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ZOJ Problem Set - 1627
Disk

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Given N disks, try to calculate the area that is covered by them.


Input

The first line contains only the integer N (1 <= N <= 4).

The following N lines contain information about the N disks.

Xi Yi Ri (3 floating-point numbers)

Here (Xi, Yi) is the centre of the ith disk and Ri (0 < Ri <= 1) is its radius.

There are several testcases, so process to the end-of-file.


Output

For each testcase, output a line containing only the area that is covered by the disks.

The result should be a floating-point number, having 3 digits after radix point.


Sample Input

1
0 0 1
2
0 0 1
1 0 1


Sample Output

3.142
5.055



Author: SHI, Xiaohan
Source: ZOJ Monthly, June 2003
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