Collision balls#485
Two balls, each with a radius of meters, roll on a horizontal flat surface. At the initial moment, the centers of the balls are located at coordinates (x_1, y_1) and (x_2, y_2) meters. The projections of their velocities on the coordinate axes are (dx_1, dy_1) and (dx_2, dy_2) meters per second, respectively.
You are required to find the time in seconds after which the balls will collide, or determine that this will not happen.
The input contains the real numbers R, x_1, y_1, dx_1, dy_1, x_2, y_2, dx_2, dy_2.
Output a real number — the collision time, to digits after the decimal point, or output if no collision occurs.
1 \le R \le 1000
-1000 \le x_1, y_1, dx_1, dy_1, x_2, y_2, dx_2, dy_2 \le 1000
Example 1