Codeforces E. Weakness and Poorness（三分最大子列和）

题目描述：

E. Weakness and Poorness

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given a sequence of n integers a1, a2, ..., a**n.

Determine a real number x such that the weakness of the sequence a1 - x, a2 - 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 a1, a2, ..., a**n (|a**i| ≤ 10 000).

Output

Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., a**n - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

Copy

31 2 3

Output

Copy

1.000000000000000

Input

Copy

41 2 3 4

Output

Copy

2.000000000000000

Input

Copy

101 10 2 9 3 8 4 7 5 6

Output

Copy

4.500000000000000

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.

思路：

这道题是要求一个数列减去一个数$x$后的子列和的绝对值最大(poorness)的情况下的可能的最小值(weakness)。（有点绕哈