Democracy Advances#4938
The superpower Limerica, a beacon of world democracy, has a strong aversion to countries rich in chewing gum. For this reason, Limerica, in the name of spreading goodness and delivering mercy, occasionally starts bombing these countries. At the moment, the generals are targeting a city comprised of houses.
It so happens that the missile-bombing navigation system requires that every strike zone must cover at least three houses in the city. Therefore, the impact area is defined as a circle whose boundary passes through at least three houses.
For obvious reasons, Limerica's top strategists want all the city's houses to be within the impact zone. Moreover, since the cost of the operation is proportional to the radius of the corresponding circle, they wish the radius to be as small as possible.
Help the city's residents—find the minimal possible size and location of the impact zone.
The first line contains the integer (3 \le N \le 1000). Each of the next lines contains two integers x_i, y_i (-300 \le x_i, y_i \le 300) — the coordinates of the houses in the city. No two houses have the same position. It is guaranteed that not all houses are in a straight line.
Print three numbers , , to a precision of at least , where is the center of the missile-bombing strike, and is its radius. It is guaranteed that r < 10^3.
Esempio 1