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.
输入描述:
The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence.The second line contains n integers a1, a2, ..., an (ai ≤ 10 000).
输出描述:
Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.
示例1
输入
3<br />1 2 3<br />4<br />1 2 3 4<br />10<br />1 10 2 9 3 8 4 7 5 6<br />
输出
1.000000000000000<br />2.000000000000000<br />4.500000000000000<br />
备注:
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.
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