You recently joined an elven guild in the new Sword Art Online immersive virtual-reality MMORPG released in Japan, and you have kind of gotten stuck in the game. Your guild is travelling on a quest through the Forest of Aincrad, known to be infested with orcs. Fortunately, you recently acquired a new sword, the Elucidator, that glows as a warning whenever an orc is within the circle of your guild companions.
The input will contain multiple test cases. Each test case will consist of two sets of points in the plane, representing the positions of you and your elven companions and the enemy orcs, respectively. All of these points will be represented by integer coordinates, with component values between 0 and 100 inclusive. Every point in each case will be unique. The total number of points from both sets — you and your guild companions and the orcs — in any single problem instance will be at most 300, and there will be at most 10 test cases with more than 200 points.
Companions: (0,0) (1,1) Orcs: (1,0) (0,1) Companions: (0,0) (0,1) (1,1) (1,0) Orcs: none Companions: (0,0) (0,1) (1,1) Orcs: (1,0) Companions: (0,0) Orcs: none
You need to determine the radius of the smallest circle that contains all of the points of you and your companions' positions, but that excludes all of the points of the orcs' positions. Whenever such a circle does not exist, your sword, the Elucidator, glows, and your guild is in danger. In this case, print, “The Orcs are close”. If such a circle does exist, print the radius of the smallest such circle given as a decimal value that is within a relative error of 1e-7.
In the first example, no circle is possible that includes both you and your companions but that excludes both orcs; any such circle would need to have a radius of at least √(1/2), but any circle that large would include at least one of the orcs. In the third example, a circle may be placed with its center at (1/2,1/2) and a radius of √(1/2). The fourth example is a degenerate case with only one companion (that is, just you), in which case a circle of zero radius works.
The Orcs are close 0.707106781186548 0.707106781186548 0