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)

def selection_sort size, raw_array
  target_array = raw_array.dup
  size.times {|i|
    unsorted = target_array[i..(size - 1)]
    min = unsorted.min{|a, b| a[/\d+/] <=> b[/\d+/]}
    index_min = unsorted.index(min)
    if min[/\d+/] < target_array[i][/\d+/]
      target_array[i], target_array[i + index_min] = target_array[i + index_min], target_array[i]
    end
  }
  target_array
end

def bubble_sort size, raw_array
  target_array = raw_array.dup
  swapped = true
  while swapped do
    swapped = false
    (size - 1).downto(1) do |i|
      if target_array[i][/\d+/] < target_array[i - 1][/\d+/]
        target_array[i], target_array[i - 1] = target_array[i - 1], target_array[i]
        swapped = true
      end
    end
  end
  target_array
end

def stable? unsorted_array, sorted_array
  unsorted_array = unsorted_array.dup
  sorted_array = sorted_array.dup
  until unsorted_array.size == 0
    # ????????°?????????????????????????????????
    target_num = card_to_s(unsorted_array[0])
    unsorted_target = unsorted_array.select {|i| card_to_s(i) == target_num }
    sorted_target = sorted_array.select      {|i| card_to_s(i) == target_num }
    # ??????????????£????????????????????????
   # p unsorted_target
   # p sorted_target
    return 'Not stable' unless unsorted_target == sorted_target
    # ?????????????????????????????????
    unsorted_array = unsorted_array - unsorted_target
  end
  return 'Stable'

end

def card_to_s card
  card[/\d+/].to_i
end

size = STDIN.gets.chomp.to_i
raw_array = STDIN.gets.chomp.split(' ')

bubbled_array = bubble_sort size, raw_array
selected_array = selection_sort size, raw_array

puts bubbled_array.join ' '
puts stable? raw_array, bubbled_array
puts selected_array.join ' '
puts stable? raw_array, selected_array