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 n, a[200100];
double b[5];
int main() {
  scanf("%d", &n);
  for (int i = (0); i < (n); i++) scanf("%d", &a[i]);
  sort(a, a + n);
  double l = 0, r = a[n - 1], x;
  while (r - l > 1e-8) {
    x = (r + l) / 2;
    int j = 0;
    b[j] = a[0] + x;
    for (int i = (0); i < (n); i++)
      if (abs(a[i] - b[j]) - x > 1e-8) {
        b[++j] = a[i] + x;
        if (j == 3) break;
      }
    if (j == 3)
      l = x;
    else
      r = x;
  }
  x = r;
  int j = 0;
  b[j] = a[0] + x;
  for (int i = (0); i < (n); i++)
    if (abs(a[i] - b[j]) - x > 1e-8) {
      b[++j] = a[i] + x;
      if (j == 3) break;
    }
  if (j == 0) b[1] = b[2] = b[0];
  printf("%.7lf\n", x);
  for (int i = (0); i < (3); i++) printf("%.7lf ", b[i]);
}