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 JAVA (judge verdict: WA: Presentation Error)

import java.util.Arrays;

public class Main {
    // field

    // method
    public static void main(String[] args) {
	//System.out.print("> ");
	java.util.Scanner scan = new java.util.Scanner(System.in);
	int arraySize = scan.nextInt();
	String[] input = new String[arraySize];
	Cards[] cardsArray = new Cards[arraySize];
	//System.out.print("> ");
	for (int i = 0; i < arraySize; i++){
	    input[i] = scan.next();
	    cardsArray[i] = new Cards(input[i]);
	}    
	
	  BubbleSort bs = new BubbleSort(cardsArray.clone()); // バブルソート
	  bs.bubbleSort(); // ソート
	  bs.display();    // 表示
	  printCheck(bs.checkSort());   // 成功したかを表示
	  System.out.println();
	  
	  SelectionSort ss = new SelectionSort(cardsArray.clone()); // セレクションソート
	  ss.selectionSort(); // ソート
	  ss.display();       // 表示
	  printCheck(ss.checkSort());   // 成功したかを表示
	  
    }
    private static void printCheck(boolean checkSort) {
	if(checkSort) {
	    System.out.print("Stable");
	} else{
	    System.out.print("Not stable");
	}
    }
}

class Cards {
    private String name;
    private int value;
    private int id;
    private static int count;

    public Cards(String str) {
	this.name = str;
	this.value = str.charAt(1)-48;
	this.id = this.count;
	this.count++;
    }

    public String getName() {
	return this.name;
    }
    
    public int getValue() {
	return this.value;
    }

    public int getId() {
	return this.id;
    }
    
    public void print() {
	System.out.print(this.name);
    }
}
class BubbleSort {
    // -- field
    private Cards[] sort_array;
    // -- Constructor
    private BubbleSort() {}
    public BubbleSort(Cards[] sort_array) {
	this.sort_array = sort_array;
    }
    
    // -- Method
    public void display() {
	for (int i = 0; i < this.sort_array.length; i++) {
	    this.sort_array[i].print();
	    System.out.print(" ");
	}
	System.out.println();
    }

    public void swap(int x, int y) {
	Cards temp = this.sort_array[x];
	this.sort_array[x] = this.sort_array[y];
	this.sort_array[y] = temp;
    }

    public void bubbleSort() {
	for (int i = this.sort_array.length - 1; i > 0; i--) {
	    for (int j = 0; j < i; j++) {
		if (this.sort_array[j].getValue() > this.sort_array[j + 1].getValue()) {
		    swap(j, j + 1);
		}
		// this.display(); // 動作チェック
	    }
	}
    }

    public boolean checkSort() {
	for (int i = 0; i < this.sort_array.length - 1; i++) {
	    if(this.sort_array[i].getValue() == this.sort_array[i + 1].getValue()) {
		if(this.sort_array[i].getId() > this.sort_array[i].getId()) {
		    return false;
		}
	    }
	}
	return true;
    }

}

class SelectionSort {
    // -- Field
    private Cards[] sort_array;
    // -- Constructor
    private SelectionSort() {}
    public SelectionSort(Cards[] sort_array) {
	this.sort_array = sort_array;
    }
    
    // -- Method
    public void display() {
	for (int i = 0; i < this.sort_array.length; i++) {
	    this.sort_array[i].print();
	    System.out.print(" ");
	}
	System.out.println();
    }


    public void swap(int x, int y) {
	Cards temp = this.sort_array[x];
	this.sort_array[x] = this.sort_array[y];
	this.sort_array[y] = temp;
    }

    public void selectionSort() {
	int out, in, min;
	for (out = 0; out < this.sort_array.length - 1; out++) {
	    min = out;
	    for (in = out + 1; in < this.sort_array.length; in++) {
		if (this.sort_array[in].getValue() < this.sort_array[min].getValue()) {
		    min = in;
		}
	    }
	    // System.out.println("min = " + this.sort_array[min]); // 動作確認
	    this.swap(out, min);
	    // this.display(); // 動作確認
	}
    }

    public boolean checkSort() {
	for (int i = 0; i < this.sort_array.length - 1; i++) {
	    if(this.sort_array[i].getValue() == this.sort_array[i + 1].getValue()) {
		if(this.sort_array[i].getId() > this.sort_array[i + 1].getId()) {
		    return false;
		}
	    }
	}
	return true;
    }
}