Circle through three points

Input

Each test case consists of a line containing six real numbers $A_{x}$ A_x, $A_{y}$ A_y, $B_{x}$ B_x, $B_{y}$ B_y, $C_{x}$ C_x, $C_{y}$ C_y — the coordinates of three points $A (A_{x}, A_{y})$ A~(A_x, A_y), $B (B_{x}, B_{y})$ B~(B_x, B_y), and $C (C_{x}, C_{y})$ C~(C_x, C_y). Numbers are separated by one or more spaces.

Output

For each test case, print the equation of the circle in the two formats shown above. The values $a$ , $b$ , $r$ , $c$ , $d$ , and $e$ in equations (1) and (2) must be printed with three decimal places. If any of $a$ , $b$ , $c$ , $d$ , or $e$ is zero, omit the corresponding term. Adjust plus and minus signs as necessary to avoid multiple signs before a number. The plus, minus, and equal signs must each be separated from adjacent characters by a single space. No other extra spaces should appear in the equations. Print a single blank line after each pair of equations. See the output format in the example.

Examples

Example 1

Loading