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;
vector<int> a;
int n, l, r, m, ans[4];
bool chk(int d2) {
  ans[0] = a[0] + d2;
  int t = 0;
  ans[1] = ans[2] = 2000000000;
  for (int i = 0; i < n; i++)
    if (t >= 3)
      return false;
    else if (ans[t] < a[i])
      ans[++t] = a[i] + d2;
  return t < 3;
}
int main() {
  cin >> n;
  a.resize(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  sort(a.begin(), a.end());
  l = -1, r = a[n - 1] + 1;
  while (l + 1 < r) {
    m = (l + r) / 2;
    if (chk(m))
      r = m;
    else
      l = m;
  }
  chk(r);
  printf("%.7f\n%.7f %.7f %.7f", r * 0.5, ans[0] * 1.0 - 0.5 * r,
         ans[1] * 1.0 - 0.5 * r, ans[2] * 1.0 - 0.5 * r);
  return 0;
}