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Place the balloon

Problem code: L5

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Given a set of points on a plane, find the largest possible disc which does not "cover" any of these points (i.e., they can lie on the boundary of the disc, but not inside it) and which is constrained by this set of points (i.e., the disc cannot be moved to infinity along a continuous trajectory).

Input

Input will be consist of several test cases. First will be given 1≤t≤20, then number of testcases. Then t testcases follow. Each testcase is of following form. First, 1≤n≤50000, the number of points. The following n lines define the points; the i-th line contains two integers: -10000≤xi,yi≤10000

.

Output

Output exactly one value: the radius of largest possible disc satisfying the given property. If there is no such disc, output the value -1. Answers should be exact up to 10-6

Example

Input:
2
3
0 1
-1 -1
1 -1
4
0 1
-1-1
1 -1
0 0

Output:
1.25
-1

Date:2009-12-15
Time limit:1s-10s
Source limit:50000B
Languages:All except: TCL PERL6


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

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