Problem: You are given a sequence of n integers a1, a2, ..., an. 

Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - x is as small as possible.

The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.

The poorness of a segment is defined as the absolute value of sum of the elements of segment.

Input

The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence.

The second line contains n integers a1, a2, ..., an (|ai| ≤ 10 000).

Output

Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

3
1 2 3


Output

1.000000000000000


Input

4
1 2 3 4


Output

2.000000000000000


Input

10
1 10 2 9 3 8 4 7 5 6


Output

4.500000000000000

Note

For the first case, the optimal value of x is 2 so the sequence becomes  - 1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case. 

For the second sample the optimal value of x is 2.5 so the sequence becomes  - 1.5, - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case.

Solution (in PYTHON3):

Solution:
def weakness(a, x):
    a = [elem-x for elem in a]
    acumulado = maximo = 0
    for elem in a:
        if acumulado + elem > 0:
            acumulado += elem
        else:
            acumulado = 0
        if acumulado > maximo:
            maximo = acumulado
    acumulado = minimo = 0
    for elem in a:
        if acumulado + elem < 0:
            acumulado += elem
        else:
            acumulado = 0
        if acumulado < minimo:
            minimo = acumulado
    return max(maximo, -minimo)


n, a = input(), list(map(int, input().split()))

inf, sup = min(a), max(a)
for _ in range(70):
    c1, c2 = (2*inf+sup)/3, (inf+2*sup)/3
    if weakness(a, c1) < weakness(a, c2):
        sup = c2
    else:
        inf = c1

print(weakness(a, (inf+sup)/2))