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())
s=0
for i in range (n):
   a=int(input())
   s+=a
print(s/n)