Xiangling, one of the greatest chef in Teyvat, is preparing for the Moonchase banquet. Xiangling has bought round plates and her friend and companion Guoba will help place these plates on the table in a line. The -th plate placed has radius and the center of this plate locates at 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

输入描述:

The first line contains an integer  , indicating the number of plates Xiangling has bought.

Then follow  lines, the -th of which contains two integers   and  , indicating that the -th plate placed by Guoba has radius  and the center of this plate locates at  on the table.

输出描述:

Output  lines, the -th of which contains a real number, indicating the total area covered by the plates on the table after Guoba places the first -th plates.

Your answer is acceptable if its absolute or relative error does not exceed . Formally speaking, suppose that your output is  and the jury's answer is , your output is accepted if and only if .

4
0 1
2 1
3 1
1 1

3.141592653589793
6.283185307179586
8.196408262160623
8.881261518532902

In the sample case:
1.The total area covered by the first plate is ;

2.The total area covered by the first two plates is ;

3.The total area covered by the first three plates is ;

4.The total area covered by all the four plates is .