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.Arrays;
import java.util.HashSet;

/**
 * Created by IntelliJ IDEA.
 * User: piyushd
 * Date: 12/28/10
 * Time: 10:35 PM
 * To change this template use File | Settings | File Templates.
 */
public class ThreeBaseStations {

	int next(Integer[] x, double val){
		int low = 0, high = x.length - 1, mid = -1;
		if(x[high] <= (int)(val + 1e-7)) return high + 1;
		while(low < high){
			mid = low + (high - low) / 2;
			if(x[mid] <= (int)(val + 1e-7)) low = mid + 1;
			else high = mid;
		}
		return low;
	}

	boolean canCover(Integer[] x, double d){
		int pos = 0, nx = -1;
		for(int i = 0; i < 3; i++){
			nx = next(x, x[pos] + 2 * d);
			pos = nx;
			if(nx == x.length) break;
		}
		return (nx == x.length) ? true : false;
	}

    void run(){
		int N = nextInt();
		HashSet<Integer> set = new HashSet<Integer>();
		for(int i = 0; i < N; i++) set.add(nextInt());
		Integer[] loc = new Integer[set.size()];
		set.toArray(loc);
		Arrays.sort(loc);

		double low = 0, high = 2e9, mid = -1.0;
		for(int step = 0; step < 100; step ++){
			mid = low + (high - low) / 2;
			if(canCover(loc, mid)) high = mid;
			else low = mid;
		}

		System.out.printf("%.6f\n", low + 1e-7);
		double[] pos = new double[3];
		Arrays.fill(pos, loc[0]);
		int ps = 0, nx = -1;
		for(int i = 0; i < 3; i++){
			pos[i] = loc[ps] + low + 1e-7;
			nx = next(loc, pos[i] + low);
			ps = nx;
			if(nx == loc.length) break;
		}
		for(int i = 0; i < 3; i++) System.out.printf("%.6f ", pos[i]);
    }

    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 ThreeBaseStations().run();
    }
}