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.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();


        boolean allTheSame = true;
        int[] a = new int[n];
        for (int i = 0; i < n; ++i) {
            a[i] = fs.nextInt();
            allTheSame = allTheSame && (i > 0? a[i] == a[i - 1]: true);
        }

        if (allTheSame) {
            System.out.println(0.00);
            return;
        }

        double l = -10 * 1001;
        double r = 10 * 1001 + new Random().nextInt(3000);


        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, -15.)) {
                System.out.println(m1Weakness);
                return;
            }
        }
    }
}