Little Petya likes numbers a lot. He found that number 123 in base 16 consists of two digits: the first is 7 and the second is 11. So the sum of digits of 123 in base 16 is equal to 18.

Now he wonders what is an average value of sum of digits of the number A written in all bases from 2 to A - 1.

Note that all computations should be done in base 10. You should find the result as an irreducible fraction, written in base 10.

Input

Input contains one integer number A (3 ≤ A ≤ 1000).

Output

Output should contain required average value in format «X/Y», where X is the numerator and Y is the denominator.

Examples

Input

5


Output

7/3


Input

3


Output

2/1

Note

In the first sample number 5 written in all bases from 2 to 4 looks so: 101, 12, 11. Sums of digits are 2, 3 and 2, respectively.
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

public class GetTheGift {
    private InputReader in;
    private PrintWriter out;
    
    
    private void solve() {
        int A = in.readInt();
        int sum = 0;
        for (int i = 2 ; i < A ; i++) {
            int b = A;
            int s = 0;
            while (b > 0) {
                s += b % i;
                b /= i;
            }
            sum += s;
        }
        A -= 2;
        int gcd = BigInteger.valueOf(sum).gcd(BigInteger.valueOf(A)).intValue();
        sum /= gcd;
        A /= gcd;
        System.out.println(sum +"/"+A);
    }   
    
    
    public static void main(String[] args) {
        new GetTheGift().run();
    }

    private GetTheGift() {

        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
    }

    private void run() {

        solve();
        exit();
    }

    @SuppressWarnings({ "UnusedDeclaration" })
    private void exit() {
        out.close();
        System.exit(0);
    }

    @SuppressWarnings({ "UnusedDeclaration" })
    private static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar, numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0)
                s = readLine0();
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines)
                return readLine();
            else
                return readLine0();
        }

        public BigInteger readBigInteger() {
            try {
                return new BigInteger(readString());
            } catch (NumberFormatException e) {
                throw new InputMismatchException();
            }
        }

        public char readCharacter() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            return (char) c;
        }

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = readInt();
            return array;
        }

        public long[] readLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; i++)
                array[i] = readLong();
            return array;
        }

        public double[] readDoubleArray(int size) {
            double[] array = new double[size];
            for (int i = 0; i < size; i++)
                array[i] = readDouble();
            return array;
        }

        public String[] readStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; i++)
                array[i] = readString();
            return array;
        }

        public char[][] readTable(int rowCount, int columnCount) {
            char[][] table = new char[rowCount][columnCount];
            for (int i = 0; i < rowCount; i++) {
                for (int j = 0; j < columnCount; j++)
                    table[i][j] = readCharacter();
            }
            return table;
        }

        public void readIntArrays(int[]... arrays) {
            for (int i = 0; i < arrays[0].length; i++) {
                for (int j = 0; j < arrays.length; j++)
                    arrays[j][i] = readInt();
            }
        }
    }
}
