20248번 - Circles 스페셜 저지다국어

문제

There are n magical circles on a plane. They are centered at (x₁, y₁),(x₂, y₂), . . . ,(x_n, y_n), respectively. In the beginning, the radius of each circle is 0, and the radii of all magical circles will grow at the same rate. When a magical circle touches another, then it stops growing. Write a program to calculate the total area of all magical circles at the end of growing.

입력

The first line contains an integer n to indicate the number of magical circles. The i-th of the following n lines contains two space-separated integers x_i and y_i indicating that the i-th magical circle is centered at (x_i, y_i).

A relative error of 10⁻⁶ is acceptable.

출력

Output the total area of the circles.

제한

• 2 ≤ n ≤ 2000
• x_i, y_i ∈ [−10⁹, 10⁹] for i ∈ {1, 2, . . . , n}.
• All (x_i, y_i)’s are disinct points.

힌트