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: Wrong Answer)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*);
    }
}

#[allow(unused_imports)]
use std::cmp::{min, max};
#[allow(unused_imports)]
use std::io::{stdout, stdin, BufWriter, Write};

use std::cmp::Ordering;
use std::collections::BinaryHeap;

#[derive(Debug, Copy, Clone, Eq, PartialEq)]
struct Rev(usize);

impl Ord for Rev {
    fn cmp(&self, other: &Rev) -> Ordering {
        other.0.cmp(&self.0)
    }
}

impl PartialOrd for Rev {
    fn partial_cmp(&self, other: &Rev) -> Option<Ordering> {
        Some(other.0.cmp(&self.0))
    }
}

#[derive(Debug, Copy, Clone, Eq, PartialEq)]
struct Range {
    l: usize,
    r: usize,
    a: usize,
    b: usize,
}
impl Range {
    fn new(l:usize,r:usize,a:usize,b:usize) ->Self {
        Range {
            l: l,
            r: r,
            a: a,
            b: b,
        }
    }
}

fn solve_sub_range(l:usize,r:usize,a:&Vec<usize>) -> Range {
    let mut li = l;
    let mut ri = l+1;
    for i in l..r {
        if i%2==l%2 {
            if a[i] < a[li] {
                li = i;
            }
        } else {
            if a[i] < a[ri] {
                ri = i
            }
        }
    }
    Range::new(li, ri+1, l, r)
}



fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (write!(out,$($format)*).unwrap());
    }

    input!{
      n: usize,
      ps: [usize; n],
    }

    let mut tbl = vec![None; n];
    let mut heap = BinaryHeap::new();
    {
        let range = solve_sub_range(0, n, &ps);
        heap.push(
            (Rev(ps[range.l]), range.l)
        );
        tbl[range.l] = Some(range);
    }

    let mut ans = vec![];
    while heap.len() >0 {
        let (_, l) = heap.pop().unwrap();

        let range = tbl[l].unwrap();
        ans.push(range.l);
        ans.push(range.r-1);

        let rs = [
            (range.a, range.l),
            (range.l+1, range.r-1),
            (range.r, range.b),
        ];
        for &(l, r) in rs.iter() {
            if l < r {
                let sub_range = solve_sub_range(l, r, &ps);
                heap.push(
                    (Rev(ps[sub_range.l]), sub_range.l)
                );
                tbl[sub_range.l] = Some(sub_range);
            }
        }
    }
    for a in ans {
        puts!("{} ", ps[a]);
    }
    puts!("{}\n", "");
}