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;
double x[200010];
vector<double> a;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> x[i];
  sort(x, x + n);
  double lo = 0, hi = 1e9;
  for (int i = 0; i < 60; i++) {
    double mi = (lo + hi) / 2;
    int cur = 0;
    vector<double> v;
    for (int j = 0; j < 3; j++) {
      double to = x[cur] + mi * 2;
      v.push_back(x[cur] + mi);
      int l = -1, h = n;
      while (l + 1 < h) {
        int m = (l + h) / 2;
        if (to + 1e-9 > x[m])
          l = m;
        else
          h = m;
      }
      cur = l + 1;
      if (cur == n) break;
    }
    if (cur == n)
      hi = mi, a = v;
    else
      lo = mi;
  }
  cout << setprecision(11) << lo << endl;
  for (int i = 0; i < a.size(); i++) cout << a[i] << " ";
  for (int i = 0; i < 3 - a.size(); i++) cout << 0 << " ";
}