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 Main {
    static long[] road;
    static long min = 0, max;
    static Answer ans = new Answer(Double.MAX_VALUE, null);

    public static void main(String[] args) {
        FastReader fr = new FastReader();
        int n = fr.nextInt();
        road = new long[n];
        for (int i = 0; i < n; i++)
            road[i] = fr.nextLong();

        Arrays.sort(road);
        max = road[n - 1] - road[0];

        Answer answer = findAnswer(min, max, ans);
        System.out.println(answer);
    }

    private static Answer findAnswer(double min, double max, Answer ans) {
        if (min > max)
            return ans;
        min = (double) Math.round(min * 1000000d) / 1000000d;
        max = (double) Math.round(max * 1000000d) / 1000000d;
        double middle = (min + max) / 2;
        middle = (double) Math.round(middle * 1000000d) / 1000000d;
        ArrayList<Double> answers = new ArrayList<>(road.length);
        double lastAdded = road[0] + middle;
        answers.add(lastAdded);
        int size = 1;
        for (int i = 1; i < road.length; i++) {
            if (lastAdded + middle >= road[i]) {
                continue;
            }
            lastAdded = road[i] + middle;
            answers.add(lastAdded);
            size++;
            if (size > 3)
                break;
        }

        if (answers.size() > 3) {
            return findAnswer(middle + 0.000001, max, ans);
        } else {
            return findAnswer(min, middle - 0.000001, (ans.value < middle) ? ans : new Answer(middle, answers));
        }
    }

}

class Answer implements Comparable<Answer> {
    double value;
    ArrayList<Double> answers;

    public Answer(double value, ArrayList<Double> answers) {
        this.value = value;
        this.answers = answers;
    }

    @Override
    public String toString() {
        if(answers.size() == 1) {
            answers.add(2 * answers.get(0));
        }

        if(answers.size() == 2) {
            answers.add(1, (answers.get(1) + answers.get(0)) / 2);
        }
        StringBuilder sb = new StringBuilder();
        for (Double d : answers)
            sb.append(d).append(" ");

        return value + "\n" +
                sb.toString();

    }

    @Override
    public int compareTo(Answer o) {
        return Double.compare(value, o.value);
    }
}

class FastReader {
    private BufferedReader br;
    private StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}