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.PrintWriter;
import java.util.Scanner;
 
public class D {

	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

    static void exit() {
    	sc.close();
    	out.close();
    	System.exit(0);
    }
    
    public static void main(String[] args) {
    	int t = sc.nextInt();
    	while(t > 0) {
    		t--;
    		long n = sc.nextLong();
    		long v = v(n);
    		long u = u(n);
        	long nu = v*u + 2*(n-u-v+1);
        	long de = 2*u*v;
        	if(nu % 2 == 0) {
        		nu /= 2;
        		de /= 2;
        	}
        	if(nu % v == 0) {
        		nu /= v;
        		de /= v;
        	}
        	if(nu % u == 0) {
        		nu /= u;
        		de /= u;
        	}
        	out.println(nu+"/"+de);
    	}
        exit();
    }
    static long v(long n) {
    	for(long i = n; i >= 2; i--) {
    		if(prime(i)) return i;
    	}
    	return 0;
    }
    static long u(long n) {
    	for(long i = n+1; ; i++) {
    		if(prime(i)) return i;
    	}
    }
    static boolean prime(long n) {
    	long m = (long) Math.sqrt(n);
    	for(int i = 2; i <= m; i++) {
    		if(n % i == 0) return false;
    	}
    	return true;
    }
}