Xiangling, one of the greatest chef in Teyvat, is preparing for the Moonchase banquet. Xiangling has bought $$$n$$$ round plates and her friend and companion Guoba will help place these $$$n$$$ plates on the table in a line. The $$$i$$$-th plate placed has radius $$$r_i$$$ and the center of this plate locates at $$$(x_i, 0)$$$ on the table.
However, Paimon the emergency food has been tired of waiting for the banquet a long time and begins finding the total area covered by the plates on the table after each placement.
Pixiv ID: 93526437
The first line contains an integer $$$n$$$ $$$(1 \le n \le 10^5)$$$, indicating the number of plates Xiangling has bought.
Then follow $$$n$$$ lines, the $$$i$$$-th of which contains two integers $$$x_i$$$ $$$(-10^5 \le x_i \le 10^5)$$$ and $$$r_i$$$ $$$(1 \le r_i \le 10^6)$$$, indicating that the $$$i$$$-th plate placed by Guoba has radius $$$r_i$$$ and the center of this plate locates at $$$(x_i, 0)$$$ on the table.
Output $$$n$$$ lines, the $$$i$$$-th of which contains a real number, indicating the total area covered by the plates on the table after Guoba places the first $$$i$$$-th plates.
Your answer is acceptable if its absolute or relative error does not exceed $$$10^{-9}$$$. Formally speaking, suppose that your output is $$$x$$$ and the jury's answer is $$$y$$$, your output is accepted if and only if $$$\frac{|x - y|}{\max(1, |y|)} \leq 10^{-9}$$$.
4
0 1
2 1
3 1
1 1
3.141592653589793
6.283185307179586
8.196408262160623
8.881261518532902
In the sample case:
- The total area covered by the first plate is $$$\pi$$$;
- The total area covered by the first two plates is $$$2\pi$$$;
- The total area covered by the first three plates is $$$\frac{14\pi+3\sqrt{3}}{6}$$$;
- The total area covered by all the four plates is $$$\frac{4\pi+3\sqrt{3}}{2}$$$.
