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.

Input

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.

Output

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.