Disk

Time Limit: 1 Second    Memory Limit: 32768 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

Submit

Source: ZOJ Monthly, June 2003