Description

It is said that the 2012 disaster is related to sunspot eruptions. Therefore, the Earth Defense Team decides to build a special protective umbrella to block the regions where sunspots erupt and reduce their impact on Earth. Since the Sun is huge compared to Earth, we can treat the Sun’s surface as a plane, with its center at $(0, 0)$. According to intelligence, in the year $2012$, there will be $N$ sunspot regions on the Sun’s surface, and each sunspot is treated as a point. The special protective umbrella can be modeled as a large circular disk. The team decides to place its center at one of the sunspots and then use the umbrella to cover the other sunspots. Because the material cost is extremely high, we want the umbrella to be as small as possible.

Input Format

The first line: an integer $N$, the number of sunspots.

Lines $2$ to $N+1$: each line contains two integers, the coordinates $(x, y)$ of a sunspot.

Output Format

The first line: a real number representing the area of the umbrella.

3
0  1 
-8  -4 
-1  4 

279.6017

Hint

Constraints and Conventions

• For $50\%$ of the testdata: $2 \le N \le 100$.
• For $100\%$ of the testdata: $2 \le N \le 1000$, $-10000 \le x, y \le 10000$.

Notes

• Round to $4$ decimal places.
• Take $\pi$ as $3.1415926535$.

Translated by ChatGPT 5