10
-405 -230 252 -393 -390 -259 97 163 81 -129
 3
10000 -10000 10000
 1
-10000
 20
-16 -23 29 44 -40 -50 -41 34 -38 30 -12 28 -44 -49 15 50 -28 38 -2 0

702.333333333333712
 10000.000000000016371
 0.000000000000000
 113.875000000000043

import java.io.*;
import java.util.Random;
import java.util.StringTokenizer;

public class WeaknessAndPoorness {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }
    }

    private static double weakness(int[] a, double x) {

        // find segment such that its sum gives the max value
        double max = 0;
        double curr = 0;
        for (int el: a) {
            if (el - x >= 0) {
                curr = curr + el - x;
                max = Math.max(curr, max);
            }
            else {
                curr = curr + el - x;
                if (curr <= 0) {
                    curr = 0;
                }
            }
        }

        // find segment such that its sum gives the min value
        double min = 0;
        curr = 0;
        for (int el: a) {
            if (el - x <= 0) {
                curr = curr + el - x;
                min = Math.min(curr, min);
            }
            else {
                curr = curr + el - x;
                if (curr >= 0) {
                    curr = 0;
                }
            }
        }

        return Math.max(-min, max);
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();

        int[] a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = fs.nextInt();
        }


        double l = -10 * 1001;
        double r = 10 * 1001 + 100  + new Random().nextInt(10000);


        while (true) {
            double dis = r - l;
            double m1 = l + (dis) / 3;
            double m2 = l + (2 * dis) / 3;

            double m1Weakness = weakness(a, m1);
            double m2Weakness = weakness(a, m2);

            if (m1Weakness < m2Weakness) {
                r = m2;
            } else if (m1Weakness > m2Weakness) {
                l = m1;
            } else {
                System.out.println(m1Weakness);
                return;
            }

            if (Math.abs(m1Weakness - m2Weakness) < Math.pow(10, -16.)) {
                System.out.println(m1Weakness);
                return;
            }
        }
    }
}
