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.*;

public class C320C
{
    public static StringTokenizer st;
    public static void nextLine(BufferedReader br) throws IOException
    {
        st = new StringTokenizer(br.readLine());
    }
    
    public static String next()
    {
        return st.nextToken();
    }
    
    public static int nextInt()
    {
        return Integer.parseInt(st.nextToken());
    }
    
    public static long nextLong()
    {
        return Long.parseLong(st.nextToken());
    }
    
    public static double nextDouble()
    {
        return Double.parseDouble(st.nextToken());
    }
    
    static int n;
    
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        nextLine(br);
        n = nextInt();
        long[] a = new long[n];
        long[] ca = new long[n+1];
        nextLine(br);
        for (int i = 0; i < n; i++)
        {
            a[i] = nextInt();
        }
        if (n == 1)
        {
            System.out.println(0);
            return;
        }
        ca[0] = 0;
        for (int i = 0; i < n; i++)
        {
            ca[i+1] = ca[i] + a[i];
        } // so sum from x (incl) to y (excl) = ca[y] - ca[x]
        
        double left = -10000;
        double right = 10000;
        double ans = Long.MAX_VALUE;
        for (int kk = 0; kk < 100; kk++)
        {
            double mid = (left + right) / 2;
            
            double max1 = 0, max2 = 0;
            double min1 = 0, min2 = 0;
            for (int i = 0; i < n; i++)
            {
                max1 = Math.max(0, max1 + a[i] - mid);
                max2 = Math.max(max2, max1);
                min1 = Math.min(0, min1 + a[i] - mid);
                min2 = Math.min(min2, min1);
            }
            
            if (max2 < -min2)
            {
                right = mid;
                ans = Math.min(-min2, ans);
            }
            else
            {
                left = mid;
                ans = Math.min(max2, ans);
            }
        }
        System.out.printf("%.7f", ans);
    }
    
}