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:
n = int(input())
houses = sorted(set(map(int, input().split())))

if len(houses) <= 3:
    print(0)
    result = houses[:]
    while len(result) < 3:
        result.append(result[-1])
    print('%.6f %.6f %.6f' % tuple(result))
    import sys; sys.exit()

span = 0
left = 1
right = len(houses) - 2
#print(houses)
#print('span = %d, houses[%d] = %d, houses[%d] = %d' % (span,
#    left, houses[left], right, houses[right]))

while houses[right] - houses[left] > span:
    left_gap = houses[left] - houses[0] - span
    right_gap = houses[-1] - houses[right] - span
    middle = houses[right] - houses[left]
    if left_gap <= right_gap:
        if span + left_gap > middle:
            span = middle
            break
        left += 1
        if left_gap == right_gap:
            right -= 1
        span += left_gap
    else:
        if span + right_gap > middle:
            span = middle
            break
        right -= 1
        span += right_gap
    #print('span = %d, houses[%d] = %d, houses[%d] = %d' % (span,
    #    left, houses[left], right, houses[right]))

print('%.6f' % (span / 2))
print('%.6f %.6f %.6f' % ((houses[0] + houses[left - 1]) / 2,
                          (houses[left] + houses[right]) / 2,
                          (houses[right + 1] + houses[-1]) / 2))