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 p578c {
    public static double[] a = new double[200010];
    public static double[] b = new double[200010];

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            a[i] = in.nextDouble();
        }
        double low = Double.MAX_VALUE, high = Double.MIN_VALUE;
        for (int i = 0; i < n; i++) {
            low = Math.min(low, a[i]);
            high = Math.max(high, a[i]);
        }
        double[] res = new double[2];
        double x1, x2;
        for (int i = 1; i <= 120; i++) {
            double mid = (low + high) / 2.0;
            res = f(mid, n);
            x1 = res[0]; x2 = res[1];
            if (x1 > x2) low = mid;
            else high = mid;
        }
        double mid = (low + high) / 2.0;
        res = f(mid, n);
        x1 = res[0]; x2 = res[1];
        out.println(Math.max(x1, x2));
        out.close();
    }

    public static double[] f(double x, int n) {
        double[] res = new double[2];
        for (int i = 0; i < n; i++) {
            b[i] = a[i] - x;
        }
        double x1 = g(b, n);
        for (int i = 0; i < n; i++) {
            b[i] *= -1;
        }
        double x2 = g(b, n);
        res[0] = x1; res[1] = x2;
        return res;
    }

    public static double g(double[] arr, int n) {
        double max = 0.0, cur = 0.0;
        for (int i = 0; i < n; i++) {
            cur += arr[i];
            if (cur > max) max = cur;
            if (cur < 0) cur = 0;
        }
        return max;
    }

    static class Pair implements Comparable<Pair> {
        int x;
        int y;

        public Pair(int x, int y) {
            super();
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Pair p) {
            return x < p.x ? -1 : x > p.x ? 1 : 0;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return null;
        }

        public boolean hasMoreElements() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                String s;
                try {
                    s = reader.readLine();
                } catch (IOException e) {
                    return false;
                }
                tokenizer = new StringTokenizer(s);
            }
            return tokenizer.hasMoreElements();
        }
    }
}