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.
//package codeforces.br13;

import java.io.*;

/**
 * User: Kandy
 * Date: 12.07.2010
 * Time: 21:51:52
 */
public class ProblemA {

    private int gcd(int a,int b) {
        if (a == 0 || b == 0)
            return a + b;
        if (a < b)
            return gcd(b, a);
        return gcd(b, a % b);
    }

    public void solve() {
        boolean oj = true;

        try {
            Reader reader = oj ? new InputStreamReader(System.in) : new FileReader("A.in");
            Writer writer = oj ? new OutputStreamWriter(System.out) : new FileWriter("A.out");
            BufferedReader br = new BufferedReader(reader);
            StreamTokenizer st = new StreamTokenizer(reader);
            PrintWriter out = new PrintWriter(writer);

            MyTokenizer tok = new MyTokenizer(br.readLine());

            int a = (int)tok.getNum();

            int allsum = 0;

            for(int base=2;base<a;base++) {
                int num = a;
                int sum = 0;
                while (num > 0) {
                    sum += num % base;
                    num /= base;
                }
                allsum += sum;
            }

            int n = allsum;
            int d = a - 2;
            int g = gcd(n, d);
            n /= g;
            d /= g;

            out.printf("%d/%d", n, d);

            br.close();
            out.close();
            reader.close();
            writer.close();
        }
        catch (Exception ex) {
            ex.printStackTrace();
        }
        finally {
        }
    }


    public static void main(String[] args) {
        ProblemA f = new ProblemA();
        f.solve();
    }

    private class MyTokenizer {
        private String s;
        private int cur;

        public MyTokenizer(String s) {
            this.s = s;
            cur = 0;
        }

        public void skip() {
            while (cur < s.length() && (s.charAt(cur) == ' ' || s.charAt(cur) == '\n')) {
                cur++;
            }
        }

        public double getNum() {
            skip();
            String snum = "";
            while (cur < s.length() && (s.charAt(cur) >= '0' && s.charAt(cur) <= '9' || s.charAt(cur) == '.' || s.charAt(cur) == '-')) {
                snum += s.charAt(cur);
                cur++;
            }
            return Double.valueOf(snum);
        }

        public String getString() {
            skip();
            String s2 = "";
            while (cur < s.length() && (((s.charAt(cur) >= 'a' && s.charAt(cur) <= 'z')) || ((s.charAt(cur) >= 'A' && s.charAt(cur) <= 'Z')))) {
                s2 += s.charAt(cur);
                cur++;
            }
            return s2;
        }

        public char getCurrentChar() throws Exception {
            if (cur < s.length())
                return s.charAt(cur);
            else
                throw new Exception("Current character out of string length");
        }

        public void moveNextChar() {
            if (cur < s.length())
                cur++;
        }

        public boolean isFinished() {
            return cur >= s.length();
        }
    }
}
