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 (in JAVA):

Solution:
/*
If you want to aim high, aim high
Don't let that studying and grades consume you
Just live life young
******************************
If I'm the sun, you're the moon
Because when I go up, you go down
*******************************
I'm working for the day I will surpass you
https://www.a2oj.com/Ladder16.html
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class x579E
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         double[] arr = new double[N];
         st = new StringTokenizer(infile.readLine());
         for(int i=0; i < N; i++)
            arr[i] = Double.parseDouble(st.nextToken());
         double low = -11000.00;
         double high = 11000.00;
         int T = 100;
         while(T-->0)
         {
            double third = (high-low)/3;
            double lmid = low+third;
            double rmid = high-third;
            if(solve(arr, lmid) <= solve(arr, rmid))
               high = rmid;
            else
               low = lmid;
         }
         System.out.println(solve(arr, low));
      }
      public static double solve(double[] arr, double K)
      {
         double[] copy = new double[arr.length];
         int N = copy.length;
         for(int i=0; i < N; i++)
            copy[i] = arr[i]-K;
         double max = copy[0];
         double sum = copy[0];
         for(int i=1; i < N; i++)
         {
            if(sum < 0.00)
               sum = 0.0;
            sum += copy[i];
            max = Math.max(max, sum);
         }
         double min = copy[0];
         sum = copy[0];
         for(int i=1; i < N; i++)
         {
            if(sum > 0.0)
               sum = 0.0;
            sum += copy[i];
            min = Math.min(min, sum);
         }
         return Math.max(max, -1*min);
      }
   }