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 long long N = 1e6;
int d() {
  int ret;
  scanf("%d", &ret);
  return ret;
}
long long lld() {
  long long ret;
  scanf("%lld", &ret);
  return ret;
}
bool cmp(pair<int, int> s, pair<int, int> f) {
  if (f.first > s.first)
    return true;
  else if (f.first == f.second && f.second < s.second)
    return true;
  else
    return false;
}
long long arr[N], n;
bool IsCover(long long d) {
  long long lastcover = -1, used = 0;
  for (int i = 0; i < n; i++) {
    if (arr[i] > lastcover) {
      lastcover = arr[i] + (2 * d);
      used++;
    }
  }
  return used <= 3;
}
long long PS() {
  long long hi = 4e9, lo = 0, mid;
  while (hi - lo > 0) {
    mid = (lo + hi) / 2;
    if (IsCover(mid))
      hi = mid;
    else
      lo = mid + 1;
  }
  return lo;
}
int main() {
  n = d();
  for (int i = 0; i < n; i++) {
    scanf("%lld", arr + i);
    arr[i] <<= 1;
  }
  sort(arr, arr + n);
  int d = PS();
  printf("%lf\n", d / 2.0);
  long long lastcover = -1, used = 0;
  for (int i = 0; i < n; i++) {
    if (arr[i] > lastcover) {
      lastcover = arr[i] + (2 * d);
      printf("%lf ", (arr[i] + d) / 2.0);
      used++;
    }
  }
  while (used < 3) {
    printf("%lld ", arr[0] / 2);
    used++;
  }
  puts("");
}