You are given a sequence of n integers $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$.

Determine a real number $*x*$ such that the weakness of the sequence $*a*_{1} - *x*, *a*_{2} - *x*, ..., *a*_{*n*} - *x*$ 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.

Input

The first line contains one integer $*n*$ ($1 ≤ *n* ≤ 200 000$), the length of a sequence.

The second line contains $*n*$ integers $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ ($|*a*_{*i*}| ≤ 10 000$).

Output

Output a real number denoting the minimum possible weakness of $*a*_{1} - *x*, *a*_{2} - *x*, ..., *a*_{*n*} - *x*$. Your answer will be considered correct if its relative or absolute error doesn't exceed $10^{ - 6}$.

Note

For the first case, the optimal value of $*x*$ is $2$ so the sequence becomes $- 1$, $0$, $1$ and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to $1$ in this case.

For the second sample the optimal value of $*x*$ is $2.5$ so the sequence becomes $- 1.5,  - 0.5, 0.5, 1.5$ and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to $2$ in this case.