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).
# UCSD ICPC SP22 Meeting 3
import sys
input = sys.stdin.readline
ii = lambda : int(input())
iil = lambda: [int(x) for x in input().split()]

n, = iil()
a = iil()

mini = min(a)
maxi = max(a)

def poorness(a,x):
    res = 0
    last = 0
    for i in a:
        it = i-x
        if last * it >= 0:
            last += it
        else:
            if abs(res) < abs(last):
                res = last
            last = 0
    return res

# binary search, precision 10 ** -6
EPS = 10 ** -6
p = 0
mid = 0
while maxi - mini > EPS:
    mid = (maxi + mini) / 2 
    p = poorness(a, mid)
    if p > 0:
        mini = mid 
    if p < 0:
        maxi = mid
print(mid)
 		 	   	 	 				  	 	  	  	   	