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
def isPrime(n):
    i = 2
    while i * i <= n:
        if n % i == 0:
            return False
        i += 1
    return True

def prevPrime(n):
    while not isPrime(n):
        n -= 1
    return n

def nextPrime(n):
    n += 1
    while not isPrime(n):
        n += 1
    return n

def gcd(a, b):
    while(a):
        b %= a
        a, b = b, a
    return b;

def solve():
    n = int(input())
    prev = prevPrime(n);
    next = nextPrime(n);
    num1 = prev - 2;
    den1 = prev * 2;
    g = gcd(num1, den1);
    num1 //= g;
    den1 //= g;
    num2 = n - prev + 1;
    den2 = prev * next;
    g = gcd(num2, den2);
    num2 //= g;
    den2 //= g;
    g = gcd(num1 * den2 + num2 * den1, den1 * den2);
    x = (num1 * den2 + num2 * den1) // g;
    y = den1 * den2 // g;
    print('{}/{}'.format(x, y))

t = int(input())
while t:
    t -= 1
    solve()
