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.*;
import java.math.*;

public class Z implements Runnable{

    BufferedReader in;
    StringTokenizer st;
    PrintWriter out;
    
    void solve() throws IOException{
        int n = nextInt();
        int[] a = new int[n];
        
        for(int i = 0; i < n; i++)
            a[i] = nextInt();
        Arrays.sort(a);
        
        double l = 0, r = 1e9, q, eps = 1e-6, ans = 0, pos1 = 0, pos2 = 0, pos3 = 0, tmp1, tmp2, tmp3;
        while(l - r <= eps) {
            q = (l + r) / 2;
            tmp1 = a[0] + q;
            tmp2 = a[n - 1];
            tmp3 = a[n - 1];
            for(int i = 0; i < n; i++)
                if(a[i] > tmp1 + q) {
                    tmp2 = a[i] + q;
                    break;
                }
            for(int i = 0; i < n; i++)
                if(a[i] > tmp2 + q) {
                    tmp3 = a[i] + q;
                    break;
                }
            boolean flag = a[n - 1] > tmp3 + q ? false : true;
            if(flag) {
                r = q - eps;
                ans = q;
                pos1 = tmp1;
                pos2 = tmp2;
                pos3 = tmp3;
            }
            else
                l = q + eps;
        }
        
        out.printf("%.10f\n", ans);
        out.printf("%.10f %.10f %.10f", pos1, pos2, pos3);
    }
    
    public void run() {
        try {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            eat("");
            solve();
            out.close();
            in.close();
        } catch (IOException ex) {
            throw new RuntimeException(ex);
        }
    }
    
    void eat(String s) {
        st = new StringTokenizer(s);
    }
    
    String next() throws IOException {
        while (!st.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null) {
                return null;
            }
            eat(line);
        }
        return st.nextToken();
    }
    
    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    
    long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    
    double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    
    public static void main(String[] args) {
        Locale.setDefault(Locale.US);
        new Thread(new Z()).start();
    }

}