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.math.*;
import static java.lang.Character.isDigit;
import static java.lang.Character.isLowerCase;
import static java.lang.Character.isUpperCase;
import static java.lang.Math.*;
import static java.math.BigInteger.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;
import static java.lang.Character.isDigit;

public class Main{
    static void debug(Object...os){
        System.err.println(deepToString(os));
    }
    
    void run(){
        n=nextInt();
        xs=new double[n];
        for(int i=0;i<n;i++)xs[i]=nextDouble();
        solve();
    }
    int n;
    double[] xs;
    void solve(){
        sort(xs);
        double left=0,right=1e10;
        double[] cor= null;
        for(int i=0;i<100;i++) {
            double mid=(left+right)/2;
            double[] tmp=new double[3];
            int k=0;
            for(int j=0;j<3;j++)if(k<n) {
                tmp[j]=xs[k] + mid;
                while(k<n && xs[k] < tmp[j]+mid)k++;
            }
//          debug(left,right,k,n);
            if(k==n) {
                right=mid;
                cor=tmp;
            }
            else left=mid;
        }
        System.out.printf("%.06f\n",right);
        System.out.printf("%.06f %.06f %.06f\n",cor[0],cor[1],cor[2]);
    }
    
    int nextInt(){
        try{
            int c=System.in.read();
            if(c==-1) return c;
            while(c!='-'&&(c<'0'||'9'<c)){
                c=System.in.read();
                if(c==-1) return c;
            }
            if(c=='-') return -nextInt();
            int res=0;
            do{
                res*=10;
                res+=c-'0';
                c=System.in.read();
            }while('0'<=c&&c<='9');
            return res;
        }catch(Exception e){
            return -1;
        }
    }
    
    long nextLong(){
        try{
            int c=System.in.read();
            if(c==-1) return -1;
            while(c!='-'&&(c<'0'||'9'<c)){
                c=System.in.read();
                if(c==-1) return -1;
            }
            if(c=='-') return -nextLong();
            long res=0;
            do{
                res*=10;
                res+=c-'0';
                c=System.in.read();
            }while('0'<=c&&c<='9');
            return res;
        }catch(Exception e){
            return -1;
        }
    }
    
    double nextDouble(){
        return Double.parseDouble(next());
    }
    
    String next(){
        try{
            StringBuilder res=new StringBuilder("");
            int c=System.in.read();
            while(Character.isWhitespace(c))
                c=System.in.read();
            do{
                res.append((char)c);
            }while(!Character.isWhitespace(c=System.in.read()));
            return res.toString();
        }catch(Exception e){
            return null;
        }
    }
    
    String nextLine(){
        try{
            StringBuilder res=new StringBuilder("");
            int c=System.in.read();
            while(c=='\r'||c=='\n')
                c=System.in.read();
            do{
                res.append((char)c);
                c=System.in.read();
            }while(c!='\r'&&c!='\n');
            return res.toString();
        }catch(Exception e){
            return null;
        }
    }
    public static void main(String[] args){
        new Main().run();
    }
}