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
#include <bits/stdc++.h>
using namespace std;
int t;
long long int x, u, v, q, p, g;
long long int gcd(long long int x, long long int y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
bool isPrime(long long int x) {
  int k = sqrt(x);
  for (int i = 2; i <= k; i++) {
    if (x % i == 0) return false;
  }
  return true;
}
int main() {
  cin >> t;
  for (int a = 0; a < t; a++) {
    cin >> x;
    v = x;
    u = x + 1;
    while (!isPrime(v)) v--;
    while (!isPrime(u)) u++;
    p = (u * (v - 2)) + (2 * (x - v + 1));
    q = 2 * u * v;
    g = gcd(p, q);
    p /= g;
    q /= g;
    cout << p << "/" << q << endl;
  }
  return 0;
}
