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.

新瓦斯尤基村沿高速公路延伸，因此村中每栋房屋的位置都由其相对于某个固定点的偏移量——即坐标 $x_i$ 来表征。该村共有 $n$ 栋房屋，第 $i$ 栋房屋位于坐标 $x_i$ 处。

通信运营商 TELE3 计划设置三座基站，以确保村中所有房屋均能接入蜂窝通信网络。一座功率为 $d$、位于位置 $t$ 的基站，可为区间 $[t - d,\, t + d]$（含端点）内的所有房屋提供通信服务。

为简化系统集成（并避免混淆），这三座基站将采用相同的功率 $d$。问：能够覆盖全村所有房屋的最小功率值 $d$ 是多少？

The first line contains an integer n (1 ≤ n ≤ 2·105) 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 ≤ 109). It is possible that two or more houses are located on one point. The coordinates are given in a arbitrary order.

第一行包含一个整数 $n$（$1 \leq n \leq 2 \cdot 10^5$），表示村庄中房屋的数量。
第二行包含房屋的坐标——一串整数序列 $x_1,\ x_2,\ \dots,\ x_n$（$1 \leq x_i \leq 10^9$）。可能有两座或更多房屋位于同一点上。坐标以任意顺序给出。

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 2·109 inclusively. It is accepted for the base stations to have matching coordinates. If there are many solutions, print any of them.

输出所需的最小功率 $d$。
第二行输出三个数——基站可能的坐标位置。坐标的精度为小数点后 6 位。
基站的位置可以是 $0$ 到 $2\cdot10^9$（含端点）之间的任意实数。
允许不同基站具有相同的坐标。
若存在多个解，输出任意一个即可。