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 (1.42.0) (judge verdict: Time Limit Exceeded)

use proconio::input;

fn cal(a: &[u32]) -> Box<dyn Iterator<Item = (u32, u32)>> {
    assert!(a.len() % 2 == 0);
    if a.is_empty() {
        Box::new(Vec::new().into_iter())
    } else {
        let n = a.len();
        let u = (0..n)
            .filter(|&i| i % 2 == 0)
            .min_by_key(|&i| a[i])
            .unwrap();
        let v = (u + 1..n)
            .filter(|&i| i % 2 == 1)
            .min_by_key(|&i| a[i])
            .unwrap();
        Box::new(std::iter::once((a[u], a[v])).chain(itertools::kmerge(vec![
            cal(&a[0..u]),
            cal(&a[u + 1..v]),
            cal(&a[v + 1..n]),
        ])))
    }
}

fn main() {
    input!(n: usize, a: [u32; n]);
    let ans = cal(a.as_slice());
    println!(
        "{}",
        ans.map(|(x, y)| format!("{} {}", x, y))
            .fold(String::new(), |acc, x| if acc.is_empty() {
                x
            } else {
                acc + " " + x.as_ref()
            })
    );
}