You are given a sequence of n integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub>. 

Determine a real number *x* such that the weakness of the sequence *a*<sub class="lower-index">1</sub> - *x*, *a*<sub class="lower-index">2</sub> - *x*, ..., *a*<sub class="lower-index">*n*</sub> - *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.
The first line contains one integer *n* (1 ≤ *n* ≤ 200 000), the length of a sequence.

The second line contains *n* integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (|*a*<sub class="lower-index">*i*</sub>| ≤ 10 000).
n = int(input())
A = list(map(int,input().split()))

def f(A,x,sign=1):
    cur = 0
    mn = 0
    ans = -1<<32

    for y in A:
        cur += sign*(y-x)
        ans = max(ans, cur - mn)
        mn = min(cur, mn)

    return ans

lo,hi = -10000,10000
while hi-lo > 1e-7:
    mid = (lo+hi)/2
    X = f(A,mid,sign=1)
    Y = f(A,mid,sign=-1)
    if X > Y:
        lo = mid
    else:
        hi = mid

print(abs(f(A,lo)))

