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:
import sys
n = int(sys.stdin.readline())
a = [int(x) for x in sys.stdin.readline().split()]

eps = 1e-12

def f(x):
    mx = a[0] - x
    tsmx = 0.0
    mn = a[0] - x
    tsmn = 0.0
    for ai in a:
        tsmx = max(tsmx + ai - x, ai - x)
        mx = max(tsmx, mx)
        tsmn = min(tsmn + ai - x, ai - x)
        mn = min(tsmn, mn)

    return abs(mx), abs(mn)

l = min(a)
r = max(a)
f1, f2 = f(l)
for i in range(0, 90):
    m = (l + r) / 2
    f1, f2 = f(m)
    if f1 > f2:
        l = m
    else:
        r = m

A, B = f(l)
print(min(A,B))