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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.to_i
p = gets.split.map(&:to_i)
set = [p]
q = []
until set.empty? 
  r = nil
  r_index = nil
  min = n + 1
  from = nil
  set.each_with_index{|a, r_i|
    m, i = a.each_slice(2).each_with_index.min_by{|b, i| b[0]}.reduce{|b, i| [b[0], i*2]}
    if m < min
      min = m
      from = i
      r = a
      r_index = r_i
    end
  }
  set.delete_at(r_index)
  sec, to = r[from..-1].each_slice(2).each_with_index.min_by{|b, j| b[1]}.reduce{|b, j| [b[1], from + j*2+1]}
  q << min << sec
  set << r[0...from] if r[0...from] != []
  set << r[from+1...to] if r[from+1...to] != []
  set << r[to+1..-1] if r[to+1..-1] != []
end
puts q.join(' ')