CF578C Weakness and Poorness

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.

The first line contains one integer $ n $ ( $ 1

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} $ .

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.