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.*;
import java.math.*;
import java.util.*;

/**
* 
* @author Togrul Gasimov (ttogrul30@gmail.com)
*         Created on 11.09.2013
*/

public class Main {
   public static void main(String[] args) /*throws FileNotFoundException*/ { 
       InputStream inputStream = System.in;
       OutputStream outputStream = System.out;
       FastScanner in = new FastScanner(inputStream);
       FastPrinter out = new FastPrinter(outputStream);
       TaskA solver = new TaskA();
       solver.solve(1, in, out);
       out.close();
   }
}

class TaskA{
   static int gcd(int m, int n){
	   if(m < n)return gcd(n, m);
	   else if(m % n == 0)return n;
	   else return gcd(n, m % n);
   }
   
   public void solve(int testNumber, FastScanner scan, FastPrinter out) /*throws FileNotFoundException*/ {
       //Scanner sscan = new Scanner(new File("input.txt"));
       //PrintStream oout = new PrintStream(new File("output.txt"));
	  int n = scan.nextInt();
	  int sum = 0;
	  for(int i = 2; i < n; i++){
		  int k = 0, t = n;
		  while(t > 0){
			  k += t % i; 
			  t /= i;
		  }
		  sum += k;
	  }
	  out.println(sum / gcd(sum, n - 2) + "/" + (n - 2) / gcd(sum, n - 2));
       //sscan.close();
       //oout.close();
   }
}

class FastScanner extends BufferedReader {
   public FastScanner(InputStream is) {
       super(new InputStreamReader(is));
   }
   
   public int read() {
       try{
           int ret = super.read();
           return ret;
       }catch(Exception e){
           throw new InputMismatchException();
       }
   }
   
   public String next() {
       StringBuilder sb = new StringBuilder();
       int c = read();
       while (isWhiteSpace(c)) {
           c = read();
       }
       if (c < 0) {
           return null;
       }
       while (c >= 0 && !isWhiteSpace(c)) {
           sb.appendCodePoint(c);
           c = read();
       }
       return sb.toString();
   }
   
   static boolean isWhiteSpace(int c) {
       return c >= 0 && c <= 32;
   }
   
   public int nextInt() {
       int c = read();
       while (isWhiteSpace(c)) {
           c = read();
       }
       int sgn = 1;
       if (c == '-') {
           sgn = -1;
           c = read();
       }
       int ret = 0;
       while (c >= 0 && !isWhiteSpace(c)) {
           if (c < '0' || c > '9') {
               throw new NumberFormatException("digit expected " + (char) c
                       + " found");
           }
           ret = ret * 10 + c - '0';
           c = read();
       }
       return ret * sgn;
   }
   
   public long nextLong() {
       return Long.parseLong(next());
   }
   
   public double nextDouble() {
       return Double.parseDouble(next());
   }
   
   public BigInteger nextBigInteger() {
       return new BigInteger(next());
   }
   
   public BigDecimal nextBigDecimal(){
       return new BigDecimal(next());
   }
   
   public String readLine(){
       try{
           return super.readLine();
       }catch(IOException e){
           return null;
       }
   }
}

class FastPrinter extends PrintWriter {
   
   public FastPrinter(OutputStream out) {
       super(out);
   }
   public FastPrinter(Writer out) {
       super(out);
   }
}