Problem: You are given a broken clock. You know, that it is supposed to show time in 12- or 24-hours HH:MM format. In 12-hours format hours change from 1 to 12, while in 24-hours it changes from 0 to 23. In both formats minutes change from 0 to 59.

You are given a time in format HH:MM that is currently displayed on the broken clock. Your goal is to change minimum number of digits in order to make clocks display the correct time in the given format.

For example, if 00:99 is displayed, it is enough to replace the second 9 with 3 in order to get 00:39 that is a correct time in 24-hours format. However, to make 00:99 correct in 12-hours format, one has to change at least two digits. Additionally to the first change one can replace the second 0 with 1 and obtain 01:39.

Input

The first line of the input contains one integer 12 or 24, that denote 12-hours or 24-hours format respectively.

The second line contains the time in format HH:MM, that is currently displayed on the clock. First two characters stand for the hours, while next two show the minutes.

Output

The only line of the output should contain the time in format HH:MM that is a correct time in the given format. It should differ from the original in as few positions as possible. If there are many optimal solutions you can print any of them.

Examples

Input

24
17:30


Output

17:30


Input

12
17:30


Output

07:30


Input

24
99:99


Output

09:09

Solution (in JAVA):

Solution:
import java.awt.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
import java.util.List;

import static java.lang.Math.max;
import static java.lang.Math.min;


public class A implements Runnable{

    private final static Random rnd = new Random();

    // SOLUTION!!!
    // HACK ME PLEASE IF YOU CAN!!!
    // PLEASE!!!
    // PLEASE!!!
    // PLEASE!!!

    private void solve() {
        int n = readInt();

        delim = ":";
        int h = readInt();
        int m = readInt();

        if (n == 12) {
            if (h < 1) {
                h = 1;
            } else if (h > 12) h = minDelta(h, 1, 12);
        } else {
            if (h > 23) {
                h = minDelta(h, 0, 23);
            }
        }

        if (m > 59) {
            m = minDelta(m, 0, 59);
        }

        out.println(two(h)+ ":" + two(m));
    }

    int minDelta(int x, int min, int max) {
        int minDelta = 100500;
        int minX = -1;
        for (int i = min; i <= max; ++i) {
            int delta = delta(x, i);
            if (delta < minDelta) {
                minDelta = delta;
                minX = i;
            }
        }

        return minX;
    }

    String two(int x) {
        if (x < 10) return "0" + x;
        return "" + x;
    }

    int delta(int x, int y) {
        String xS = Integer.toString(x);
        String yS = Integer.toString(y);

        while (xS.length() < yS.length()) {
            xS = "0" + xS;
        }

        while (xS.length() > yS.length()) {
            yS = "0" + yS;
        }

        int count = 0;
        for (int i = 0; i < xS.length(); ++i) {
            count += (xS.charAt(i) == yS.charAt(i) ? 0 : 1);
        }

        return count;
    }

    /////////////////////////////////////////////////////////////////////

    private final static boolean FIRST_INPUT_STRING = false;
    private final static boolean MULTIPLE_TESTS = true;
    private final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    private final static int MAX_STACK_SIZE = 128;

    private final static boolean OPTIMIZE_READ_NUMBERS = false;

    /////////////////////////////////////////////////////////////////////

    public void run(){
        try{
            timeInit();
            Locale.setDefault(Locale.US);

            init();

            if (ONLINE_JUDGE) {
                solve();
            } else {
                do {
                    try {
                        timeInit();
                        solve();
                        time();

                        out.println();
                    } catch (NumberFormatException e) {
                        break;
                    } catch (NullPointerException e) {
                        if (FIRST_INPUT_STRING) break;
                        else throw e;
                    }
                } while (MULTIPLE_TESTS);
            }

            out.close();
            time();
        }catch (Exception e){
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    /////////////////////////////////////////////////////////////////////

    private BufferedReader in;
    private OutputWriter out;
    private StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args){
        new Thread(null, new A(), "", MAX_STACK_SIZE * (1L << 20)).start();
    }

    /////////////////////////////////////////////////////////////////////

    private void init() throws FileNotFoundException{
        Locale.setDefault(Locale.US);

        if (ONLINE_JUDGE){
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new OutputWriter(System.out);
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new OutputWriter("output.txt");
        }
    }

    ////////////////////////////////////////////////////////////////

    private long timeBegin;

    private void timeInit() {
        this.timeBegin = System.currentTimeMillis();
    }

    private void time(){
        long timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    private void debug(Object... objects){
        if (ONLINE_JUDGE){
            for (Object o: objects){
                System.err.println(o.toString());
            }
        }
    }

