Maximal Quadrilateral

Input

The first line of the input file contains an integer $n$ (n \leq 100) that indicates how many sets of input there are. Each of the next $n$ lines contains three integers $p$, $a$, $b$. Here, $p$ is the perimeter and $a$, $b$ are the lengths of two adjacent sides of the quadrilateral.

Output

For each line of input except the first one, produce one line of output. This line should contain the serial number, and then the maximum possible radius of the circle. The radius should have six digits after the decimal point. If the formation of such a quadrilateral is impossible, print the line Eta Shombhob Na. (Sorry! It is a sentence in Bangla, which means "This is impossible."). The lengths of all sides of a valid quadrilateral should be positive.

Examples