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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int h[1001000];
int main() {
  cout << fixed << setprecision(6);
  int n, i, j, help, helpp, chek = 0;
  double x, y, d, ans;
  cin >> n;
  for (i = 0; i < n; i++) cin >> h[i];
  sort(h, h + n);
  x = h[0], y = h[n - 1];
  while (y - x > 0.00000002 || chek == 0) {
    d = (x + y);
    d /= 2;
    d -= h[0];
    help = upper_bound(h, h + n, 2 * d + h[0]) - h;
    if (h[help] == 2 * d + h[0]) help++;
    helpp = upper_bound(h, h + n, 2 * d + h[help]) - h;
    if (h[helpp] - h[help] == 2 * d) helpp++;
    if (h[n - 1] - h[helpp] <= 2 * d || helpp >= n)
      chek = 1;
    else
      chek = 0;
    (chek == 0) ? (x = d + h[0]) : (y = d + h[0]);
  }
  cout << d << endl;
  h[n] = h[n - 1];
  cout << h[0] + d << " " << h[help] + d << " " << h[helpp] + d << endl;
  return 0;
}