    /////////////////////////////////////////////////////////////////////

    private String delim = " ";

    private String readLine() {
        try {
            return in.readLine();
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private String readString() {
        try {
            while(!tok.hasMoreTokens()){
                tok = new StringTokenizer(readLine());
            }

            return tok.nextToken(delim);
        } catch (NullPointerException e) {
            return null;
        }
    }

    /////////////////////////////////////////////////////////////////

    private final char NOT_A_SYMBOL = '\0';

    private char readChar() {
        try {
            int intValue = in.read();

            if (intValue == -1){
                return NOT_A_SYMBOL;
            }

            return (char) intValue;
        } catch (IOException e) {
            throw new RuntimeIOException(e);
        }
    }

    private char[] readCharArray() {
        return readLine().toCharArray();
    }

    private char[][] readCharField(int rowsCount) {
        char[][] field = new char[rowsCount][];
        for (int row = 0; row < rowsCount; ++row) {
            field[row] = readCharArray();
        }

        return field;
    }

    /////////////////////////////////////////////////////////////////

    private long optimizedReadLong() {
        long result = 0;
        boolean started = false;
        while (true) {
            try {
                int j = in.read();
                if (-1 == j) {
                    if (started) return result;
                    throw new NumberFormatException();
                }

                if ('0' <= j && j <= '9') {
                    result = result * 10 + j - '0';
                    started = true;
                } else if (started) {
                    return result;
                }
            } catch (IOException e) {
                throw new RuntimeIOException(e);
            }
        }
    }

    private int readInt() {

        if (!OPTIMIZE_READ_NUMBERS) {
            return Integer.parseInt(readString());
        } else {
            return (int) optimizedReadLong();
        }
    }

    private int[] readIntArray(int size) {
        int[] array = new int[size];

        for (int index = 0; index < size; ++index){
            array[index] = readInt();
        }

        return array;
    }

    private int[] readSortedIntArray(int size) {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    private int[] readIntArrayWithDecrease(int size) {
        int[] array = readIntArray(size);

        for (int i = 0; i < size; ++i) {
            array[i]--;
        }

        return array;
    }

    ///////////////////////////////////////////////////////////////////

    private int[][] readIntMatrix(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArray(columnsCount);
        }

        return matrix;
    }

    private int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) {
        int[][] matrix = new int[rowsCount][];

        for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
            matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
        }

        return matrix;
    }

    ///////////////////////////////////////////////////////////////////

    private long readLong() {
        if (!OPTIMIZE_READ_NUMBERS) {
            return Long.parseLong(readString());
        } else {
            return optimizedReadLong();
        }
    }

    private long[] readLongArray(int size) {
        long[] array = new long[size];

        for (int index = 0; index < size; ++index){
            array[index] = readLong();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private double readDouble() {
        return Double.parseDouble(readString());
    }

    private double[] readDoubleArray(int size) {
        double[] array = new double[size];

        for (int index = 0; index < size; ++index){
            array[index] = readDouble();
        }

        return array;
    }

    ////////////////////////////////////////////////////////////////////

    private BigInteger readBigInteger() {
        return new BigInteger(readString());
    }

    private BigDecimal readBigDecimal() {
        return new BigDecimal(readString());
    }

    /////////////////////////////////////////////////////////////////////

    private Point readPoint() {
        int x = readInt();
        int y = readInt();
        return new Point(x, y);
    }

    private Point[] readPointArray(int size) {
        Point[] array = new Point[size];

        for (int index = 0; index < size; ++index){
            array[index] = readPoint();
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    private List<Integer>[] readGraph(int vertexNumber, int edgeNumber) {
        @SuppressWarnings("unchecked")
        List<Integer>[] graph = new List[vertexNumber];

        for (int index = 0; index < vertexNumber; ++index){
            graph[index] = new ArrayList<Integer>();
        }

        while (edgeNumber-- > 0){
            int from = readInt() - 1;
            int to = readInt() - 1;

            graph[from].add(to);
            graph[to].add(from);
        }

        return graph;
    }

    /////////////////////////////////////////////////////////////////////

    private static class IntIndexPair {

        static Comparator<IntIndexPair> increaseComparator = new Comparator<A.IntIndexPair>() {

            @Override
            public int compare(A.IntIndexPair indexPair1, A.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return value1 - value2;

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        static Comparator<IntIndexPair> decreaseComparator = new Comparator<A.IntIndexPair>() {

            @Override
            public int compare(A.IntIndexPair indexPair1, A.IntIndexPair indexPair2) {
                int value1 = indexPair1.value;
                int value2 = indexPair2.value;

                if (value1 != value2) return -(value1 - value2);

                int index1 = indexPair1.index;
                int index2 = indexPair2.index;

                return index1 - index2;
            }
        };

        int value, index;

