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
  include Comparable
  def initialize(val)
    @val = val
  end

  def mark
    @val[0]
  end

  def number
    @val[1].to_i
  end

  def <=>(other)
    number <=> other.number
  end

  def to_s
    @val.dup
  end
end

def bubble_sort(arr)
  n = arr.size - 1
  0.upto(n) do |i|
    n.downto(i + 1) do |j|
      arr[j-1], arr[j] = arr[j], arr[j-1] if arr[j] < arr[j-1]
    end
  end
end

def selection_sort(arr)
  n = arr.size - 1
  0.upto(n) do |i|
    mini_j = i
    i.upto(n) do |j|
      mini_j = j if arr[j] < arr[mini_j]
    end
    arr[i], arr[mini_j] = arr[mini_j], arr[i]
  end
end

def stable?(cards, sorted)
  orig_order = order_hash(cards)
  sorted_order = order_hash(sorted)
  orig_order.map{|k, v| sorted_order[k] == v}.all?
end

def order_hash(cards)
  order = Hash.new {|h, k| h[k] = ''}
  cards.each{|c| order[c.number] << c.mark }
  order
end


n = gets.to_i
cards = gets.split.map{|v| Card.new(v)}

bubble = cards.dup
selection = cards.dup

bubble_sort(bubble)
puts bubble.join("\s")
puts stable?(cards, bubble) ? 'Stable' : 'Not stable'

selection_sort(selection)
puts selection.join("\s")
puts stable?(cards, selection) ? 'Stable' : 'Not stable'