Four points
On a plane, you are given four points. Your task is to construct a circle that is equidistant from all these points.
The distance from point A to the circle is defined as the minimum distance from point A to any point B on the circle.
Input
The first line of the input contains a single integer T - the number of test cases (1 ≤ T ≤ 10^4). Each of the following T lines provides the coordinates of four points: x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4. These coordinates are integers with absolute values not exceeding 100.
Output
For each test case, output a single line with the number K - the number of distinct circles that meet the condition. Then, for each circle, output three numbers on separate lines: the coordinates of the circle's center and its radius (x_i, y_i, r_i). If more than 42 different circles can be constructed, output the string "-1" instead of the number K. In this case, do not output the circles themselves.
An absolute error of no more than 10^{-5} is allowed.