Carl is an abstract artist painting figures. Each figure is described as a segment on a plane with ends in and having radius ; this means every point with a distance from the segment is part of figure . Carl wants to make sure he has enough paint for all the figures, so he wants to know the total area they will cover.
Given the locations for all the figures, find and print a real number denoting the total area covered by all figures with an absolute or relative error of at most .
Input Format
The first line contains single integer, , denoting the number of figures.
Each line of the subsequent lines contains five space-separated integers describing the respective values of , , , , and for figure .
Constraints
- .
- It's guaranteed that each segment's length and values are positive.
Output Format
Print a real number denoting the total area covered by all figures with an absolute or relative error of at most .
Sample Input 0
2
0 1 1 1 1
1 1 1 0 1
Sample Output 0
6.9269908170
Explanation 0
The diagram below depicts the locations of the two figures on the canvas:
We then calculate the total area covered, which is , and print it as our answer.