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.util.*;
import java.io.*;
public class C578 {
public static void main(String[] args) throws IOException
{
    input.init(System.in);
    PrintWriter out = new PrintWriter(System.out);
    int n =input.nextInt();
    int[] a = new int[n];
    for(int i = 0; i<n; i++) a[i] = input.nextInt();
    double lo = -10000, hi = 10000;
    for(int iter = 0; iter<100; iter++)
    {
        double m1 = (lo+lo+hi)/3, m2 = (lo+hi+hi)/3;
        if(go(a, m1) < go(a, m2)) hi = m2;
        else lo = m1;
    }
    out.println(go(a, (lo+hi)/2));
    out.close();
}
static double go(int[] a, double x)
{
    double res = 0;
    double min = 0, max = 0, sum = 0;
    for(int i =0 ; i<a.length; i++)
    {
        sum += a[i] - x;
        res = Math.max(res, Math.max(max-sum, sum-min));
        min = Math.min(min, sum);
        max = Math.max(max, sum);
    }
    return res;
}
public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(reader.readLine());
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}
}