + 1 {
            if i % 2 == 0 {
                pairs.push((1, i));
                pairs.push((i, i + 1));
                pairs.push((1, get_pair(i + 1, n)));
                pairs.push((get_pair(i, n), get_pair(i + 1, n)));
            }
        }
    } else {
        for i in 4..n {
            if i % 2 == 0 {
                pairs.push((1, i));
                pairs.push((i, i + 1));
                pairs.push((1, get_pair(i + 1, n)));
                pairs.push((get_pair(i, n), get_pair(i + 1, n)));
            }
        }

        let mut one_pairs = HashSet::new();
        for &(a, b) in pairs.iter() {
            if a == 1 {
                one_pairs.insert(b);
            } else if b == 1 {
                one_pairs.insert(a);
            }
        }

        if one_pairs.contains(&(max_full_bit + 1)) {
            pairs.push((max_full_bit + 1, n));
        } else {
            pairs.push((n + max_full_bit + 1, n));
        }

        if one_pairs.contains(&(n - max_full_bit)) {
            pairs.push((n - max_full_bit, 2 * n));
        } else {
            pairs.push((2 * n - max_full_bit, 2 * n));
        }
    }

    for pair in pairs {
        println!("{0} {1}", pair.0, pair.1);
    }
}

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()
}

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