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.
• $2 \leq N \leq 2 \times 10^5$
• $p$ 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.

4
3 2 4 1

3 1 2 4

The solution above is obtained as follows:

2
1 2

1 2

8
4 6 3 2 8 5 7 1

3 1 2 7 4 6 8 5

The solution above is obtained as follows: