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.util.*;

public class SolutionC {
    static BufferedReader br = null;
    static PrintWriter pw = null;
    static StringTokenizer st = null;
    static String FILENAME = "";

    void nline() {
        try {
            st = new StringTokenizer(br.readLine());
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
    }

    int ni() {
        while (st == null || !st.hasMoreTokens())
            nline();
        return Integer.parseInt(st.nextToken());
    }

    long nl() {
        while (st == null || !st.hasMoreTokens())
            nline();
        return Long.parseLong(st.nextToken());
    }

    double nd() {
        while (st == null || !st.hasMoreTokens())
            nline();
        return Double.parseDouble(st.nextToken());
    }

    String ns() {
        while (st == null || !st.hasMoreTokens())
            nline();
        return st.nextToken();
    }

    String nstr() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }
        return s;
    }

    class Point implements Comparable<Point> {
        long x,y;

        public Point(long x, long y) {
            super();
            this.x = x;
            this.y = y;
        }

        public int compareTo(Point o) {
            if (x<o.x) return -1;
            if (x==o.x&&y<o.y) return -1;
            if (x==o.x&&y==o.y) return 0;
            return 1;
        }
        
    }

    boolean cw(Point a, Point b, Point c) {
        return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) < 0;
    }
    
    boolean ccw (Point a, Point b, Point c) {
        return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y) > 0;
    }

    
    public void solve() {
        Locale.setDefault(Locale.ENGLISH);
        int n = ni();
        int[] a = new int[n];
        TreeSet<Integer> ts = new TreeSet<Integer>();
        for (int i=0;i<n;i++) {
            a[i] = ni();
            ts.add(a[i]);
        }
        if (n<=3) {
            pw.println(0);
            pw.printf("%.6f %.6f %.6f",a[0]*1.0,a[(1%n)]*1.0,a[(2%n)]*1.0);
        } else {
            int l = 0;
            int r = 1000000000;
            for (int i=0;i<200;i++) {
                int d = (l+r)/2;
                Integer f = ts.first();
                Integer s = ts.higher(f+d);
                if (s==null) s = f;
                Integer t = ts.higher(s+d);
                if (t==null) t = s;
                if (ts.higher(t+d)==null)
                    r=d;
                else 
                    l=d+1;
            }
            int d = r;
            pw.println(d*0.5);
            Integer f = ts.first();
            Integer s = ts.higher(f+d);
            if (s==null) s = f;
            Integer t = ts.higher(s+d);
            if (t==null) t = f;
            pw.printf("%.6f %.6f %.6f",(f+d*0.5),(s+d*0.5),(t+d*0.5));
        }
    }

    public void run() {
        solve();
        pw.close();
    }

    public static void main(String[] args) {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);

        new SolutionC().run();
    }

}