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.util.*;
import static java.lang.Math.*;
import java.io.*;

public class Main
{
    BufferedReader in;
    //StreamTokenizer in;
    PrintWriter out;

    public static void main( String[] args ) throws IOException
    {
        new Main().run();
    }
    /*
    int ni() throws IOException
    {
        in.nextToken();
        return (int) in.nval;
    }

    String ns() throws IOException
    {
        in.nextToken();
        return in.sval;
    }
    */
    BufferedReader initBufFromFile() throws IOException
    {
        return new BufferedReader( new FileReader( "input.txt" ) );
    }

    BufferedReader initBufFromStream() throws IOException
    {
        return new BufferedReader( new InputStreamReader( System.in ) );
    }

    StreamTokenizer initStrFromFile() throws IOException
    {
        return new StreamTokenizer( new BufferedReader( new FileReader( "input.txt" ) ) );
    }

    StreamTokenizer initStrFromStream() throws IOException
    {
        return new StreamTokenizer( new BufferedReader( new InputStreamReader( System.in ) ) );
    }

    PrintWriter initWrtFromFile() throws IOException
    {
        return new PrintWriter( new FileWriter( "output.txt" ) );
    }

    PrintWriter initWrtFromStream() throws IOException
    {
        return new PrintWriter( new OutputStreamWriter( System.out ) );
    }

    void run() throws IOException
    {
        in = initBufFromStream();
        out = initWrtFromStream();
        
        solve();

        out.flush();
    }

    void solve() throws IOException
    {
        int a = Integer.parseInt(in.readLine());
        int sum = 0;
        for(int radix = 2; radix < a; radix++) {
            int num = a;
            while(num > 0) {
                sum += num % radix;
                num /= radix;
            }
            sum += num;
        }
        int g = gcd( sum, a - 2 );
        out.print( sum / g );
        out.print('/');
        out.print( (a - 2) / g );
    }

    int gcd( int a, int b )
    {
        if( b == 0 ) return a;
        return gcd( b, a % b );
    }
}