Overlapping discs

Problem code: M5

All submissions for this problem are available.

You are given n discs on plane, of the same radius (r=1). Output the area of the part of the plane which is covered by each disc.

Input

First, 1<=t<=10, the number of tests. Each testcase is of the following form: 1<=n<=100000, then n pairs of floating point coordinates follow: -1000<=x_i,y_i<=1000, representing the location of the i-th disc.

Output

For each testcase, output the total area covered by the intersection of all discs. Round the answer to 6 decimal digits after the point.

Example

Input:
1
2
0 0
0 1

Output:
1.228370

Date:	2010-01-29
Time limit:	2s-5s
Source limit:	50000B
Languages:	All except: TCL

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Program should read from standard input and write to standard output.

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