Problem:
Stable Sort

Let's arrange a deck of cards. There are totally 36 cards of 4 suits(S, H, C, D) and 9 values (1, 2, ... 9). For example, 'eight of heart' is represented by H8 and 'one of diamonds' is represented by D1.

Your task is to write a program which sorts a given set of cards in ascending order by their values using the Bubble Sort algorithms and the Selection Sort algorithm respectively. These algorithms should be based on the following pseudocode:

BubbleSort(C)
1 for i = 0 to C.length-1
2 for j = C.length-1 downto i+1
3 if C[j].value < C[j-1].value
4 swap C[j] and C[j-1]

SelectionSort(C)
1 for i = 0 to C.length-1
2 mini = i
3 for j = i to C.length-1
4 if C[j].value < C[mini].value
5 mini = j
6 swap C[i] and C[mini]

Note that, indices for array elements are based on 0-origin.

For each algorithm, report the stability of the output for the given input (instance). Here, 'stability of the output' means that: cards with the same value appear in the output in the same order as they do in the input (instance).

Input

The first line contains an integer N, the number of cards.

N cards are given in the following line. Each card is represented by two characters. Two consecutive cards are separated by a space character.

Output

In the first line, print the arranged cards provided by the Bubble Sort algorithm. Two consecutive cards should be separated by a space character.

In the second line, print the stability ("Stable" or "Not stable") of this output.

In the third line, print the arranged cards provided by the Selection Sort algorithm. Two consecutive cards should be separated by a space character.

In the fourth line, print the stability ("Stable" or "Not stable") of this output.

Constraints

1 ≤ N ≤ 36

Sample Input 1

5
H4 C9 S4 D2 C3

Sample Output 1

D2 C3 H4 S4 C9
Stable
D2 C3 S4 H4 C9
Not stable

Sample Input 2

2
S1 H1

Sample Output 2

S1 H1
Stable
S1 H1
Stable

Solution in Ruby (judge verdict: Accepted)

class Card
  attr_accessor :kind, :number, :first_index

  def initialize(str, index)
    @kind = str[0]
    @number = str[1].to_i
    @first_index = index
  end

  def Card.selection_sort(array)
    0.upto(array.size-1) do |i1|
      i_min = i1
      (i1+1).upto(array.size-1) do |i2|
        if (array[i2].number < array[i_min].number) then
          i_min = i2
        end
      end

      if (i_min != i1) then
        array[i_min], array[i1] = array[i1], array[i_min]
      end
    end
  end

  def Card.bubble_sort(array)
    for i1 in 0...array.size do
      for i2 in i1...array.size-1 do
        index = array.size - 1 - i2 + i1
        if (array[index].number < array[index-1].number) then
          array[index], array[index-1] = array[index-1], array[index]
        end
      end
    end
  end
end

def check_stability(array)
  prev = nil
  array.each do |item|
    if (prev == nil) then
      prev = item
      next
    end

    if (prev.number == item.number) then
      return false if prev.first_index > item.first_index
    end

    prev = item
  end
  return true
end

n = gets.strip.to_i
array = gets.split(' ').each_with_index.map do |item, index|
  Card.new(item, index)
end

array_bub = Array.new(array)
Card.bubble_sort(array_bub)
puts array_bub.map{|x| x.kind + x.number.to_s}.join(' ')

puts (check_stability(array_bub)) ? "Stable" : "Not stable"

array_sel = Array.new(array)
Card.selection_sort(array_sel)
puts array_sel.map{|x| x.kind + x.number.to_s}.join(' ')

puts (check_stability(array_sel)) ? "Stable" : "Not stable"