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.*;
import java.math.BigInteger;
public class Main {
    static PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    public static void main(String[] args) throws IOException {
        BufferedReader bf=new BufferedReader(new InputStreamReader( System.in));
        int t=Integer.parseInt(bf.readLine());
        int n=0;
        for (int i = 0; i <t ; i++) {
            n=Integer.parseInt(bf.readLine());
            solve(n);
        }
        pw.flush();
    }
    public static void solve(int n){
        long u = n, v = n + 1;
        while(!BigInteger.valueOf(u).isProbablePrime(10))
            u--;
        while(!BigInteger.valueOf(v).isProbablePrime(10))
            v++;
        long a = v * (u - 2) + 2 * (n - u + 1), b = 2 * u * v;
        long g = gcd(a, b);
        pw.write ( a / g+"/"+ b / g+"\n");
    }
    static long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
}