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.IOException;
import java.io.InputStreamReader;
import java.text.DecimalFormat;
import java.util.Arrays;

public class C {
    public static void main(String[] args) throws NumberFormatException,
            IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        DecimalFormat f = new DecimalFormat("0.000000");
        int n = Integer.parseInt(in.readLine());
        String[] S = in.readLine().split(" ");
        double[] A = new double[n];
        for (int i = 0; i < n; i++)
            A[i] = Double.parseDouble(S[i]);
        Arrays.sort(A);
        double lo = 0;
        double hi = 2000000000;
        double[] ans = new double[3];
        for (int t = 0; t < 70; t++) {
            double mid = lo + (hi - lo) / 2;
            int cnt = 0;
            double temp[] = new double[3];
            try {
                for (int i = 0; i < n;) {
                    int j = i;
                    while (j < n && A[j] - A[i] <= 2 * mid + 1e-7)
                        j++;
                    temp[cnt++] = A[i] + mid;
                    i = j;
                }
                while (cnt < 3)
                    temp[cnt++] = A[n - 1];
                ans = temp;
                hi = mid;
            } catch (Exception e) {
                lo = mid;
            }
        }
        System.out.println(f.format(lo));
        for (int i = 0; i < 3; i++)
            System.out.print(f.format(ans[i]) + " ");
        System.out.println();

    }
}