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 java.math.*;
import java.io.*;
public class Main {
    public static StringTokenizer st;
    public static BufferedReader scan;
    public static PrintWriter out;
    public static int gcd(int a, int b){
        if(a < b)return gcd(b, a);
        else if(b == 0)return a;
        else return gcd(b, a % b);
    }
    public static void main(String[] args) throws  IOException{
        scan = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int a = nextInt();
        int s = 0;
        Set <Integer>S = new HashSet();
        for(int i = 2; i < a; i++){

            int n = a;
            while(n > 0){
                s += n%i;
                n /= i;
            }
        }
        int x = s;
        int y = a - 2;
         out.println(s / gcd(x, y) + "/" + (y / gcd(x, y)));
        scan.close();
        out.close();
    }
    public static BigInteger nextBigInteger() throws  IOException {
        return new BigInteger(next());
    }
    public static long nextLong() throws  IOException {
        return Long.parseLong(next());
    }
    public static double nextDouble() throws  IOException {
        return Double.parseDouble(next());
    }
    public static int nextInt() throws  IOException {
        return Integer.parseInt(next());
    }
    public static String next() throws IOException {
        while(st == null || !st.hasMoreTokens()){
            st = new StringTokenizer(scan.readLine());
        }
        return st.nextToken();
    }
}