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 C {
    FastScanner in;
    PrintWriter out;

    double weakness(double[] a, double x) {
        double max = a[0] - x, min = a[0] - x, maxR = a[0] - x,  minR = a[0] - x;
        for (int i = 1; i < a.length; i++) {
            double cur = a[i] - x;
            max = Math.max(Math.max(max, maxR + cur), cur);
            min = Math.min(Math.min(min, minR + cur), cur);
            maxR = Math.max(maxR + cur, cur);
            minR = Math.min(minR + cur, cur);
        }
        min = Math.abs(min);
        max = Math.abs(max);
        return Math.max(min, max);
    }

    public void solve() throws IOException {
        int n = in.nextInt();
        double[] a = new double[n];
        Arrays.setAll(a, i -> in.nextInt());
        double l = -1_000_000;
        double r = 1_000_000;
        for (int i = 0; i < 100; i++) {
            double m1 = l + (r - l) / 3;
            double m2 = l + (r - l) / 3 * 2;
            if (weakness(a, m1) < weakness(a, m2)) {
                r = m2;
            } else {
                l = m1;
            }
        }
        out.println(/*(l + r) / 2+ " " + */weakness(a, (l + r) / 2));
    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            Locale.setDefault(Locale.US);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    public static void main(String[] arg) {
        new C().run();
    }
}