CF51C Three Base Stations

The New Vasjuki village is stretched along the motorway and that's why every house on it is characterized by its shift relative to some fixed point — the $ x_{i} $ coordinate. The village consists of $ n $ houses, the $ i $ -th house is located in the point with coordinates of $ x_{i} $ . TELE3, a cellular communication provider planned to locate three base stations so as to provide every house in the village with cellular communication. The base station having power $ d $ located in the point $ t $ provides with communication all the houses on the segment $ [t-d,t+d] $ (including boundaries). To simplify the integration (and simply not to mix anything up) all the three stations are planned to possess the equal power of $ d $ . Which minimal value of $ d $ is enough to provide all the houses in the village with cellular communication.

The first line contains an integer $ n $ ( $ 1

Print the required minimal power $ d $ . In the second line print three numbers — the possible coordinates of the base stations' location. Print the coordinates with 6 digits after the decimal point. The positions of the stations can be any from $ 0 $ to $ 2·10^{9} $ inclusively. It is accepted for the base stations to have matching coordinates. If there are many solutions, print any of them.