text: # Problem You are given a sequence of n integers a1, a2, ..., an.Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - 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, ..., an (|ai| ≤ 10 000).Output 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.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.# Solution import java.io.BufferedOutputStream; import java.io.Closeable; import java.io.DataInputStream; import java.io.Flushable; import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintStream; import java.util.Arrays; import java.util.InputMismatchException; /** * Built using CHelper plug-in * Actual solution is at the top */ public class Main { static class TaskAdapter implements Runnable { @Override public void run() { long startTime = System.currentTimeMillis(); InputStream inputStream = System.in; OutputStream outputStream = System.