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C. Weakness and Poorness

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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}.

Examples

Input

3

1 2 3

Output

1.000000000000000

Input

4

1 2 3 4

Output

2.000000000000000

Input

10

1 10 2 9 3 8 4 7 5 6

Output

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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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