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 double ESP = 1e-9;
const int N = 2e5 + 1;
int arr[N], n;
bool canCover(double d) {
  int used = 0;
  double lastcoverd = 0.0;
  for (int i = 0; i < n; ++i) {
    if (arr[i] > lastcoverd) {
      lastcoverd = arr[i] + (2 * d);
      ++used;
    }
  }
  return used <= 3;
}
double bs() {
  double low = 0, high = 2e9 + 1, mid;
  while (high - low > ESP) {
    mid = low + (high - low) / 2;
    if (canCover(mid)) {
      high = mid;
    } else {
      low = mid;
    }
  }
  return high;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d", arr + i);
  }
  sort(arr, arr + n);
  double d = bs();
  printf("%.7f\n", d);
  int used = 0;
  double lastcoverd = 0.0;
  for (int i = 0; i < n; ++i) {
    if (arr[i] - lastcoverd > ESP) {
      lastcoverd = arr[i] + (2 * d);
      printf("%.7f ", arr[i] + d);
      ++used;
    }
  }
  while (used < 3) {
    printf("%.7f ", 0.0);
    ++used;
  }
  printf("\n");
  return 0;
}