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: Wrong Answer)

class Card
	attr_reader :suit
	attr_reader :no
	attr_reader :name
	def initialize(n)
		@name = n
		@suit = n[0]
		@no = n[1].to_i
	end

	def Search(n)
		return self if n == @no
	end
end

def Swap(a, b)
	return b,a
end

def PrintArray(d)
	d.length.times { |i|
		print " " unless i == 0
		print "#{d[i].name}"
	}
	puts
end

def Stable(a, b)
	stable = true
	(1..9).each { |i|
		bt = b.each_with_object(i).map(&:Search).compact
		next if bt.length < 1
		a.each_with_object(i).map(&:Search).compact.each_with_index { |at, j|
			if at.name != bt[j].name
				stable = false
				break
			end
		}
		break if not stable
	}
	print "Not " if not stable
	puts "Stable"
end

def BubbleSort(d_o)
	d = Marshal.load(Marshal.dump(d_o))
	(d.length-1).times { |i|
		(d.length-1).step(i+1, -1) { |j|
			d[j],d[j-1] = Swap(d[j],d[j-1]) if d[j-1].no > d[j].no
		}
	}
	PrintArray(d)
	Stable(d, d_o)
end

def SelectionSort(d_o)
	d = Marshal.load(Marshal.dump(d_o))
	d.length.times { |i|
		min = i
		(i...d.length).each_with_index { |j|
			min = j if d[min].no > d[j].no
		}
		d[i],d[min] = Swap(d[i],d[min]) if i != min
	}
	PrintArray(d)
	Stable(d, d_o)
end

gets
d = Array.new
gets.chomp.split(" ").each { |c| d << Card.new(c) }
BubbleSort(d)
SelectionSort(d)