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.io.*;
import java.math.BigInteger;

public class Main implements Runnable {
	public void solution() throws IOException {
		int n = in.nextInt();
		long sum = 0;
		for (int k = 2; k < n; ++k) {
			sum += calculate(n, k);
		}
		long den = n - 2;
		long d = BigInteger.valueOf(sum).gcd(BigInteger.valueOf(den)).longValue();
		sum /= d;
		den /= d;
		out.println(sum + "/" + den);
	}

	private long calculate(int n, int k) {
		long sum = 0;
		while (n > 0) {
			sum += n % k;
			n /= k;
		}
		return sum;
	}

	public void run() {
		try {
			solution();
			in.reader.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private class Scanner {
		BufferedReader reader;
		StringTokenizer tokenizer;

		public Scanner(Reader reader) {
			this.reader = new BufferedReader(reader);
			this.tokenizer = new StringTokenizer("");
		}

		public boolean hasNext() throws IOException {
			while (!tokenizer.hasMoreTokens()) {
				String next = reader.readLine();
				if (next == null) {
					return false;
				}
				tokenizer = new StringTokenizer(next);
			}
			return true;
		}

		public String next() throws IOException {
			hasNext();
			return tokenizer.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public String nextLine() throws IOException {
			tokenizer = new StringTokenizer("");
			return reader.readLine();
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] args) throws IOException {
		new Thread(null, new Main(), "", 1 << 28).start();
	}
	PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	Scanner in = new Scanner(new InputStreamReader(System.in));
}
