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.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.Arrays;
import java.util.Comparator;

public class Main {
    private static StreamTokenizer in;
    private static PrintWriter out;
    private static BufferedReader inB;
    
    private static int nextInt() throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
    
    private static String nextString() throws Exception{
        in.nextToken();
        return in.sval;
    }
    
    static{
        inB = new BufferedReader(new InputStreamReader(System.in));
        in = new StreamTokenizer(inB);
        out = new PrintWriter(System.out);
    }
    
    public static void main(String[] args)throws Exception {
        int n = nextInt();
        int[] mas = new int[n];
        for(int i = 0; i<n; i++) {
            mas[i] = nextInt();
        }
        
        Arrays.sort(mas);
        
        if(n <= 3) {
            println(0);
            for(int i = 0; i<3; i++) {
                System.out.print((double)mas[i%n] + " ");
            }
            return; 
        }
        
        double left = 0, right = (mas[n-1]);
        
        for(;;) {
            if(right - left < 1e-7)break;
            
            double d = (right + left) / 2;
            
            int count = 1;
            int cur = mas[0];
            
            for(int i = 0; i<n && count <=3; i++) {
                if(mas[i] > cur + d) {
                    count++;
                    cur = mas[i];
                }
            }
            
            if(count <=3) {
                right = d;
            } else {
                left = d;
            }
        }
        
        double d2 = right;
        double d = d2 / 2;
        
        double cur = mas[0];
        out.println(d);
        out.print(cur + d + " " );
        int count = 1;
        for(int i = 0; i<n; i++) {
            if(mas[i] > cur + d2) {
                out.print(mas[i] + d + " ");
                cur = mas[i];
                count++;
            }
        }
        while(count < 3) {
            out.print(mas[0] + d + " ");
            count++;
        }
        out.println();
        out.flush();
    }
    
    /////////////////////////////////////////////////////////////////
    private static void println(Object o) throws Exception {
        System.out.println(o);
    }
    private static void exit(Object o) throws Exception {
        println(o);
        System.exit(0);
    }
    private static void exit() {
        System.exit(0);
    }
    //////////////////////////////////////////////////////////////////
}