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())
As = list(map(int, input().split()))

def solve(n, As):
    if n == 1:
        return 0
    if n == 2:
        return abs(As[0] - As[1]) / 2
    x = sum(As) / n
    cumAs = [0]
    cum = 0
    for a in As:
        cum += a - x
        cumAs.append(cum)
    return max(cumAs) - min(cumAs)

print(solve(n, As))
