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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            TreeSet<Integer> x = new TreeSet<>();
            for (int i = 0; i < n; i++) {
                x.add(in.nextInt());
            }
            double l = 0;
            double r = (x.lower(Integer.MAX_VALUE) - x.higher(Integer.MIN_VALUE)) / 2.0;
            double e = 0.0000001;
            while (r - l > e) {
                double m = (l + r) / 2;
                if (chk(x, m)) {
                    r = m;
                } else {
                    l = m;
                }
            }
            out.println(mid(x, r));
        }

        boolean chk(TreeSet<Integer> x, double r) {
            Integer min = x.higher(Integer.MIN_VALUE);
            Integer max = x.lower(Integer.MAX_VALUE);
            Integer left = x.higher((int) (min + 2 * r));
            Integer right = x.lower((int) Math.ceil(max - 2 * r));
            if (right == null || left == null) return true;
            return right - left <= 2 * r;
        }

        String mid(TreeSet<Integer> x, double r) {
            Integer min = x.higher(Integer.MIN_VALUE);
            Integer max = x.lower(Integer.MAX_VALUE);
            Integer left = x.higher((int) (min + 2 * r));
            Integer right = x.lower((int) Math.ceil(max - 2 * r));
            Double mid;
            if (right == null || left == null) {
                mid = (double) min;
            } else {
                mid = (left + right) / 2.0;
            }
            return String.format("%6f\n%6f %6f %6f", r, min + r, mid, max - r);
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String next() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}