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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Scanner;

public class Main {
    public static void main(String []args){
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t ;
        t = in.nextInt() ;
        while(t-- > 0){
            long n = in.nextLong() ;
            long left = n ,right = n+1 ;
            while(!isPrime(left)){
                left -- ;
            }
            while(!isPrime(right)){
                right ++ ;
            }
            long den = 2 * left * right ;
            long num = left * right - 2 * (left + right) + 2 * (n+1) ;
            long x = gcd(num,den) ;
            den /= x ;
            num /= x ;
            System.out.println(num+"/"+den) ;
        }
        return ;
    }
    static long gcd(long a ,long b){
        if(b == 0)return a ;
        return gcd(b,a%b) ;
    }
    static boolean isPrime(long n){
        for(int i = 2 ; i * i <= n ; i++){
            if(n % i == 0)return false ;
        }
        return true ;
    }
}
