A8038 | 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 $n$ ( $1<=n<=2·10^{5}$ ) which represents the number of houses in the village. The second line contains the coordinates of houses — the sequence $x_{1},x_{2},...,x_{n}$ of integer numbers ( $1<=x_{i}<=10^{9}$ ). It is possible that two or more houses are located on one point. The coordinates are given in a arbitrary order.

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.