        IntIndexPair(int value, int index) {
            super();
            this.value = value;
            this.index = index;
        }

        int getRealIndex() {
            return index + 1;
        }
    }

    private IntIndexPair[] readIntIndexArray(int size) {
        IntIndexPair[] array = new IntIndexPair[size];

        for (int index = 0; index < size; ++index) {
            array[index] = new IntIndexPair(readInt(), index);
        }

        return array;
    }

    /////////////////////////////////////////////////////////////////////

    private static class OutputWriter extends PrintWriter {

        final int DEFAULT_PRECISION = 12;

        private int precision;
        private String format, formatWithSpace;

        {
            precision = DEFAULT_PRECISION;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        OutputWriter(OutputStream out) {
            super(out);
        }

        OutputWriter(String fileName) throws FileNotFoundException {
            super(fileName);
        }

        int getPrecision() {
            return precision;
        }

        void setPrecision(int precision) {
            precision = max(0, precision);
            this.precision = precision;

            format = createFormat(precision);
            formatWithSpace = format + " ";
        }

        String createFormat(int precision){
            return "%." + precision + "f";
        }

        @Override
        public void print(double d){
            printf(format, d);
        }

        void printWithSpace(double d){
            printf(formatWithSpace, d);
        }

        void printAll(double...d){
            for (int i = 0; i < d.length - 1; ++i){
                printWithSpace(d[i]);
            }

            print(d[d.length - 1]);
        }

        @Override
        public void println(double d){
            printlnAll(d);
        }

        void printlnAll(double... d){
            printAll(d);
            println();
        }
    }

    /////////////////////////////////////////////////////////////////////

    private static class RuntimeIOException extends RuntimeException {

        /**
         *
         */
        private static final long serialVersionUID = -6463830523020118289L;

        RuntimeIOException(Throwable cause) {
            super(cause);
        }
    }

    /////////////////////////////////////////////////////////////////////
    //////////////// Some useful constants and functions ////////////////
    /////////////////////////////////////////////////////////////////////

    private static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
    private static final int[][] steps8 = {
            {-1, 0}, {1, 0}, {0, -1}, {0, 1},
            {-1, -1}, {1, 1}, {1, -1}, {-1, 1}
    };

    private static boolean checkCell(int row, int rowsCount, int column, int columnsCount) {
        return checkIndex(row, rowsCount) && checkIndex(column, columnsCount);
    }

    private static boolean checkIndex(int index, int lim){
        return (0 <= index && index < lim);
    }

    /////////////////////////////////////////////////////////////////////

    private static boolean checkBit(int mask, int bit){
        return (mask & (1 << bit)) != 0;
    }
    private static boolean checkBit(long mask, int bit){
        return (mask & (1L << bit)) != 0;
    }

    /////////////////////////////////////////////////////////////////////

    private static long getSum(int[] array) {
        long sum = 0;
        for (int value: array) {
            sum += value;
        }

        return sum;
    }

    private static Point getMinMax(int[] array) {
        int min = array[0];
        int max = array[0];

        for (int index = 0, size = array.length; index < size; ++index, ++index) {
            int value = array[index];

            if (index == size - 1) {
                min = min(min, value);
                max = max(max, value);
            } else {
                int otherValue = array[index + 1];

                if (value <= otherValue) {
                    min = min(min, value);
                    max = max(max, otherValue);
                } else {
                    min = min(min, otherValue);
                    max = max(max, value);
                }
            }
        }

        return new Point(min, max);
    }

    /////////////////////////////////////////////////////////////////////

    private static int[] getPrimes(int n) {
        boolean[] used = new boolean[n];
        used[0] = used[1] = true;

        int size = 0;
        for (int i = 2; i < n; ++i) {
            if (!used[i]) {
                ++size;
                for (int j = 2 * i; j < n; j += i) {
                    used[j] = true;
                }
            }
        }

        int[] primes = new int[size];
        for (int i = 0, cur = 0; i < n; ++i) {
            if (!used[i]) {
                primes[cur++] = i;
            }
        }

        return primes;
    }

    /////////////////////////////////////////////////////////////////////

    private static long lcm(long a, long b) {
        return a / gcd(a, b) * b;
    }

    private static long gcd(long a, long b) {
        return (a == 0 ? b : gcd(b % a, a));
    }

    /////////////////////////////////////////////////////////////////////

    private static class IdMap<KeyType> extends HashMap<KeyType, Integer> {

        /**
         *
         */
        private static final long serialVersionUID = -3793737771950984481L;

        public IdMap() {
            super();
        }

        int getId(KeyType key) {
            Integer id = super.get(key);
            if (id == null) {
                super.put(key, id = size());
            }

            return id;
        }
    }
}