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:
import java.io.*;
import java.util.*;
import java.math.*;

public class Main {
    public static double maxSum(double arr[],double val)
    {
        double sum=0;
        double max=Double.MIN_VALUE;
        for(int i=0;i<arr.length;i++)
        {
            sum+=arr[i]-val;
            if(max<sum)
                max=sum;
            if(sum<0)
                sum=0;
        }
        return max;
    }
    public static double minSum(double arr[],double val)
    {
        double sum=0;
        double min=Double.MAX_VALUE;
        for(int i=0;i<arr.length;i++)
        {
            sum+=arr[i]-val;
            if(min>sum)
                min=sum;
            if(sum>0)
                sum=0;
        }
        return Math.abs(min);
    }
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        double arr[]=new double[n];
        
        double low=Double.MAX_VALUE;
        double high=Double.MIN_VALUE;
        for(int i=0;i<n;i++)
        {
            arr[i]=sc.nextDouble();
            if(arr[i]>high)
                high=arr[i];
            if(arr[i]<low)
                low=arr[i];
        }
        int count=0;
        while(low<high&& count<300)
        {
            Double mid1=low+(high-low)/3;
            Double mid2=high-(high-low)/3;
            Double cost1=Math.max(minSum(arr,mid1),maxSum(arr,mid1));
            Double cost2=Math.max(minSum(arr,mid2),maxSum(arr,mid2));
            if(cost1>cost2)
                low=mid1;
            else high=mid2;
            count++;
        }
        System.out.println(Math.max(minSum(arr,low),maxSum(arr,low)));
        
        
    }
}