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 $$\sum_{i=2}^{n}\frac{1}{v(i)u(i)}$$.

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.

见题面 Input 部分

见题面 Output 部分