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 PYTHON3):

Solution:
from decimal import *
n=int(input())
a=sorted(map(int,input().split()))
i=1-n
j=n-2
s=0
getcontext().prec = 6
Decimal(1) / Decimal(7)
n=a[j]-a[i]
while s<n:
	l,r=a[i]-a[0],a[-1]-a[j]
	if l<r:
		if n<=l:
			s=n
			break
		i+=1
		s=l
	else:
		if n<=r:
			s=n
			break
		j-=1
		s=r
	n=a[j]-a[i]
s/=2
print(Decimal(s))
print(s+a[0]+0.0000001,float(a[j]-s),float(a[-1]-s))