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 Main {
    static final int maxn = (int) 2e5 + 100;
    
    BufferedReader br, aa;
    StringTokenizer st;
    
    double[] a = new double[maxn];
    double[] sum = new double[maxn];
    
    double getMinValue(double mid, int n) {
        
        double minValue = 1E100;
        double maxValue = -1E100;
        double minEle = 0;
        double maxEle = 0;
        
        for (int i = 0; i < n; i++) {
            sum[i] = i == 0 ? a[i] - mid : sum[i-1] + a[i] - mid;
        }
        
        for (int i = 0; i < n; i++) {
            maxValue = Math.max(maxValue, sum[i]-minEle);
            minValue = Math.min(minValue,  sum[i]-maxEle);
            if (sum[i] > maxEle) {
                maxEle = sum[i];
            }
            if (sum[i] < minEle) {
                minEle = sum[i];
            }
        }
        return Math.max(Math.abs(maxValue), Math.abs(minValue));
    }
    void out(int n) {
        System.out.println(n);
    }
    void out(double n) {
        System.out.println(n);
    }
    Main() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(next());
        
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(next());
            
        }
        double l = -1e5, r = 1e5;
        for (int i = 0; i < 300; i++) {
            if (Math.abs(r-l) < 1E-12) {
                break;
            }
            double mid1 = l+(r-l)/3.0;
            double mid2 = l+(r-l)*2.0/3.0;
            
            double val1 = getMinValue(mid1, n);
            double val2 = getMinValue(mid2, n);
            if (val1 < val2) {
                r = mid2;
            } else {
                l = mid1;
            }
        }       
        System.out.println(getMinValue(l, n));
    }

    public static void main(String[] args) throws IOException {
        new Main();
    }

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