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;
const int MAX = 2e5 + 5;
int n, arr[MAX];
bool Can(double x) {
  double lastPos = arr[0] + x;
  int cnt = 1;
  for (int i = 1; i < n; i++) {
    if (abs(arr[i] - lastPos) > x) {
      ++cnt;
      lastPos = arr[i] + x;
    }
  }
  if (cnt <= 3) return true;
  return false;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  sort(arr, arr + n);
  Can(0.5);
  int iter = 1000;
  double st = 0, en = arr[n - 1];
  while (--iter) {
    double mid = (st + en) * 0.5;
    if (Can(mid))
      en = mid;
    else
      st = mid;
  }
  cout << fixed << setprecision(6) << st << endl;
  int cnt = 1;
  double firstPos = arr[0] + st;
  cout << firstPos << " ";
  auto it = upper_bound(arr, arr + n, arr[0] + 2 * st + 1e-6);
  if (it == arr + n)
    cout << arr[n - 1] - st << " ";
  else
    cout << *it + st << " ";
  cout << arr[n - 1] - st;
  return 0;
}