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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author awh
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int n = in.nextInt();
            int[] as = new int[n];
            double[] bs = new double[n];
            double mi = Integer.MAX_VALUE;
            double ma = Integer.MIN_VALUE;
            for (int i = 0; i < n; i++) {
                as[i] = in.nextInt();
                mi = Math.min(mi, as[i]);
                ma = Math.max(ma, as[i]);
            }
            int iter = 100;
            while (iter-- > 0) {
                double mid = (mi + ma) / 2.0;
                for (int i = 0; i < n; i++) {
                    bs[i] = as[i] - mid;
                }
                double upside = calc(bs);
                for (int i = 0; i < n; i++) {
                    bs[i] = -bs[i];
                }
                double downside = calc(bs);
                if (upside > downside) {
                    mi = mid;
                } else {
                    ma = mid;
                }
            }
            double upside = calc(bs);
            for (int i = 0; i < n; i++) {
                bs[i] = -bs[i];
            }
            double downside = calc(bs);
            out.println(String.format("%.15f", Math.min(upside, downside)));
        }

        private double calc(double[] bs) {
            double max = 0, now = 0;
            for (int i = 0; i < bs.length; i++) {
                now += bs[i];
                if (now > max) max = now;
                if (now < 0) now = 0;
            }
            return max;
        }

    }

    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

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

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

    }
}