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>
int Test_num, n;
long long u, v, t, fz, fm;
inline bool check(int x) {
  for (int i = 2; i * i <= x; ++i)
    if (!(x % i)) return 0;
  return 1;
}
inline long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
int main() {
  scanf("%d", &Test_num);
  while (Test_num--) {
    scanf("%d", &n);
    if (n == 1) {
      puts("0");
      continue;
    }
    for (int i = n;; --i)
      if (check(i)) {
        u = i;
        break;
      }
    for (int i = n + 1;; ++i)
      if (check(i)) {
        v = i;
        break;
      }
    t = gcd(fz = u * v - 2 * v + 2 * n - 2 * u + 2, fm = 2 * u * v), fz /= t,
    fm /= t, printf("%lld", fz);
    if (fm > 1) printf("/%lld", fm);
    puts("");
  }
  return 0;
}
