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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;


public class CF_320_E {
    
    private static double p(int[] arr1, double mid){
        
        double[] arr = new double[arr1.length];
        
        for(int i = 0; i < arr.length; i++){
            arr[i] = (double)arr1[i] - mid;
        
        }
        int index = 0;
        while(index < arr.length && arr[index] < 0)index++;
        double max = Integer.MIN_VALUE;
        double cum = 0;
        for(int i = index; i < arr.length; i++){
            if(arr[i] >= 0){
                cum += arr[i];
                max = Math.max(max, cum);
            }else{
                if(cum + arr[i] <= 0){
                    cum = 0;
                }else{
                    cum += arr[i];
                }
            }
        }
        
        //-ve
        for(int i = 0; i < arr.length; i++){
            arr[i] *= -1;
        
        }
            
        
         index = 0;
    
        while(index < arr.length && arr[index] < 0)index++;
        double max1 = Integer.MIN_VALUE;
        cum = 0;
        for(int i = index; i < arr.length; i++){
        
            if(arr[i] >= 0){
                cum += arr[i];
                max1 = Math.max(max1, cum);
            }else{
                if(cum + arr[i] <= 0){
                    cum = 0;
                }else{
                    cum += arr[i];
                }
            }
        }
        
    
        if(max == Integer.MIN_VALUE){
            return -1*max1;
        }else if(max1 == Integer.MIN_VALUE){
            return max;
        }
        return (max > max1)? max:-1*max1;
    }
    
    public static void main(String[] args) throws IOException{
        PrintWriter pw = new PrintWriter(System.out, true);
        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        String[] line;
        int n = Integer.parseInt(input.readLine());
        int[] N = new int[n];
        line = input.readLine().split(" ");
        for(int i = 0; i < n; i++){
            N[i] = Integer.parseInt(line[i]);
        }
        double lo = -100001, hi = 100001, mid;
        double val;
        int iter = 100;
        while((hi-lo) > 1e-15){
        
            if(iter-- == 0){
                break;
            }
            mid = lo+(hi-lo)/2;
        
            val = p(N, mid);
    
        
            if(val < 0){
                hi = mid;
            }else{
                lo = mid;
            }
        }
        if(n == 1){
            pw.println(0);
        }else{
            pw.println(Math.abs(p(N, lo)));
        }
        
        pw.close();
        input.close();
    }
}