Three points are given on the plane that do not lie on one line. Find the equation of the circle that passes through them. Print the solution in the form $$ (x - a)^2 + (y - b)^2 = r^2~~~(1) $$ and $$ x^2 + y^2 + cx + dy + e = 0~~~(2) $$ \InputFile Each line contains six real numbers $A_x, A_y, B_x, B_y, C_x, C_y$ --- the coordinates of three points $A~(A_x, A_y)$, $B~(B_x, B_y)$, $C~(C_x, C_y)$. \OutputFile For each test case print the equation of a circle in two formats as given in a sample. The values of $h, k, r, c, d$ and $e$ in Equations 1 and 2 are to be printed with three decimal digits. If some of $h, k, c, d, e$ is zero, do not print the corresponding term. Plus and minus signs in the equations should be changed as needed to avoid multiple signs before a number. Plus, minus, and equal signs must be separated from the adjacent characters by a single space on each side. No other spaces are to appear in the equations. Print a single blank line after each equation pair. See output format in example.