Triangular Circles
The recreation base "Treugeyev Circles" was shaped like a triangle in 2010. Each year, talented students from various countries visit the base: mathematicians in June and programmers in July. Before each group's arrival, the base's territory is adjusted to meet the guests' preferences. Mathematicians always request that the base be reshaped into a circle, as a circle offers the maximum area for a given perimeter. Programmers, familiar with the "Treugeyev Circles" over the past five years, insist that the base remains a scaled-down version of the original triangle (maintaining its orientation) to facilitate Viktor Oleksandrovych's tour on the first morning of their stay.
The territory is always reduced to maximize the area after reshaping.
It's clear that the camp's area is rapidly diminishing. Mathematicians can prove, and programmers can simulate and observe, that there is precisely one point that will remain within the camp's territory in the year 3000, in the year 4000, and indefinitely.
Determine the coordinates of this point so the LKS flag can be placed there before the mathematicians arrive!
Input
The input consists of six integers x_1, y_1, x_2, y_2, x_3, y_3 - the coordinates of the triangle's vertices before any reductions. All coordinates are integers and do not exceed 10^3 in absolute value. The triangle is not degenerate.
Output
Output the coordinates of the desired point with a precision of at least 10^{-3}.