Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. The Last Hole!

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLuyi has *n* circles on the plane. The *i*-th circle is centered at (*x*_{i}, *y*_{i}). At the time zero circles start to grow simultaneously. In other words, the radius of each circle at time *t* (*t* > 0) is equal to *t*. The circles are drawn as black discs on an infinite white plane. So at each moment the plane consists of several black and white regions. Note that the circles may overlap while growing.

We define a hole as a closed, connected white region. For instance, the figure contains two holes shown by red border. During growing some holes may be created and it is easy to see that each created hole will disappear eventually. Luyi asks you to find moment of time such that the last hole disappears. In other words, you should find the first moment such that no hole can be seen after that.

Input

The first line of the input contains integer *n* (1 ≤ *n* ≤ 100). Each of the next *n* lines contains two integers *x*_{i} and *y*_{i} ( - 10^{4} ≤ *x*_{i}, *y*_{i} ≤ 10^{4}), indicating the location of *i*-th circle.

It's guaranteed that no two circles are centered at the same point.

Output

Print the moment where the last hole disappears. If there exists no moment in which we can find holes print -1.

The answer will be considered correct if the absolute or relative error does not exceed 10^{ - 4}.

Examples

Input

3

0 0

1 1

2 2

Output

-1

Input

4

0 0

0 2

2 2

2 0

Output

1.414214

Input

4

0 1

0 -1

-2 0

4 0

Output

2.125000

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/20/2017 06:29:47 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|