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Timus Top Coders: Second Challenge

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C. Beerhouse Tale

Time limit: 0.25 second
Memory limit: 64 MB


Despite the fact that Three Programmers could neither become the world champions nor reach the top of any online rating, their glory spread everywhere. That is why businessman Dmitry Blackbear, who owned the largest city beerhouse network, had heard about major achievements of the programming legends. Mr. Blackbear was looking for an optimal location of his new beerhouse, so he decided to ask for Three Programmers' help.
Dmitry thought fondly that the Programmers would use a powerful combination of economical and mathematical methods to find a location for the beerhouse to maximize its profitability. As a reward for the job, the businessman promised (very indiscreetly!) free beer at that beerhouse for Three Programmers in the course of year.


The profits of Mr. Blackbear did not worry Three Programmers at all, but then they liked bear very much. It should be told, that the Programmers lived in that city in houses with cartesian coordinates (X[1], Y[1]), (X[2], Y[2]) and (X[3], Y[3]). So the First Programmer suggested placing of the beerhouse into his house. But the Second Programmer angered with it and called to think about common good. "We should place the beerhouse in such a way that the distances between it and our houses would be equal to each other", - he said. "The problem is to find a center of the triangle's circumcircle. It can be solved via a single formula - and it is not interesting at all", - the Third Programmer objected. "Let the sum of the distances between the beerhouse and our houses be minimal", - he concluded. And this proposal was approved fully.


The only line contains the real numbers X[1], Y[1], X[2], Y[2], X[3] and Y[3] (-1000 ≤ X[i], Y[i] ≤ 1000). The numbers are given with not more than seven digits after decimal point. Neither two houses are situated at the same place.


You should output the coordinates of the desired location of the beerhouse so that the sum of the distances between the beerhouse and the houses equals to the minimal one till sixth digit after decimal point. The coordinates should be separated by single spaces. If the problem has several solutions, you should output any of them.


1.1 3.1 5.1 1.1 4.1 5.1
3.37423161 3.38281356
Problem Author: Ilya Grebnov, Dmitry Kovalioff, Nikita Rybak
Problem Source: Timus Top Coders: Second Challenge
To submit the solution for this problem go to the Problem set: 1451. Beerhouse Tale