Democracy Advances
The superpower nation of Limerica, known as a beacon of democracy, has a strong aversion to countries abundant in rubber gum. Consequently, Limerica occasionally initiates bombing campaigns against these nations under the guise of benevolence. Currently, their military strategists are targeting a city composed of N houses.
The missile-bombing system's navigation requires that the strike zone encompasses at least three houses. Therefore, the impact area is defined as a circle whose circumference passes through a minimum of three houses.
For strategic reasons, Limerica's top experts aim to ensure that all houses in the city are within the impact zone. Additionally, since the cost of the military operation is directly related to the circle's radius, they seek to minimize this radius.
Assist the city's residents by determining the size and potential location of the impact zone.
Input
The first line contains an integer N (3 ≤ N ≤ 1000). The following N lines each contain two integers x_i, y_i (-300 ≤ x_i, y_i ≤ 300), representing the positions of the houses in the city. No two houses share the same position. It is guaranteed that not all N houses lie on a single straight line.
Output
Output three numbers x, y, r with a precision of at least 0.0001, where (x, y) is the center of the missile-bombing strike, and r is its radius. It is guaranteed that r < 10^3.