Triangular Circles#5237
The recreation base "Treugeyev Circles" was shaped like a triangle in . Each year, talented students from various countries visit the base: mathematicians in June and programmers in July. Before the arrival of each group, the base's territory is reduced to meet the requirements of the arriving guests. Mathematicians always request that, by their arrival, the base be reshaped as a circle, since a circle has the maximal area for a given perimeter. Programmers, meanwhile, accustomed to the "Treugeyev Circles" over the past five years, require that the base become a scaled-down copy of the original triangle (preserving its orientation)—otherwise, Viktor Oleksandrovych will have difficulty conducting a tour of the camp on the first morning of the session.
The camp's territory is always reduced so as to maximize its area after the change of shape.
It is clear to everyone that the camp's area is rapidly decreasing. Mathematicians can prove—while programmers may simulate and observe—that there is precisely one point that will always remain within the camp in the year , the year , and, in fact, will always belong to the camp.
Find the coordinates of this point so that the LKS flag can be placed there—before the mathematicians do it!
The input file contains 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 by absolute value. The triangle is not degenerate.
Print the coordinates of the desired point with precision at least 10^{-3}.
Example
0 0 9 0 0 123.0000000000 4.0000000000Example
0 0 2 5 3 11.0000000000 2.0000000000Example 1