Please subscribe to the official Codeforces channel in Telegram via the link: https://t.me/codeforces_official. ×

B. On Sum of Fractions
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 .

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