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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace CsharpSpiral {
    partial class Program {
        //https://qiita.com/NotFounds/items/7b166af69a6f52a332de
        static void Main(string[] args) {
            var sw = new StreamWriter( Console.OpenStandardOutput() ) { AutoFlush = false };
            Console.SetOut( sw );
            new Program().Solve( new ConsoleInput( Console.In, ' ' ) );
            Console.Out.Flush();
        }
        struct Card: IComparable<Card> {
            char suit { get; set; }
            int value { get; set; }
            public Card(string info) {
                suit = info[0];
                value = int.Parse( info.Substring( 1 ) );
            }
            public int CompareTo(Card y) => value.CompareTo( y.value );
            public override string ToString() => suit.ToString() + value.ToString();
        }
        public void Solve(ConsoleInput cin) {
            var N = cin.ReadInt;
            var D = cin.ReadStrArray( N ).Select( s => new Card( s ) ).ToArray();
            var C = new Card[N];
            Array.Copy( D, C, N );
            BubbleSort( C );
            Console.WriteLine( C.Join() );
            Console.WriteLine( isStable( D, C, N )?"Stable":"Not stable" );
            Array.Copy( D, C, N );
            SelectionSort( C );
            Console.WriteLine( C.Join() );
            Console.WriteLine( isStable( D, C, N ) ? "Stable" : "Not stable" );

        }
        public void BubbleSort<T>(T[] A) where T : IComparable<T> {
            var N = A.Length;
            var flag = true;
            while (flag) {
                flag = false;
                for (int i = N - 2; i >= 0; i--) {
                    if (A[i].CompareTo( A[i + 1] ) > 0) {
                        A.Swap( i, i + 1 );
                        flag = true;
                    }
                }
            }
        }
        public void SelectionSort<T>(T[] A) where T : IComparable<T> {
            var N = A.Length;
            for (int i = 0; i < N; i++) {
                var mi = i;
                for (int j = i + 1; j < N; j++) {
                    if (A[j].CompareTo(A[mi])<0) {
                        mi = j;
                    }
                }
                if (i != mi) 
                    A.Swap( i, mi );
            }
        }   

        public bool isStable<T>(T[] src, T[] dst, int N) where T: IComparable<T> {
            int[] map = new int[N];
            for (int i = 0; i < N; i++) {
                map[i] = Array.IndexOf( dst, src[i] );
            }
            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    if (src[i].CompareTo( src[j] ) == 0) {
                        if (i<j && map[i] > map[j]) return false;
                    }
                }
            }
            return true;
        }
    }

    static class ExtendClass {
        public static void Swap<T>(this T[] X, int i, int j) {
            T tmp = X[i];
            X[i] = X[j];
            X[j] = tmp;
        }
        public static string Join<T> (this T[] X, string separator = " ") => string.Join( separator, X);
    }

    class ConsoleInput {
        private readonly TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;
        public ConsoleInput(TextReader stream, char separator = ' ') {
            this._separator = separator;
            this._stream = stream;
            inputStream = new Queue<string>();
        }
        public string Read {
            get {
                if (inputStream.Count != 0) return inputStream.Dequeue();
                string[] tmp = _stream.ReadLine().Split( _separator );
                for (int i = 0; i < tmp.Length; ++i)
                    inputStream.Enqueue( tmp[i] );
                return inputStream.Dequeue();
            }
        }
        public string ReadLine { get { return _stream.ReadLine(); } }
        public int ReadInt { get { return int.Parse( Read ); } }
        public long ReadLong { get { return long.Parse( Read ); } }
        public double ReadDouble { get { return double.Parse( Read ); } }
        public string[] ReadStrArray(long N) {
            var ret = new string[N];
            for (long i = 0; i < N; ++i)
                ret[i] = Read;
            return ret;
        }
        public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
        public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
    }
}