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: Runtime Error)

#![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 main() {
    let v = read_vec::<usize>();
    let (n, m) = (v[0], v[1]);
    let mut edges = vec![HashSet::new(); n];
    for _ in 0..m {
        let v = read_vec::<usize>();
        let (a, b) = (v[0] - 1, v[1] - 1);
        edges[a].insert(b);
        edges[b].insert(a);
    }
    if n % 2 == 1 {
        println!("-1");
        return;
    }

    let mut que = VecDeque::new();
    for i in 0..n {
        if edges[i].len() == 1 {
            que.push_back(i);
        }
    }

    let mut answers = vec![];
    let mut used = vec![0; n];

    let mut que2 = VecDeque::new();

    'outer: while answers.len() != n {
        while let Some(a) = que.pop_back() {
            if edges[a].is_empty() {
                if used[a] % 2 == 1 {
                    println!("-1");
                    return;
                }
                continue;
            }
            let to = edges[a].iter().cloned().next().unwrap();
            if used[a] % 2 == 0 {
                used[to] += 1;
                answers.push((to, a));
            } else {
                if edges[to].len() == 1 && used[to] % 2 == 1 {
                    println!("-1");
                    return;
                }
                used[a] += 1;
                answers.push((a, to));
            }
            edges[a].remove(&to);
            edges[to].remove(&a);
            if edges[to].len() == 1 {
                que.push_front(to);
            } else if used[to] % 2 == 1 {
                que2.push_front(to);
            }
        }

        while let Some(a) = que2.pop_back() {
            if !edges[a].is_empty() && used[a] % 2 == 1 {
                let to = edges[a].iter().cloned().next().unwrap();
                edges[a].remove(&to);
                edges[to].remove(&a);
                used[a] += 1;
                answers.push((a, to));
                if edges[a].len() == 1 {
                    que.push_front(a);
                }
                if edges[to].len() == 1 {
                    que.push_front(to);
                }
            }
        }
        for a in 0..n {
            if !edges[a].is_empty() {
                let to = edges[a].iter().cloned().next().unwrap();
                edges[a].remove(&to);
                edges[to].remove(&a);
                used[a] += 1;
                answers.push((a, to));

                if edges[a].len() == 1 {
                    que.push_front(a);
                } else if used[a] % 2 == 1 {
                    que2.push_front(to);
                }
                if edges[to].len() == 1 {
                    que.push_front(to);
                }
                continue 'outer;
            }
        }
    }

    for ans in answers {
        println!("{} {}", ans.0 + 1, ans.1 + 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()
}