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;
struct Tpoint {
  double x, y;
  Tpoint() {}
  Tpoint(double _x, double _y) {
    x = _x;
    y = _y;
  }
  inline void read() { scanf("%lf%lf", &x, &y); }
  inline void show() { printf("%lf %lf\n", x, y); }
  inline double norm() { return sqrt(((x) * (x)) + ((y) * (y))); }
};
inline Tpoint operator+(const Tpoint &a, const Tpoint &b) {
  return Tpoint(a.x + b.x, a.y + b.y);
}
inline Tpoint operator-(const Tpoint &a, const Tpoint &b) {
  return Tpoint(a.x - b.x, a.y - b.y);
}
inline Tpoint operator*(const Tpoint &a, const double &b) {
  return Tpoint(a.x * b, a.y * b);
}
inline Tpoint operator/(const Tpoint &a, const double &b) {
  return Tpoint(a.x / b, a.y / b);
}
inline double det(const Tpoint &a, const Tpoint &b) {
  return a.x * b.y - a.y * b.x;
}
inline double dot(const Tpoint &a, const Tpoint &b) {
  return a.x * b.x + a.y * b.y;
}
int x[200005], n;
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) scanf("%d", &x[i]);
  sort(x, x + n);
  int l = -1, r = 1000000001;
  while (l + 1 < r) {
    int mid = (l + r) / 2;
    int s = 0;
    for (int i = 0; i < 3; ++i) {
      int t = s + 1;
      while (t < n && x[t] - x[s] <= mid) ++t;
      s = t;
    }
    if (s >= n)
      r = mid;
    else
      l = mid;
  }
  printf("%lf\n", r / 2.0);
  int s = 0;
  for (int i = 0; i < 3; ++i) {
    int t = s + 1;
    while (t < n && x[t] - x[s] <= r) ++t;
    if (i) printf(" ");
    printf("%lf", (x[s] + x[t - 1]) / 2.0);
    s = t;
  }
  puts("");
  return 0;
}