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.util.*;
import java.io.*;

/**
 *
 * @author usquare
 */

public class Problem{
    
    public static int mod = (int) (1e9+7);
    public static InputReader in;
    public static PrintWriter out;
    public static int[] p = new int[100001];
    public static ArrayList<Integer> list=new ArrayList<>();
    
    public static void prime(){
        p[0]=-1;
        p[1]=-1;
        for(int i=2;i<p.length;i++){
            if(p[i]!=-1){
                p[i]=1;
                list.add(i);
                for(int j=2*i;j<p.length;j+=i){
                    p[j]=-1;
                }
            }
        }
    }
    
    public static boolean isPrime(long n){
        
        for(int j:list){
            if(n==j) return true;
            if(n%j==0) return false;
        }
        
        return true;
    }
    
    public static void main(String[] args) throws FileNotFoundException {
 
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        prime();
        int t=in.ni();
        
        while(t-->0){
            int n=in.ni();
            long sp=n;
            while(!isPrime(sp))  sp--;
            long lp=n+1;
            while(!isPrime(lp))  lp++;
            long n1=sp-2;
            long n2=n-sp+1;
            long nn=n1*lp+n2*2;
            long dd=sp*2*lp;
            long g=gcd(nn,dd);
            nn/=g;
            dd/=g;
            out.println(nn+"/"+dd);
        }
        
        out.close();
    }
    
    static class Pair implements Comparable<Pair>{

        long x;
        int y,i;
        
	Pair (long x,int y,int i){
		this.x=x;
		this.y=y;
		this.i=i;
	}

	public int compareTo(Pair o) {
            return -Long.compare(this.x,o.x);
		//return 0;
	}

            public boolean equals(Object o) {
            if (o instanceof Pair) {
                Pair p = (Pair)o;
                return p.x == x && p.y == y && p.i==i;
            }
            return false;
        }

        @Override
        public String toString() {
            return x+" "+y+" "+i;
        }
        
    } 
    
    public static class Merge {
        
        public static void sort(int inputArr[]) {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }
        
        private static void doMergeSort(int[] arr,int lowerIndex, int higherIndex) {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }
        
        private static void mergeParts(int[]array,int lowerIndex, int middle, int higherIndex) {
            int[] temp=new int[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex){
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }

    }
    
    public static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }

    public static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }
    
    public static long mul(long a,long b){
        a%=mod;
        b%=mod;
        long x=(a*b);
        return x%mod;
    }

    
    public static boolean isPal(String s){
        for(int i=0, j=s.length()-1;i<=j;i++,j--){
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
    }
    public static String rev(String s){
		StringBuilder sb=new StringBuilder(s);
		sb.reverse();
		return sb.toString();
    }
    
    public static long gcd(long x,long y){
	if(x%y==0)
		return y;
	else
		return gcd(y,x%y);
    }
    
    public static int gcd(int x,int y){
	if(x%y==0)
		return y;
	else 
		return gcd(y,x%y);
    }
    
    public static long gcdExtended(long a,long b,long[] x){
        
        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);
        
        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];
        
        return gcd;
    }
    

    public static long mulmod(long  a,long b,long m) {
        if (m <= 1000000009) return a * b % m;
 
        long res = 0;
        while (a > 0) {
            if ((a&1)!=0) {
                res += b;
                if (res >= m) res -= m;
            }
            a >>= 1;
            b <<= 1;
            if (b >= m) b -= m;
        }
        return res;
    }
    
    public static int abs(int a,int b){
	return (int)Math.abs(a-b);
    }

    public static long abs(long a,long b){
	return (long)Math.abs(a-b);
    }
    
    public static int max(int a,int b){
	if(a>b)
		return a;
	else
		return b;
    }

    public static int min(int a,int b){
	if(a>b)
		return b;
	else 
		return a;
    }
    
    public static long max(long a,long b){
	if(a>b)
		return a;
	else
		return b;
    }

    public static long min(long a,long b){
	if(a>b)
		return b;
	else 
		return a;
    }

    public static long pow(long n,long p,long m){
	 long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
    }
    
    public static long pow(long n,long p){
	long  result = 1;
	  if(p==0)
	    return 1;
          
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;	    
	    p >>=1;
	    n*=n;	    
	}
	return result;
    }
    
     public static void debug(Object... o) {
            System.out.println(Arrays.deepToString(o));
    }
     
    static class InputReader {
    
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

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

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

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

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

        public int[] nextIntArray(int n) {
                int a[] = new int[n];
                for (int i = 0; i < n; i++) {
                        a[i] = ni();
                }
                return a;
        }

        public long[] nextLongArray(int n) {
                long a[] = new long[n];
                for (int i = 0; i < n; i++) {
                        a[i] = nl();
                }
                return a;
        }

        public String readString() {
                int c = snext();
                while (isSpaceChar(c)) {
                        c = snext();
                }
                StringBuilder res = new StringBuilder();
                do {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isSpaceChar(c));
                return res.toString();
        }

        public String nextLine() {
                int c = snext();
                while (isSpaceChar(c))
                        c = snext();
                StringBuilder res = new StringBuilder();
                do {
                        res.appendCodePoint(c);
                        c = snext();
                } while (!isEndOfLine(c));
                return res.toString();
        }

        public boolean isSpaceChar(int c) {
                if (filter != null)
                        return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
                return c == '\n' || c == '\r' || c == -1;
        }

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

