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.util.*;
import java.io.*;
import static java.util.Arrays.*;
import static java.lang.Math.*;
import java.math.*;

public class Main {    

    void run() throws IOException {
        int n = nint();
        int[] x = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = nint();
        }
        sort(x);

        //обработать случай n <= 3?

        double left = 0, right = 2000000000;
        loop: //while (abs(left - right) >= eps) {
            for (int z = 0; z < 100; z++) {
            double m = (left + right) / 2;
            int k = 0, s = 0;
            for (int j = 0; j < 3; j++) {
                for (k = s; k < n; k++) {
                    if (!less(x[k], x[s] + 2 * m)) {
                        break;
                    }
                }
                if (k == n) {
                    right = m;
                    continue loop;
                }
                s = k;
            }
            left = m;
        }
        left = right;
        out.println(left);
        int k = 0, s = 0;
        ArrayList <Double> ans = new ArrayList();
        //for (int j = 0; j < 3; j++) {
        while (true) {
            ans.add(x[s] + left);
            for (k = s; k < n; k++) {
                if (!less1(x[k], x[s] + 2 * left)) {
                    break;
                }
            }
            if (k == n) {
                break;
            }
            s = k;
        }
        while (ans.size() < 3) {
            ans.add(ans.get(ans.size() - 1));
        }
        for (int i = 0; i < ans.size(); i++) {
            out.print(ans.get(i) + " ");
        }
    }

    final double eps = 1e-10;

    boolean less (double x, double y) {
        return (x < y) || (abs(x - y) < eps);
    }

    boolean less1 (double x, double y) {
        double eps1 = 1e-7;
        return (x < y) || (abs(x - y) < eps1);
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        //final String FILENAME = "";
        //in = new BufferedReader(new FileReader(new File(FILENAME + ".in")));
        //out = new PrintWriter(new File(FILENAME + ".out"));
        in = new BufferedReader(new InputStreamReader(System.in));
        //in = new Scanner(System.in);
        out = new PrintWriter(System.out);
        st = new StringTokenizer(" ");
        new Main().run();
        out.close();
    }

    static BufferedReader in;
    //static Scanner in;
    static PrintWriter out;
    static StringTokenizer st;

    String token() throws IOException {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    int nint() throws IOException {
        return Integer.parseInt(token());
    }

    long nlong() throws IOException {
        return Long.parseLong(token());
    }

    double ndouble() throws IOException {
        return Double.parseDouble(token());
    }
}