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;
bool solve(long long x);
double l = 0, h = 10000000000, mid, mid1 = 0.0, pos1, pos2, pos3;
long long arr[1000000];
int n;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  sort(arr, arr + n);
  for (int i = 0; i < 1000; i++) {
    mid = (h + l) / 2;
    if (solve(mid)) {
      h = mid;
    } else {
      l = mid;
    }
  }
  if (n == 3) {
    mid = 0.0;
  }
  printf("%.6f\n", mid / 2);
  printf("%.6f", arr[0] + mid / 2);
  cout << " ";
  printf("%.6f", *upper_bound(arr, arr + n, arr[0] + mid) + mid / 2);
  cout << " ";
  printf("%.6f", *upper_bound(arr, arr + n,
                              *upper_bound(arr, arr + n, arr[0] + mid) + mid) +
                     mid / 2);
  return 0;
}
bool solve(long long x) {
  double d = arr[0] + x;
  int test = *upper_bound(arr, arr + n, d);
  if (!test) {
    return 1;
  }
  d = test + x;
  test = *upper_bound(arr, arr + n, d);
  if (!test) {
    return 1;
  }
  d = test + x;
  test = *upper_bound(arr, arr + n, d);
  if (!test) {
    return 1;
  }
  return 0;
}