Problem Description

A given coefficient $K$ leads an intersection of two curves $f(x)$ and $g_K(x)$. In the first quadrant, the curve $f$ is a monotone increasing function that $f(x)=\sqrt{x}$. The curve $g$ is decreasing and $g(x)=K/x$.
To calculate the $x$-coordinate of the only intersection in the first quadrant is the following question. For accuracy, we need the nearest rational number to $x$ and its denominator should not be larger than $100000$.

Input

The first line is an integer $T~(1\le T \le 100000)$ which is the number of test cases.
For each test case, there is a line containing the integer $K~(1\le K\le 100000)$, which is the only coefficient.

Output

For each test case, output the nearest rational number to $x$. Express the answer in the simplest fraction.

5
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1/1
153008/96389
50623/24337
96389/38252
226164/77347