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

def fun(m):
    pr=[]
    for i in arr:
        pr.append(i-m)
    for i in range(1,n):
        pr[i]+=pr[i-1]
    neg,pos,aneg,apos=0,0,0,0
    for i in pr:
        if i<0:
            neg=min(neg,i)
            aneg=min(aneg,i-pos)
        else:
            pos=max(pos,i)
            apos=max(i-neg,apos)
    return max(apos,-aneg)

l,r=-10**4,10**4
eps=1e-11

while r-l>eps:
    m1,m2=l+(r-l)/3,r-(r-l)/3
    if fun(m1)>fun(m2):
        l=m1
    else:
        r=m2
print(fun(l))