409042: GYM103427 A A Bite of Teyvat

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 ≤ n ≤ 10⁵), indicating the number of plates Xiangling has bought.

Then follow n lines, the i-th of which contains two integers x_i ( - 10⁵ ≤ x_i ≤ 10⁵) and r_i (1 ≤ r_i ≤ 10⁶), 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 .

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 π;
2. The total area covered by the first two plates is 2π;
3. The total area covered by the first three plates is ;
4. The total area covered by all the four plates is .