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.util.HashSet;
import java.util.Locale;
import java.util.Set;
import java.util.StringTokenizer;

public class Main {
	static int n;
	static int[] array;
	static double e=0.000000000009;
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		n=Integer.parseInt(br.readLine());
		StringTokenizer st=new StringTokenizer(br.readLine());
		int naux = n;
		array = new int[n];
		Set<Integer> set=new HashSet<Integer>();
		for (int i = 0; i < array.length; i++) {
			array[i] = Integer.parseInt(st.nextToken());
			set.add(array[i]);
		}
		if (set.size()==1){ System.out.printf(Locale.US,"%.15f\n",0.0);return;}
		double res=check(ts(-20000,20000,100));
		System.out.printf(Locale.US,"%.15f\n",res);
	}
	
	static double ts(double l, double r,int its){
		if (its==0) return l;
		double middle = (l+r)/2;
		double check1=check(middle);
		double check0=check(middle-e);
		if(check0 > check1){
			return ts(middle,r,its-1);
		}
		else if(check0 < check1){
			return ts(l,middle,its-1);
		}
		return middle;
	}

	private static double check(double d) {
		double[] dp1=new double[n+1];
		double[] dp2=new double[n+1];
		double[] a=new double[n];
		for (int i = 0; i < n; i++) {
			a[i]=array[i]+d;
		}
		for (int i = n-1; i >= 0; i--) {
			dp1[i]=a[i]+dp1[i+1];
			dp2[i]=a[i]+dp2[i+1];
			if (dp1[i]<0){
				dp1[i]=0;
			}
			else if (dp2[i]>0){
				dp2[i]=0;
			}
		}
		double max=0;
		double min=0;
		for (int i = 0; i < n; i++) {
			max=Math.max(max, dp1[i]);
			min=Math.min(min, dp2[i]);
		}
		min*=-1;
		return Math.max(max, min);
	}
}