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.util.Arrays;
import java.util.Vector;

public class C {
    static double eps = 1e-9;
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(in.readLine());
        int[] a = new int[n];
        String[] ss = in.readLine().split("\\s+");
        for (int i = 0; i < a.length; i++) {
            a[i] = new Integer(ss[i]);
        }
        Arrays.sort(a);
        double lo = 0, hi = 2000000001, mid;
        for (int iter = 0; iter < 100; iter++) {
            mid = (lo + hi) / 2;
            if (ok(a, mid) != null)
                hi = mid;
            else
                lo = mid;
        }
        System.out.printf("%.6f\n", hi);
        Vector<Double> v = ok(a, hi);
        System.out.printf("%.6f %.6f %.6f\n", v.get(0), v.get(1), v.get(2));
    }

    private static Vector<Double> ok(int[] a, double d) {
        int index = 0;
        Vector<Double> ans = new Vector<Double>();
        for (int k = 1; k <= 3; k++) {
            double cur = a[index] + d;
            ans.add(cur);
            for (int i = 0; i < a.length; i++) {
                if (cur + d < a[i] + eps) {
                    index = i;
                    break;
                }
            }
        }
        return ans.get(2) + d < a[a.length - 1] + eps? null : ans;
    }
}