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 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

The problem statement has recently been changed. View the changes.

×
E. Space Rescuers

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Galaxy contains *n* planets, there are many different living creatures inhabiting each planet. And each creature can get into troubles! Space rescuers know it perfectly well and they are always ready to help anyone who really needs help. All you need to do is call for them.

Now the space rescuers plan to build the largest in the history of the Galaxy rescue station; however, the rescue station's location is yet to be determined. As some cases are real emergencies, the rescuers want to find such a point in the Galaxy from which it would be possible to get to the remotest planet in the minimum possible time. In other words, the rescuers need such point in the space that the distance between it and the planet remotest from it was minimal (if we compare this point with all other possible points in the space). Unfortunately, the rescuers can't sole this problem.

As the planets are quite remote from each other, they can be considered as points in Euclidean three-dimensional space. The distance between points (*x*_{i}, *y*_{i}, *z*_{i}) and (*x*_{j}, *y*_{j}, *z*_{j}) can be calculated by the formula . The rescue station can be positioned in any point in the space. It can also coincide with some planet.

Galaxy is in danger! Save the space rescuers and find the required point for them.

Input

The first line of the input file contains integer *n* — the number of planets (1 ≤ *N* ≤ 100). Each of the following *n* lines contains information about the planets. The *i*-th line contains three integers *x*_{i}, *y*_{i}, *z*_{i} — the coordinates of the *i*-th planet ( - 10^{4} ≤ *x*_{i}, *y*_{i}, *z*_{i} ≤ 10^{4}, 1 ≤ *i* ≤ *n*). No two planets coincide.

Output

Print on the first line of the output file three space-separated real numbers *x*_{0}, *y*_{0}, *z*_{0} — the coordinates for the future base. If there are several solutions, you are allowed to print any of them. The answer will be accepted if the distance from this point to the remotest planet will differ from the juries' variant in no more than 10^{ - 6} in absolute or relative value.

Examples

Input

5

5 0 0

-5 0 0

0 3 4

4 -3 0

2 2 -2

Output

0.000 0.000 0.000

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/06/2021 10:11:39 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|