Four points#2899
On a plane, you are given four points. Your task is to construct all circles that are equidistant from each of these points.
The distance from point to the circle is defined as the minimum distance from to any point on the circle.
The first line of the input contains a single integer (1 \leq T \leq 10^4) — the number of test cases. Each of the following lines contains the coordinates of four points: x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4. The coordinates are integers and their absolute values do not exceed .
For each test case, output a single line containing the integer — the number of distinct circles that satisfy the condition. Then, output lines, each containing the coordinates of the center and the radius of a circle (x_i, y_i, r_i). If it is possible to construct more than distinct circles, output the string "-1" instead of the number . In this case, do not output the circles themselves.
An absolute error of no more than 10^{-5} is allowed.
Example 1