Let's assume that 

  * v(n) is the largest prime number, that does not exceed n;
  * u(n) is the smallest prime number strictly greater than n. 



Find <image>.

Input

The first line contains integer t (1 ≤ t ≤ 500) — the number of testscases. 

Each of the following t lines of the input contains integer n (2 ≤ n ≤ 109).

Output

Print t lines: the i-th of them must contain the answer to the i-th test as an irreducible fraction "p/q", where p, q are integers, q > 0.

Examples

Input

2
2
3


Output

1/6
7/30
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BOnSumOfFractions solver = new BOnSumOfFractions();
        solver.solve(1, in, out);
        out.close();
    }

    static class BOnSumOfFractions {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int t = in.readInt();
            while (t-- > 0) {
                int n = in.readInt();
                if (n == 2) {
                    out.println("1/6");
                    continue;
                }
                long s = smallerPrime(n);
                long l = largerPrime(n);
                long ap = s * l - 2 * l + 2 * n - 2 * s + 2;
                long aq = l * s * 2;
                long g = gcd(ap, aq);
                ap /= g;
                aq /= g;
                out.println(ap + "/" + aq);
            }

        }

        int smallerPrime(int n) {
            for (int i = n; ; i--) {
                if (isPrime(i)) return i;
            }
        }

        int largerPrime(int n) {
            for (int i = n + 1; ; i++) {
                if (isPrime(i)) return i;
            }
        }

        boolean isPrime(int n) {
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) return false;
            }
            return true;
        }

        long gcd(long a, long b) {
            while (b > 0) {
                long t = a % b;
                a = b;
                b = t;
            }
            return a;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

