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;
long long gcd(long long a, long long b) { return !b ? a : gcd(b, a % b); }
inline bool ok(long long x) {
  long long h = sqrt(x + 0.5);
  for (long long i = 2; i <= h; ++i)
    if (x % i == 0) return false;
  return true;
}
int main(int argc, char const *argv[]) {
  int T;
  cin >> T;
  while (T--) {
    long long n;
    cin >> n;
    long long p, q;
    p = n;
    q = n + 1;
    while (!ok(p)) --p;
    while (!ok(q)) ++q;
    long long a = p * q + 2 * (n - p + 1) - 2 * q;
    long long b = 2 * p * q;
    long long g = gcd(a, b);
    a /= g, b /= g;
    cout << a << "/" << b << "\n";
  }
  return 0;
}
