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
  def initialize(s)
    @suit = s[0]
    @num = s[1].to_i
  end
  def suit
    return @suit
  end
  def num
    return @num
  end
  def val
    return @suit + @num.to_s
  end
end

def bubbleSort(a,n)
  for i in 0..n-1 do
    for j in (i+1..n-1).to_a.reverse
      if a[j].num < a[j-1].num
        a[j],a[j-1] = a[j-1],a[j]
      end
    end
  end
end

def selectionSort(a,n)
  for i in 0..n-1 do
    minj = i
    for j in i..n-1 do
      if a[j].num < a[minj].num
        minj = j
      end
    end
    if i != minj
      a[i],a[minj] = a[minj],a[i]
    end
  end
end

def isStable(a,b,n)
  for ai in 0..n-2 do
    for bi in 1..n-1 do
      if a[ai]!=b[bi]
        next
      end
      for aj in ai+1..n-1 do
        if a[ai].num!=a[aj].num
          next
        end
        for bj in 0..bi-1 do
          if a[aj]==b[bj]
            return "Not stable"
          end
        end
      end
    end
  end
  return "Stable"
end 

n = gets.chomp.to_i
cards = gets.chomp.split(" ").map{|x| Card.new(x)}
cards_bubble = cards.clone
cards_selection = cards.clone
bubbleSort(cards_bubble,n)
selectionSort(cards_selection,n)
printf("%s\n", cards_bubble.map{|x| x.val}.join(" "))
printf("%s\n", isStable(cards,cards_bubble,n))
printf("%s\n", cards_selection.map{|x| x.val}.join(" "))
printf("%s\n", isStable(cards,cards_selection,n))