Jack and Jill and Joe

Jill and Jack each buy one plot of land. Jill's plot is a square with side length $a$. Jack's plot is a rectangle whose sides are $b$ and $b + a$, so its longer side exceeds its shorter side by exactly the side length of Jill's square.

Their father Joe sets the following rules.

• $a$ and $b$ are integers, measured in feet.
• $100 \le a \le N$ and $100 \le b \le N$. The longer side $b + a$ of Jack's plot is not limited by $N$.
• The square of the difference of the two areas is at most 900 square feet, that is $(a^2 - b(b + a))^2 \le 900$.
• Among all pairs that satisfy the rules above, the sum of the two areas $a^2 + b(b + a)$ is as large as possible.

Find that pair $(a, b)$. The pair that maximizes the sum is always unique.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains one integer $N$.

Constraints

• $1 \le T \le 12000$
• $100 < N < 2^{31}$

Print one line for each test case. If no pair satisfies the rules, print impossible. Otherwise print $a$ and $b$ separated by one space, where $a$ is the side length of Jill's square and $b$ is the shorter side of Jack's rectangle.