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)

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();

    if n == 1 || n == 2 || n % 4 == 0 {
        println!("No");
        return;
    } else if n == 3 {
        println!("Yes");
        println!("1 2");
        println!("2 3");
        println!("3 4");
        println!("4 5");
        println!("5 6");
        return;
    }

    let w = (n + 1) / 4 * 4 - 1;
    let mut row = vec![];
    row.push(w);
    row.push(1);
    if w != 3 {
        row.push(3);
    }
    row.push(2);
    for i in 4..w {
        row.push(i);
    }
    let s = row.len();
    let mut ans = vec![];
    for i in 1..s {
        ans.push((row[i - 1], row[i]));
        ans.push((row[i - 1] + n, row[i] + n));
    }

    ans.push((row[s - 1], row[0] + n));
    if w + 2 <= n {
        ans.push((w + 1, 1));
        ans.push((w + 1, w + 2));

        ans.push((w + 2 + n, 1));
        ans.push((w + 2 + n, w + 1 + n));
    }
    if w + 3 <= n {
        ans.push((w + 3, w + 1));
        ans.push((w + 3 + n, 3));
    }

    println!("Yes");
    for (i, j) in ans.into_iter() {
        println!("{} {}", i, j);
    }
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}