Problem: 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 xi coordinate. The village consists of n houses, the i-th house is located in the point with coordinates of xi.

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 ≤ 2·105) which represents the number of houses in the village. The second line contains the coordinates of houses — the sequence x1, x2, ..., xn of integer numbers (1 ≤ xi ≤ 109). 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 2·109 inclusively. It is accepted for the base stations to have matching coordinates. If there are many solutions, print any of them.

Examples

Input

4
1 2 3 4


Output

0.500000
1.500000 2.500000 3.500000


Input

3
10 20 30


Output

0
10.000000 20.000000 30.000000


Input

5
10003 10004 10001 10002 1


Output

0.500000
1.000000 10001.500000 10003.500000

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class ThreeBaseStations {
    static double res[] = new double[3];
    static int x[];
    public static boolean valid(double d) {
        double cd[] = new double[3];
        int index;
        cd[0] = x[0] + d;
        index = Arrays.binarySearch(x, (int)Math.ceil(cd[0] + d));
        cd[1] = (index >= 0) ? x[index] + d : x[Math.min(x.length - 1, -(index + 1))] + d;
        index = Arrays.binarySearch(x, (int)Math.ceil(cd[1] + d));
        cd[2] = (index >= 0) ? x[index] + d : x[Math.min(x.length - 1, -(index + 1))] + d;
        if(cd[2] + d >= x[x.length - 1]) {
            res = Arrays.copyOf(cd, 3);
            return true;
        }
        return false;
    }
    public static void main(String[] args) throws  IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        //BufferedReader br = new BufferedReader(new FileReader("A.txt"));
        StringTokenizer st = null;
        int n = Integer.parseInt(br.readLine());
        st = new StringTokenizer(br.readLine());
        x = new int[n];
        for(int i = 0; i < n; ++i)
            x[i] = Integer.parseInt(st.nextToken());
        Arrays.sort(x);
        double h = 1e9, l = 0, mid;
        while(Math.abs(h - l) > 1e-7) {
            mid = (l + h) / 2.0;
            if(valid(mid)) h = mid;
            else l = mid;
        }
        System.out.printf("%.6f\n", h);
        System.out.printf("%.6f %.6f %.6f\n", res[0], res[1], res[2]);
    }
}