Problem:
Score : 800 points

Problem Statement

Let N be a positive even number.

We have a permutation of (1, 2, ..., N), p = (p_1, p_2, ..., p_N).
Snuke is constructing another permutation of (1, 2, ..., N), q, following the procedure below.

First, let q be an empty sequence.
Then, perform the following operation until p becomes empty:

Select two adjacent elements in p, and call them x and y in order. Remove x and y from p (reducing the length of p by 2), and insert x and y, preserving the original order, at the beginning of q.

When p becomes empty, q will be a permutation of (1, 2, ..., N).

Find the lexicographically smallest permutation that can be obtained as q.

Constraints

N is an even number.

2 ≤ N ≤ 2 × 10^5

p is a permutation of (1, 2, ..., N).

Input

Input is given from Standard Input in the following format:

N
p_1 p_2 ... p_N

Output

Print the lexicographically smallest permutation, with spaces in between.

Sample Input 1

4
3 2 4 1

Sample Output 1

3 1 2 4

The solution above is obtained as follows:

p

q

(3, 2, 4, 1)

()

↓

↓

(3, 1)

(2, 4)

↓

↓

()

(3, 1, 2, 4)

Sample Input 2

2
1 2

Sample Output 2

1 2

Sample Input 3

8
4 6 3 2 8 5 7 1

Sample Output 3

3 1 2 7 4 6 8 5

The solution above is obtained as follows:

p

q

(4, 6, 3, 2, 8, 5, 7, 1)

()

↓

↓

(4, 6, 3, 2, 7, 1)

(8, 5)

↓

↓

(3, 2, 7, 1)

(4, 6, 8, 5)

↓

↓

(3, 1)

(2, 7, 4, 6, 8, 5)

↓

↓

()

(3, 1, 2, 7, 4, 6, 8, 5)

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::io::{BufRead, Write};
use std::io;

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let _: usize = s.trim().parse().unwrap();
    s.clear();
    input.read_line(&mut s).unwrap();
    let mut a: Vec<usize> = s.split_whitespace().map(|x| x.parse().unwrap()).collect();
    let mut b: Vec<usize> = Vec::with_capacity(a.len());
    while !a.is_empty() {
        let (max_index, _) = a.windows(2)
            .enumerate()
            .max_by_key(|&(_, w)| (w[0] + w[1], w[1]))
            .unwrap();
        b.push(a.remove(max_index + 1));
        b.push(a.remove(max_index));
    }
    let result: Vec<_> = b.iter().rev().map(|x| x.to_string()).collect();
    writeln!(output, "{}", result.join(" ")).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test(
            "4
3 2 4 1\n",
            "3 1 2 4\n",
        );
    }
    #[test]
    fn case2() {
        test(
            "2
1 2\n",
            "1 2\n",
        );
    }
    #[test]
    fn case3() {
        test(
            "8
4 6 3 2 8 5 7 1\n",
            "3 1 2 7 4 6 8 5\n",
        );
    }
}